Multi-Step Nonlinear User’s Guide · 2017. 11. 1. · Chapter1: Introd uction withtheExecutiveSystemandwithothermodulesthroughparameters,whichmaybeinputand/or …

SIEMENSSIEMENSSIEMENS

Multi-Step NonlinearUser’s Guide

Contents

Proprietary & Restricted Rights Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

Overview of nonlinear capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1Program architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1Nonlinear characteristics and general recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1

Supported inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1Case control section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1Bulk data section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4Nonlinear Parameters: NLCNTL entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4Iteration related output data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5Supported output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5Solver Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6Parallel support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

Subcase Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

Subcase analysis type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1Subcase sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1Cyclic symmetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2Fourier harmonic solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8Nonlinear buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10

Element support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1

Element Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1Elements in nonlinear analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2Shell elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3Bar and beam elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6Spring elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7Rigid elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9Generalized plane strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11Error estimator for mesh refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13Progressive failure analysis in solid composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14Chocking elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27Cohesive elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30Crack simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32Stress output coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34Formulation of isoparametric elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35

Multi-Step Nonlinear User’s Guide (SOL 401) 3

Contents

Isoparametric coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35Shape functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38Example element matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40Volume integration of element matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41Element loads and equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42Element coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43Stress data recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-44

Material support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1

Material overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1Support for plasticity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1Overview of Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3User defined materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7Creep analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-24Overview of the Creep Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-31Disable plasticity and creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34

Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1

Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1Multipoint constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1Enforced displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2

Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1

Loads overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1Mechanical loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-1Thermal loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4Defining solution time steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-9Bolt preload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11Initial stress-strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16Distributed force to a surface or edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-21

Contact conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1

Contact Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1Contact Subcase Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1Contact Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-2Contact Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-6Contact kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7Contact Penalty Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-17Contact Sliding and Geometry Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18Contact and rigid body motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19Contact Offsets and Initial Penetrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-21Contact Surface and Edge Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-22Contact Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23Contact Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25

Glue conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1

Overview of Gluing Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1

4 Multi-Step Nonlinear User’s Guide (SOL 401)

Contents

Contents

Glue Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2Defining and Selecting Glue Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-3Glue Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-5Glue preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-7

Considerations for nonlinear analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1

Discrete system for a nonlinear continuum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1Finite element formulation for equilibrium equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-2Coordinate transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-6Displacement sets and reduction of system equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-8Nonlinear solution procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-11

Geometric nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1

Overview and user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1Updated element coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-6

Concept of convective coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-6Updated coordinates and net deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-7Provisions for global operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-9

Follower forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-10Basic definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-11Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-11

Solution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1

Solution Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1Adaptive Solution Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-2Newton’s method of iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-2Stiffness update strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-6

Update principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-6Divergence criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-7

Convergence criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-9Rudimentary considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-9Convergence conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-10Error functions and weighted normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-11Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-12


Contents

Proprietary & Restricted Rights Notice

© 2017 Siemens Product Lifecycle Management Software Inc. All Rights Reserved.

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TAUCS Copyright and License

TAUCS Version 2.0, November 29, 2001. Copyright (c) 2001, 2002, 2003 by Sivan Toledo, Tel-AvivUniversity, [email protected]. All Rights Reserved.

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8 Multi-Step Nonlinear User’s Guide (SOL 401)


Chapter 1: Introduction

1.1 Overview of nonlinear capabilitiesThis book covers nonlinear structural analysis with the solution sequence, SOL 401 - NLSTEP. SOL401 is a multistep, structural solution which supports a combination of static (linear or nonlinear)subcases and modal (real eigenvalue) subcases.

SOL 401 is the structural solution used by the Simcenter Multiphysics environment within thePre/Post application. The Multiphysics environment supports all combinations of structural-to-thermaland thermal-to-structural coupling with the Simcenter Thermal solution. SOL 401 is also supported asa stand-alone NX Nastran solution.

Primary operations for nonlinear elements are updating element coordinates and applied loadsfor large displacements. The geometric nonlinearity becomes discernible when the structure issubjected to large displacement and rotation. Geometric nonlinear effects are prominent in twodifferent aspects: geometric stiffening due to initial displacements and stresses, and follower forcesdue to a change in loads as a function of displacements. The large deformation effect resulting inlarge strains has not been implemented.

Material nonlinearity is an inherent property of any engineering material. Material nonlinear effectsmay be classified into many categories. Included are plasticity, nonlinear elasticity, creep, andviscoelasticity. SOL 401 supports plasticity and creep.

The primary solution operations are time increments, iterations with convergence tests for acceptableequilibrium error, and stiffness matrix updates. The iterative process is based on variations ofNewton's method. The stiffness matrix updates are performed to improve the computationalefficiency, but may be overridden at your discretion.

1.2 Program architectureThe software has a modular structure to separate functional capabilities which are organized under anefficient executive system. The program is divided into a series of independent subprograms, calledfunctional modules. A functional module is capable of performing a pre-defined subset of operations.It is the Executive System that identifies every module to execute by MPL (Module Properties List).

The Executive System processes the input data by IFP (Input File Processor) and the generalinitialization, which are known as Preface,operations. It then establishes and controls the sequenceof module executions in the OSCAR (Operation Sequence Control Array) based on the user-specifiedDMAP (Direct Matrix Abstraction Program) or solution sequence. The Executive System allocatessystem files to the data blocks in the FIAT (File Allocation Table) and maintains a parameter table formodule interface. The Executive System is also responsible for the database management and allthe input and output operations by GINO (General Input/Output Routines).

The functional module consists of a number of subroutines. Modules communicate with each otheronly through secondary storage files, called data blocks (matrix or table). Each module performs acertain function with input data blocks and produces output data blocks. A module may communicate

Multi-Step Nonlinear User’s Guide (SOL 401) 1-1


with the Executive System and with other modules through parameters, which may be input and/oroutput variables of the module. Modules utilize main memory dynamically. If the size of the mainmemory is insufficient to complete an operation, the module uses scratch files, which reside in thesecondary storage as an extension of the main memory. This is known as a spill operation.

DMAP is a kind of macro program using a data block oriented language. The solution sequence is acollection of module statements written in the DMAP language tailored to process a sequential seriesof operations, resulting in a specific type of structural analysis. A typical solution sequence consistsof three phases of functional operations: formation, assembly, and reduction of matrices; solutionof equations; and data recovery. Solution sequences that process superelements have built-insuperelement loops in the first and the last phases.

The nonlinear solution sequences have built-in loops in the second phase for subcase changes, loadincrements, and stiffness matrix updates. Nested in this DMAP loop, nonlinear solution processescomprise a number of internal iteration loops. Confining the discussion to SOL 401, the hierarchyof the nonlinear looping is shown in the table below. Central to the nonlinear processes is moduleNLTRD3. The module is self-contained to perform iterations for converged solutions.

Table 1-1. Hierarchy of Nonlinear LoopingName or Loop Type

1 Subcases (boundaries, temperatures, loads,outputs) DMAP Control

2 Time Steps (NLTRD3) Module Control

3 Stiffness Matrix Updates

The actual stiffness update is underDMAP control, but the request fora stiffness update in the middle ofa solution is under Module control.Decomposition is under modulecontrol.

4 Iterations (Vector Arithmetic) Module Control5 Elements (NLEMG) Subroutine Control6 Volume Integration (Gauss Points) Subroutine Control

1.3 Nonlinear characteristics and general recommendationsThe modeling guidelines for nonlinear analysis and linear analysis are summarized as follows:

• The analyst should have some insight into the behavior of the structure to be modeled; otherwise,a simple model should be the starting point.

• The size of the model should be determined based on the purpose of the analysis, the trade-offsbetween accuracy and efficiency, and the scheduled deadline.

• Prior contemplation of the geometric modeling will increase efficiency in the long run. Factorsto be considered include selection of coordinate systems, symmetric considerations forsimplification, and systematic numbering of nodal points and elements for easy classificationof locality.

1-2 Multi-Step Nonlinear User’s Guide (SOL 401)


Introduction

• Discretization should be based on the anticipated stress gradient, i.e., a finer mesh in the area ofstress concentrations.

• Element types and the mesh size should be judiciously chosen. For example, avoid highlydistorted and/or stretched elements (with high aspect ratio).

• The model should be verified prior to the analysis by some visual means, such as plots andgraphic displays.

Nonlinear analysis requires better insight into structural behavior. First of all, the type of nonlinearitiesinvolved must be determined. The geometric nonlinearity is characterized by large rotations whichusually cause large displacements. Intuitively, geometric nonlinear effects should be significant if thedeformed shape of the structure appears distinctive from the original geometry without amplifying thedisplacements. There is no distinct limit for large displacements because geometric nonlinear effectsare related to the dimensions of the structure and the boundary conditions. The key to this issue is toknow where the loading point is in the load-deflection curve of the critical area.

Additional recommendations are important for nonlinear analysis:

• PARAM,LGDISP,1 must be defined to turn on geometry nonlinearity.

• Material nonlinear effects can also be included. See Support for plasticity analysis and Supportfor creep analysis.

• The nonlinear region usually requires a finer mesh. Use a finer mesh if severe element distortionsor stress concentrations are anticipated.

• The subcase structure should be utilized properly to divide the load or time history forconveniences in data recovery, and database storage control, not to mention changing constraintsand loading paths.

• Many options are available in solution methods to be specified on the NLCNTL and the TSTEP1bulk entries. The defaults should be used on all options before gaining experience.


Introduction

Chapter 2: User Interface

2.1 Supported inputsThe input data structure includes an optional header, executive control section, case control section,and the bulk data section. In general, features and principles for the user interface are consistent withother solution sequences. Any exceptions for SOL 401 are explained in this guide.

Mechanical design is dictated by the strength, dynamic, and stability characteristics of the structure.The software provides the analysis capabilities of these characteristics with solution sequences,each of which is designed for specific applications. The type of desired analysis is specified inthe executive control section by using a solution sequence identification. SOL 401 is designed forstatic and quasi-static.

The basic input data required for a finite element analysis may be classified as follows:

• Geometric data

• Element data

• Material data

• Boundary conditions and constraints

• Loads and enforced motions

• Solution methods

The first three classes of data may not be changed during the course of an analysis whereas the lastthree classes of data may be changed in midcourse via subcases under the case control section.

2.1.1 Case control section

The primary purpose of the case control is to define subcases. The subcase structure provides ameans of changing loads, boundary conditions, and solution methods by making selections fromthe bulk data. In SOL 401, loads and solution methods may change from subcase to subcase.Constraints can be changed from subcase to subcase. As a result, the subcase structure determinesa sequence of loading and constraint paths. The subcase structure also allows you to select andchange output requests. Any commands defined above the subcase specifications are applicable toall the subcases. Commands defined in a subcase supersede any made above the subcases. Thetable below lists the case control commands supported by SOL 401.



Table 2-1. Summary of CaseControlADAPTERRANALYSISBCRESULTSBCSETBEGIN BULKBGRESULTSBGSETBOLTLDBOLTRESULTSCKGAPCRSTRNCYCFORCESCYCSETCZRESULTSDISPLACEMENTDLOADDTEMPECHOEKEELSTRNELSUMESEFORCEGCRSTRNGELSTRN

GPFORCEGPKEGPLSTRNGROUNDCHECKGSTRAINGSTRESSGTHSTRNHARMONICSHOUTPUTIMPERFINCLUDEINITSJINTEGLABELLINEMAXLINESMEFFMASSMETHODMONVARMPCMPCFORCESNLARCLNLCNTLNSMOLOAD

OMODESOPRESSOSTNINIOTEMPPARAMPFRESULTSPLSTRNSEQDEPSETSETMCNAMESMETHODSPCSPCFORCESSTATVARSTRAINSTRESSSUBCASESUBTITLETEMPERATURETHSTRNTITLETSTEPWEIGHTCHECK

2.1.2 Bulk data section

The following table lists the bulk entries supported by SOL 401.

ACCELACCEL1BCPROPBCPROPSBCRPARABCTPARMBCTSETBEDGEBGADDBGPARMBGSETBOLTBOLTFORBOLTFRCBOLTLDBOLTSEQBSURF

CPENTACPENTCZCPLSTN3CPLSTN4CPLSTN6CPLSTN8CPLSTS3CPLSTS4CPLSTS6CPLSTS8CPYRAMCQUAD4CQUAD8CQUADRCQUADX4CQUADX8CRAKTP

IMPRADDINCLUDEINITADDINITSINITSOMAT1MAT2MAT8MAT9MAT11MATCIDMATCRPMATCZMATDMGMATFTMATS1MATT1

PLOADPLOAD1PLOAD2PLOAD4PLOADE1PLOADX1PLOTELPMASSPSHELLPSOLCZPSOLIDRBARRBE2RBE3RFORCERFORCE1SLOAD



User Interface

BSURFSCBARCBEAMCBUSHCBUSH1DCCHOCK3CCHOCK4CCHOCK6CCHOCK8CELAS1CELAS2CHEXACHEXCZCMASS1CMASS2CMASS3CMASS4CONM1CONM2CORD1CCORD1RCORD1SCORD2CCORD2RCORD2SCORD3G

CTETRACTRAX3CTRAX6CTRIA3CTRIA6CTRIARCYCADDCYCAXISCYCSETDAREADLOADDTEMPDTEMPEXECHOOFFECHOONEIGRLENDDATAFORCDSTFORCEFORCE1FORCE2GRAVGRDSETGRIDGROUPIMPERF

MATT2MATT8MATT9MATT11MOMENTMOMENT1MOMENT2MPCMPCADDMUMATNLARCLNLCNTLPARAMPBARPBARLPBEAMPBEAMLPBUSHPBUSH1DPBUSHTPCHOCKPCOMPG1PCOMPSPELASPELASTPGPLSN

SNORMSPCSPC1SPCADDSPCDSPOINTTABLED1TABLED2TABLED3TABLED4TABLEM1TABLEM2TABLEM3TABLEM4TABLEM5TEMPTEMPDTEMPEXTLOAD1TLOAD3TSTEP1VCEV

2.1.3 Parameters

Parameters are used for requesting special features or specifying miscellaneous data. Parametersare initialized in the MPL, which can be overridden by a DMAP initialization. Modules may change theparameter values while the program is running.

There are two types of parameters: user parameters (V,Y,name in the DMAP) and DMAP (non-user)parameters. You can change the default value of user parameters by specifying PARAM data inthe bulk data section, or for some parameters, in the case control section. See the ParameterApplicability Tables in the NX Nastran Quick Reference Guide. The following table lists theparameters supported in SOL 401.


User Interface


Table 2-2.COLPHEXACOUPMASSF56GRDPNTK6ROTLGDISPMATNLMAXRATIONLAYERSNOFISROGEOM

OMAXROMPTOPGOUGCORDPOSTPOSTEXTPOSTOPTPRGPSTPROUT

RGBEAMARGBEAMERGLCRITRGSPRGKSNORMUNITSYSTINYWTMASS

2.2 Nonlinear EffectsThe parameter LGDISP turns the nonlinear large displacement capability on/off for the staticsubcases. If you define the parameter LGDISP for SOL 401, you must include it in the bulk dataportion of your input file. The single PARAM,LGDISP setting applies to all static subcases.

• PARAM,LGDISP,-1 (default) – Large displacement effects are turned off. Subcases which includeANALYSIS=STATIC are linear static subcases.

• PARAM,LGDISP,1 – Large displacement effects are turned on. Subcases which includeANALYSIS=STATIC are nonlinear static subcases.

PARAM,LGDISP,1 turns on large displacement effects, but small strains are assumed.

Material nonlinear effects can also be included. See Support for plasticity analysis and Support forcreep analysis.

2.3 Nonlinear Parameters: NLCNTL entryThe NLCNTL bulk entry can be used to define strategies for the incremental and iterative solutionprocesses. It is difficult to choose the optimal combination of all the options for a specific problem.However, based on a considerable number of numerical experiments, the default option was intendedto provide the best workable method for a general class of problems. You should start with thedefault settings.

The NLCNTL bulk entry defines the parameters for SOL 401 control. The NLCNTL=n case controlcommand selects the NLCNTL bulk entry, and can be defined in a subcase or globally. You can definethe parameters on the NLCNTL bulk entry using the following format.

1 2 3 4 5 6 7 8 9 10NLCNTL ID Param1 Value1 Param2 Value2 Param3 Value3

Param4 Value4 Param5 Value5 -etc-

For example,NLCNTL 1 EPSU 1E-3 EPSP 1E-3 EPSW 1E-7 +



User Interface

+ CONV PW KSTEP 5 MAXITER 25

See the NLCNTL bulk entry in the NX Nastran Quick Reference Guide for the list of parametersand descriptions.

2.4 Iteration related output dataAt the end of every iteration, the relevant data from the iteration process are printed under thefollowing heading:

TIME Solution time

ITERATION NO Iteration count for the current timestep

DISP Relative error in terms of displacements. See Error functions and weightednormalization.

LOAD Relative error in terms of loads. See Error functions and weightednormalization.

WORK Relative error in terms of work. See Error functions and weighted normalization.

TOTAL STIFFNESSUPDATES

Number of stiffness updates in the current time step.

NO. OFBISECTIONS

Number of occurrences of bisection conditions during the iteration. SeeDivergence criteria.

NO. OF ITR DIV Number of occurrences of probable divergence during the iteration. SeeDivergence criteria.

STIFFNESSPARAMETERCURRENT

Value for the current stiffness parameter for the current iteration.

STIFFNESSPARAMETER %CHANGE

% Change in the value for the current stiffness parameter between and prioriteration.

2.5 Supported outputCase Control DescriptionADAPTERR Requests error estimates computed in a statics subcase.

BCRESULTS Requests contact forces, tractions, separation distance, and the totaland incremental slide distances.BGRESULTS Requests glue forces and tractions.

BOLTRESULTS Requests the bolt force and the axial strain output in a bolt preloadsubcase.CKGAP Requests gap result output for chocking elements.CRSTRN Requests grid point creep strains on elements.CZRESULTS Requests results output for cohesive elements.


User Interface


DISPLACEMENT Requests displacement output.EKE Requests element kinetic energy output.ELSTRN Requests elastic strain at grid points on elements.ESE Requests the output of the strain energy.FORCE Requests element force output.GCRSTRN Requests gauss point creep strains on elements.GELSTRN Requests elastic strain at gauss points.GPFORCE Requests grid point force balance output.GPKE Requests kinetic energy at grid points in a modal subcase.GPLSTRN Requests gauss point plastic strain output on elements.GSTRAIN Requests strain at gauss points.

GSTRESS Requests stress at gauss points.GTHSTRN Requests thermal strain at gauss points.

HOUTPUT Requests the harmonics for results output in the cyclic and Fouriernormal modes subcase types.JINTEG Requests output of the j-integral for crack analysis.MEFFMASS Requests modal effective mass output in a modal subcase.MPCFORCES Requests multipoint constraint force output.OLOAD Requests the form and type of applied load vector output.OMODES Requests selects a set of modes for output.

OPRESSRequests the solution pressures, which are from Simcenter Thermal inthe context of a coupled Simcenter multi-physics analysis, be includedin the SOL 401 output.

OSTNINI Requests initial strain output when an intial stress or strain is defined.OTEMP Requests solution temperatures output on grid points.

PFRESULTS Requests progressive failure results output for composite solidelements.PLSTRN Requests grid point plastic strain output on elements.SPCFORCES Requests single-point force of constraint vector output.

STATVAR Requests state variable output computed by an external user definedmaterial routine.STRAIN Requests element strain output.STRESS Requests element stress output.THSTRN Requests thermal strain at grid points on elements.

2.6 Solver SupportSOL 401 supports the sparse direct solver (default), the element iterative solver, or the PARDISOsolver (NLTRD3 nonlinear solution module). To select the SOL 401 solver type, supply a pair offields on the NLCNTL bulk entry of the form “SOLVER SPARSE”, “SOLVER ELEMITER”, “SOLVERPARDISO”, or “SOLVER MUMPS” . The default is SPARSE.

• The sparse direct solver is a robust and reliable option, well-suited to sparse models whereaccuracy is desired.



User Interface

• The element iterative solver performs well with solid element-dominated models. It may be afaster choice if lower accuracy is acceptable. You can optionally define the SMETHOD casecontrol command and the ITER bulk entry to alter any of the default options available on theITER entry.

• For problems involving contact and 3D solid elements, the element iterative solver is generallyfaster as compared to the sparse direct solver.

• The PARDISO solver is a hybrid direct-iterative solver, potentially faster with larger numbers ofcores than the sparse solver but with slightly lower accuracy.

2.7 Parallel support

SOL 401 supports the Geometric Domain Static Analysis (GDSTAT) parallel solution for fast staticanalyses. The performance of GDSTAT depends on the size of the boundary produced by thegraph-based (GPART = 1) domain partition. When the boundary size is small, GDSTAT is mostefficient. For most cases, DMP = 2 or DMP = 4 is sufficient.

You can use system cell 649 to control GDSTAT in SOL 401.

= 0 (default) Does not select GDSTAT. That is, NX Nastran performs serial processing.

= 1 Selects GDSTAT with null columns in the stiffness matrix.

= 2 Selects GDSTAT after null columns are removed from the stiffness matrix.

Use sys649 = 1 for most parallel processing cases. However, for models with large open contactpatches, which generally include a large number of null columns, you may see a performanceincrease with sys649 = 2.

For more information about parallel solutions, see the Parallel Processing User's Guide.


User Interface

Chapter 3: Subcase Types

3.1 Subcase analysis typeThe ANALYSIS case control command defines the subcase analysis type. SOL 401 allows anycombination of the subcase types.

• Static subcase: You include ANALYSIS=STATIC in a subcase.

• Bolt Preload subcase: You include ANALYSIS=PRELOAD in a subcase.

• Modal subcase: You include ANALYSIS=MODAL in a subcase.

• Cyclic Normal Modes: You include ANALYSIS=CYCMODES in a subcase.

• Fourier Normal Modes: You include ANALYSIS=FOURIER in a subcase.

The ANALYSIS case control command does not have a default in SOL 401. You must define it inevery subcase, and it cannot be defined above the subcases (globally).

The modal subcase should include the METHOD case control command which selects the EIGRLbulk entry. The EIGRL entry defines the data needed to perform the real eigenvalue analysis with theLanczos method. The modal subcase automatically includes the stress stiffening from the previousstatic subcase, and can potentially include follower stiffness and spin softening depending on the typeof loading in the previous static subcase. The NLCNTL bulk entry has parameter inputs which allowyou to control the stiffness contributions for the modal subcase.

3.2 Subcase sequencingYou can use the SEQDEP case control command to define any subcase type as sequentiallydependent (SD), or non-sequentially dependent (NSD).

• SEQDEP=YES (default) – the subcase is a SD subcase.

SOL 401 uses time as the variable to increment temperatures and loads in a static subcase.An SD static subcase uses the final time from the previous static subcase for its start time.The start time is used to compute the solution time steps in a static subcase. See DefiningSolution Time Steps.

An SD subcase can receive the final state variables from the previous static subcase. Forexample, plastic strains, creep strains, and displacements.

• SEQDEP=NO – the subcase is a NSD subcase.

A NSD subcase is independent. The start time for a static NSD subcase is 0.0. See DefiningSolution Time Steps.

A NSD subcase does not use any data from a previous subcase, regardless of the parametersettings on the NLCNTL bulk entry.



3.3 Cyclic symmetricThe cyclic solution method takes advantage of cyclic symmetry to reduce the time needed to createand solve a full 360 degree model. To use this method, you create a 3D-solid element model thatrepresents a fundamental segment. The fundamental segment represents a structure that is made upof N repetitions, where each repetition can be obtained by rotating the fundamental segment an anglethat is an integer multiple of 2π/N.

An important feature of this cyclic solution method is the automatic coupling of the translational DOFon the symmetry faces. The CYCSET case control command, which selects the CYCSET bulkentry, or multiple CYCSET entries with the CYCADD bulk entry, defines the coupling. The couplingdefinition is required and must be defined globally. As a result, the MPC equations created by thesoftware are applied in every subcase.

To define the coupling, you select the cyclic source and target regions on the CYCSET bulk entry. Avery useful feature of the coupling definition is that the mesh on the source and target regions canbe dissimilar. In addition, features such as holes in one or both of the symmetry faces are alsopermitted. The software internally computes the correct coupling conditions between the grids onthe source and target faces.

The CYCAXIS bulk entry is also required to define the default cylindrical coordinate system forthe coupling. The origin of this cylindrical system must be at the center of the revolution, and theZ-axis must be consistent with the axial direction.

Also see Cyclic Symmetry Theory.

CYCMODES subcase

A cyclic modes subcase is available and designated with ANALYSIS=CYCMODES in the subcase.The cyclic modes formulation includes the harmonic index, k, which represents an additionaldimension of the vector space that is not present in an "ordinary" modal analysis. For cyclic modelswith an even number of sectors (N is even), the allowable set of harmonics is 0,1, ...., N/2. For cyclicmodels with an odd number of sectors (N is odd), the allowable set of harmonics is 0,1,…, (N-1)/2.

You request the harmonic index values in which you want modes to be computed with theHARMONICS case control command, and a cyclic modal solution occurs for each harmonic indexindependently. For example, if you request 10 modes on the EIGRL bulk entry, and you request amodal solution for the 0th, the 1st, and the 2nd harmonic, a discrete cyclic modal solution occursfor each of these harmonics.

When computing the cyclic modes, the software uses a duplicate sector method. For harmonics k=0and k=N/2, there are distinct eigenvalues, and only one eigenvector component associated with eacheigenvalue. For all other harmonics (0 < k < N/2), each eigenvalue is repeated, and the displacement

vector for each corresponding eigenvalue has two components; the cosine component and the

sine component .

Static, bolt preload, and modal (non-cyclic modes) subcases

The static, bolt preload, and modal (non-cyclic modes) subcases can also be included in the input,and are designated with ANALYSIS=STATICS, ANALYSIS=PRELOAD, or ANALYSIS=MODALdefined in the subcase. These subcases use the MPC equations automatically created by thesoftware, but the displacements in the static and modal subcases are not cyclic. That is, thedisplacements only represent the 0th harmonic, n=1 fundamental sector.



Subcase Types

Any of the subcase types (statics, preload, modal and cyclic modes) can be defined as sequentiallydependent. The parameters STRESSK, SPINK and FOLLOWK on the NLCNTL bulk entry can bedefined to request stress stiffening, spin softening, and follower stiffness, respectively.

Cyclic clocking and normalization for the CYCMODES subcase

As a result of the inherent symmetry with the cyclic modal solution, modes occur in pairs forharmonics 1 through N/2-1, where N is the total number of sectors.

Once NX Nastran computes the normal modes, it uses the initially computed global displacementvectors to do the following:

• The software clocks the eigenvector solution to the fundamental sector. This clocking ensuresthat, for the first mode in a mode pair, the maximum nodal displacement occurs on thefundamental sector.

• If you have selected either the AFNORM or DISP normalization options, the softwarerenormalizes using the maximum displacement relative to all sectors.

The clocking and normalization procedure is as follows.

The displacement result for a single mode and harmonic is represented by the equation:

The global displacement vectors and in a single mode are orthogonal to each other. In

addition, from one mode in a pair is related to from the same pair.

For a travelling wave with equal amplitude in any mode pair, every grid point traverses an ellipse inthree dimensional space. The maximum resultant displacement is the major axis of the ellipse. For agrid point i, the maximum resultant displacement is computed as follows.

is the cyclic cosine displacement vector (three components) at a specific grid point.

is the cyclic sine displacement vector (three components) at a specific grid point.

The software computes the following using the cyclic cosine and sine vectors:

The resultant displacement at each grid point i is computed as:

The software determines the grid point with the maximum resultant displacement. For this grid pointii, the phase angle is computed as:


Subcase Types


This phase angle will be used to clock the displacements to the fundamental sector.

The maximum displacement found at grid point ii is used to compute the normalization factor:

• For AF normalization, the factor is computed as:

where,

ω is the frequency for the mode, and

AFNORM is the parameter setting PARAM, AFNORM which defaults to 1.0.

For the modes considered as rigid body modes, the software sets ω = 1 when computing the AFnormalization factor. The software considers a mode to be a rigid body mode if its frequency isbelow the value of the parameter AFZERO (default=1.0 hz).

• For unit (MAX) normalization, the factor is computed as:

• For mass (MASS) normalization, the factor f=1.0 is used since the eigenvector was already massnormalized when the modes were computed initially.

The cyclic cosine and sine components are then clocked based on the computed values of .

The cyclic components for each mode are then reset to these values:

Cyclic modes subcase input summary

• The automatic coupling definition is required. The inputs for the coupling are described under the‘Automatic Coupling Details’ heading below.

• The ANALYSIS=CYCMODES case control command is defined in the specific subcases in whichyou are requesting the cyclic modes solution method.

• The HARMONICS case control command requests the specific harmonics in which modes arecomputed. "ALL" requests all possible harmonics. If you define the SID of a SET bulk entry,the SET entry lists the harmonic numbers to be computed, including "0" to request the zerothharmonic.



Subcase Types

The maximum harmonic for a model is related to the total number of segments which wouldtheoretically exist to represent the full model.

o For an even total number of segments:

Maximum harmonic = Total number of segments/2.

For example, if a 30 degree segment is modeled, the total number of segments to create afull model is 360/30 = 12. Since 12 is even, the maximum harmonic = 12/2=6.

o For an odd total number of segments:

Maximum harmonic = (Total number of segments-1)/2.

For example, if a 40 degree segment is modeled, the total number of segments is 360/40= 9. Since 9 is odd, the maximum harmonic = (9-1)/2 = 4.

o As a result of the inherent symmetry in the cyclic modal solution, mode pairs exist forharmonic numbers 1 through N/2 -1. The software automatically outputs the mode pairsfor these subcase types for the modes requested with the EIGRL entry. For example, ifyou request 10 modes on the EIGRL entry:

For harmonic index 0 and N/2, 10 modes are computed.

For harmonic numbers 1 through N/2 -1, 20 modes are computed (10 distinct modes).

This behaviour is consistent for modes requested with the OMODES case control command.See the remarks on the OMODES command for details.

• The HOUTPUT case control command optionally requests the harmonics to output modes. "ALL"requests output for every harmonic requested on the HARMONICS command. You can definean integer to select the SID of a SET bulk entry, which lists the harmonic numbers to be output.These IDs are a subset of the IDs requested on the HARMONICS command. The C, S, C*, andS* describers on the HOUTPUT command are not supported by SOL 401.

• The METHOD case control command selects the EIGRL bulk entry which then defines theeigenvalue solution options. For example, the lower and upper frequency ranges and the numberof modes. Since a single EIGRL entry is selected in a subcase, the same EIGRL options areused when the software computes the modes for each harmonic.

Automatic Coupling Details

• The symmetry faces are grouped into source and target regions. To do the automatic coupling,NX Nastran internally rotates the target region grids into the source region grids, it does a meshrefinement on both the source and target, and then creates MPC equations using the target asthe dependent DOF and the source as the independent DOF. The MPC equations are createdbetween any source and target region grids within the user defined search distance (SDISTi)using a weighted area method.

• The mesh on the source and target regions can be dissimilar. Features such as holes in one orboth of the symmetry faces are also permitted.

• It is recommended that the source and target faces have similar geometry. If the source andtarget geometry is different, the software will still couple the appropriate source and target grids,although, the solution accuracy will be comprimised.


Subcase Types


• You must define the automatic coupling globally. The resulting MPC equations are included inall subcases, including any static, preload, and modal (that is, a non-cyclic modes subcasewith ANALYSIS=MODAL).

Automatic coupling input summary

• The CYCAXIS bulk entry is required to define the default cylindrical coordinate system for thecoupling. The origin of this cylindrical system must be at the center of the revolution, and theZ-axis must be consistent with the axial direction.

• The Z-axis of every cylindrical coordinate system referenced by the CYCSET entry must havethe same origin and direction as the z-axis of the default coordinate system selected with theCYCAXIS bulk entry.

• The displacement coordinate system of grid points which are defined on the rotation axis musthave a Cartesian displacement coordinate system. For all other grid points, a cylindricaldisplcement coordinate system is recommended. See Rules for source and target DOF.

• The CYCSET case control selects the CYCSET or CYCSADD bulk entries. The CYCSETcase control must be defined above the subcase level. As a result, the MPCs generated bythe automatic coupling are used in every subcase (cyclic modes, static, and "normal" normalmodes subcases).

• The BSURFS and BCPROPS bulk entries define the regions. These are existing inputs usedto define glue and contact regions.

• The CYCSET bulk entry pairs the source and target face regions.

o The source region selected in a pair must have a smaller positive theta location than thetarget region.

o The software will use the number of segments (NSEG) field to compute the angle betweenthe source and target faces. For example, if a 30 degree segment is modeled, NSEGwould be 12 = (360/30).

o The SDIST field is used to pair source and target grids when creating the MPC equations.From each source grid, the search occurs in both the positive and negative theta DOFdirections. If the SDIST field is undefined, the software will automatically compute the searchdistance. The software computed value is reported in the f06 file.

• The CYCADD bulk entry can optionally be used to combine multiple CYCSET bulk entries. Thevalue defined in the NSEG field on all CYCSET entries referenced by a CYCADD entry must bethe same. A fatal error will occur if any are inconsistent.

• The CYCFORCES case control command optionally requests the MPC force output for the gridswhich are included in the automatic coupling. It can be defined above the subcases (globally)or in a subcase.

Rules for source and target DOF

• If you define SPC conditions on target region DOF with the SPC, SPC1, or SPCD entries, thesoftware reports a warning message that it is ignoring the SPC conditions on the target regionDOF, and the solution continues.



Subcase Types

• If you include a target region DOF on an RBE2, RBAR, or RBE3 element as a dependent DOF,the software reports a warning message that it is ignoring the rigid connections on the targetregion DOF, and the solution continues.

• If you include a source or target region DOF on an MPC bulk entry as a dependent DOF, thesolution ends with a fatal error.

• Grid points which are defined on the Z-axis of the default cylindrical coordinate system must havea Cartesian displacement coordinate system. For the grid points which are defined on the Z-axisand are included in a source or target region, in addition to any conditions that you defined, NXNastran automatically applies the following SPC conditions during the solution.

o For the harmonic index k=0, NX Nastran fixes DOF 1, 2.

o For the harmonic index k=1, NX Nastran fixes DOF 3.

o For all other harmonic index values, NX Nastran fixes all six DOF.

Post-processing the results

NX Nastran outputs results for the fundamental sector. Due to the symmetric nature of the problemand the orthogonal nature of the modes, the results for the entire structure (360 degree model) canbe inferred from the results of the fundamental sector.

• For the 0th harmonic:

=

Where,

n = sector for which results are to be inferred.

= Results corresponding to the fundamental sector at harmonic 0.

results for sector n at harmonic 0.

• For harmonic k (0 < k < N/2),

Where,

N = Total number of sectors.

n = Sector for which results are to be inferred.

k = Harmonic index

= Cosine cyclic component for the k harmonic of the mode being computed for thefundamental sector.

= Sine cyclic component for the k harmonic of the mode being computed for the fundamentalsector.

R = any output quantity of interest. For example, displacement or stress.


Subcase Types


• For harmonic N/2:

Where,

n = Sector for which results are to be inferred.

= results corresponding to the fundamental sector at harmonic N/2.

= results for sector n at harmonic N/2.

3.4 Fourier harmonic solutionA Fourier normal modes subcase is available in SOL 401 for models which include axisymmetricelements. The subcase is designated with the ANALYSIS=FOURIER and HARMONICS=N casecontrol commands in the subcase.

The conventional axisymmetric element includes radial and axial degrees-of-freedom with novariation in theta.

In the Fourier normal modes subcase, the axisymmetric element has radial, axial and thetadegrees-of-freedom. In addition, the degrees-of-freedom are represented with harmonic terms of aFourier series of the form:

where,

c=cos(kθ) and s=sin(kθ),

k is the harmonic number,

are symmetric displacements, and

are antisymmetric displacements.

Both symmetric and antisymmetric displacements are computed by NX Nastran for a particularharmonic k.

With the Fourier normal modes subcase, you request which harmonic numbers a modal solutionshould occur, and the harmonic terms for modal output. For each harmonic number in whichyou request modes and output, the software can compute the symmetric and antisymmetric



Subcase Types

displacements, stress, strain, SPC force and grid point forces. You can use the typical case controlcommands to request the output. You can then optionally use the NX post processor to display thephysical results on either a 3D segment, or on a full 360 degree model display.

The modal solution for each harmonic term is discrete, and independent of other harmonic terms. Forexample, if you request 10 modes on the EIGRL bulk entry, and you request a modal solution forthe 0th, the 1st, and the 2nd harmonic term, a discrete modal solution will occur for each of theseharmonics. You will have 10 modes for the 0th, 10 modes for the 1st, and 10 modes for the 2nd term,and there is no coupling of the mode results between the different harmonics.

Static and modal (non-Fourier normal modes) subcases can also be included in the input, and aredesignated with the case control commands ANALYSIS=STATICS or ANALYSIS=MODAL. Although,the conventional axisymmetric element formulation is used in the static and modal subcases.

The Fourier normal modes subcase can optionally be sequentially dependent on a static subcase.The parameters STRESSK, SPINK and FOLLOWK can optionally be defined on the NLCNTL bulkentry to request the additional stiffness terms computed in the previous static subcase.

In addition to axisymmetric elements, the plane stress and the chocking elements can also beincluded with the Fourier normal modes subcase. In the Fourier normal modes subcase, gausslocations on the chocking element use the axisymmetric Fourier formulation if the location isconsidered chocked. That is, it includes stiffness in the radial, axial and theta degrees-of-freedom,and all degrees-of-freedom are represented using harmonic terms of a Fourier series. To beconsidered chocked, the loads in a previous static subcase should result in the chocked condition,and the consecutive Fourier normal modes subcase should be defined as sequentially dependent. Bydefault, all gauss locations on the chocking elements are considered unchocked in a Fourier normalmodes subcase, and use the plane stress element formulation.

For grid points which are defined on the rotation axis, in addition to any conditions that you defined,NX Nastran automatically applies the following SPC and MPC conditions during the solution.

• For the harmonic index k=0, NX Nastran fixes the radial (Ur) and azimuth (Uθ) degrees-of-freedom.

• For the harmonic index k=1, NX Nastran fixes the axial degree-of-freedom, and it creates theMPC condition Ur = Uθ for the cosine terms, and the MPC condition Ur = -Uθ for the sine terms.

• For the harmonic index k>1, NX Nastran fixes all translational degrees-of-freedom.

Note:

When axisymmetric elements are defined on the XZ-plane of the basic coordinate system, the X-axisof the basic system is the radial direction, the Z-axis of the basic system is the axial direction, andthe Y-axis of the basic system is the azimuth direction. The grid points defining these elementsmust have X ≥ 0.

When axisymmetric elements are defined on the XY-plane of the basic coordinate system, the Y-axisof the basic system is the radial direction, the X-axis of the basic system is the axial direction, andthe Z-axis of the basic system is the azimuth direction. The grid points defining these elementsmust have Y ≥ 0.

Fourier normal modes subcase input summary

• The ANALYSIS=FOURIER case control command should be defined in the subcase in which youare requesting the Fourier normal modes subcase in SOL 401.


Subcase Types


• The HARMONICS case control command requests the specific harmonics in which modes willbe computed. The SET entry then lists the harmonic numbers to be computed, including "0" torequest the zeroth harmonic. Since there is an infinite number of harmonics in the Fourier normalmodes analysis, the describer "ALL" is not supported in the ANALYSIS= FOURIER subcase.

• The HOUTPUT case control command optionally requests the harmonics to output modes. "ALL"requests output for every harmonic requested on the HARMONICS command. An integer can bedefined to select the SID of a SET bulk entry listing the harmonic numbers to be output. TheseID's typically represent a subset of the ID's requested on the HARMONICS command. The C, S,C*, and S* describers on the HOUTPUT command are not supported by SOL 401.

• The METHOD case control command selects the EIGRL bulk entry, which then defines theeigenvalue solution options. For example, the lower and upper frequency ranges and the numberof modes.

3.5 Nonlinear bucklingA nonlinear buckling analysis is used to accurately determine what the critical buckling load is andhow a structure behaves after it has buckled. You can request a nonlinear buckling analysis in a SOL401 statics subcase. You can choose from one of the following three arc-length methods:

• Riks arc-length method

• Modified Riks arc-length method

• Crisfield arc-length method

To request the nonlinear buckling analysis, your statics subcase should include the standardANALYSIS=STATICS command along with the NLARCL=ID case control command. The ID on theNLARCL command selects the NLARCL bulk entry which defines the nonlinear buckling parameters.

The NLARCL command in the subcase is the trigger which the software uses to start the nonlinearbuckling analysis. The referenced NLARCL bulk entry is also required, even when the default valuesare used.

The nonlinear buckling statics subcase must be either the first subcase, or the last in a sequence ofstatic subcases. A nonlinear buckling statics subcase can only be followed by a modal subcase.

• If the nonlinear buckling statics subcase is the first subcase, all of the loads defined in the currentsubcase are incrementally applied by the software during the arc-length solution.

• If the nonlinear buckling statics subcase is the last subcase and it is sequentially dependent, theloads applied in the previous subcase are held constant in the current subcase. The differencebetween the load defined in the nonlinear buckling statics subcase and the load from the previoussubcase is computed. This load difference is incrementally applied by the software during thearc-length solution.

You select loads in a nonlinear buckling statics subcase with either the LOAD=n or DLOAD=n casecontrol commands. Although, you cannot increment loads in a nonlinear buckling statics subcasewith a TSTEP1 bulk entry since the software increments the loads for you. If you define a TSTEP1entry in a nonlinear buckling statics subcase, you must define it with a constant time. That is, it musthave an end time (Tend) which is the same as the start time for that subcase. In addition, the output



Subcase Types

frequency option Nout on the TSTEP1 entry is ignored in a nonlinear buckling statics subcase. Theoutput frequency is instead controlled by the NOUTAL parameter on the NLARCL bulk entry.

If you want to define a specific load sequence up to the point of buckling, you can do this with staticsubcases without buckling defined before your nonlinear buckling statics subcase. In these previousstatic subcases, you can increment loads with the TSTEP1 bulk entry.

The NLARCL bulk entry has the following solution parameters:

TYPE

= RIKS selects the Riks arc-length method

= MRIKS selects the modified Riks arc-length method (Default)

= CRIS selects the Crisfield arc-length method

MINALR Minimum allowable arc-length adjustment ratio between increments for the adaptivearc-length method. (0.0=1.0, Default=4.0)

MAXR Defines the overall upper and lower bounds on the load increment /arc-length inthe subcase.SCALE Scale factor for controlling loading contribution in the arc-length constraint.(Real>0.0; Default = 0.0)

DESITER Desired number of iterations for convergence to be used for the adaptive arc-lengthadjustment. (Integer>0, Default=12)

MXINC Maximum number of controlled load increments done in the arc-length subcase(Integer>0; default=20)

LDFACIN Initial load factor. This load factor will be used to compute initial arc-length (REAL>0,DEFAULT=1.0).

NOUTAL

Skip factor for output of the incremental results. Output always occurs at the finalincrement. For example, if you define NOUTAL=2, output occurs at every otherconverged solution increment and for the final increment. If you define NOUTAL=0,output only occurs at the final increment. (Integer≥0; Default=1)

MXLDFAC Maximum value of load-factor at which solution will be terminated. (Real, Default =1.0)

Initial Imperfections

You define the X,Y,Z location of a grid point on the GRID entry. An option is available to adjust thislocation with a +/- delta X,Y,Z position. For example, if a grid point is defined on the GRID entry at1.0, 1.0, 0.0, and a delta of .2, 0.0, 0.0 is defined, the modeled location for this grid point becomes1.2, 1.0, 0.0. This location adjustment is useful in the nonlinear buckling analysis to define animperfection. For example, an imperfection on the side of a cylinder which is under axial compressionwill impose a deliberate location for buckling.

The grid point imperfections are selected with the IMPERF case control command which selects theIMPERF or IMPRADD bulk entries. The IMPRADD entry allows you to combine multiple IMPERFentries, and scale the referenced imperfection sets either independently or collectively.

The IMPERF case control command must be defined globally (above the subcases). As a result, theupdated location of the referenced grid points applies to all subcases.

Restrictions

• The software issues a fatal error if LGDISP=-1 and an arc-length solution is requested.


Subcase Types


• The software issues a fatal error if an arc-length solution is requested in the context of aSimcenter Multiphysics solution.

• The software issues a fatal error if a sequentially dependent STATICS or PRELOAD subcasefollows an arc-length subcase.

• The software issues a fatal error if a sequentially dependent arc-length subcase follows anothersequentially dependent arc-length subcase.

• An enforced displacement defined with the SPCD bulk entry is held constant in a nonlinearbuckling solution.

Arc-length theory

The concept of the arc-length method is to modulate the applied loads in order to produce solutionswith displacement increments of manageable size of a given load step. In order to modulate theapplied load, an additional variable, the load factor, and a constraint equation are introduced. Thereare various approaches to providing a constraint equation.

Consider a residual load {R}.

Equation 3-1.

where F represents the internal forces, and the total external load P is expressed as:

Equation 3-2.

where P0 denotes the applied load at the end of the preceding subcase, ΔP represents the loadincrement in the current subcase, and μ is the load factor varying from 0 to 1, but not limited to thisrange, within the subcase. Linearizing {R} about (u,μ), R(u,μ) can be expressed as:

Equation 3-3.

Based on the above equations, the equilibrium condition at (u+Δu, μ+Δμ) dictates that

Equation 3-4.

where, is the follower matrix, is the stiffness matrix , and .

The iteration equation can be derived by rearranging Equation 3-4:



Subcase Types

Equation 3-5.

where the follower matrix is omitted. The iterative process can be established by decomposing theequation above into two parts:

Equation 3-6.

Then the trial solution is obtained by

Equation 3-7.

with

Equation 3-8.

where Δμ can be obtained from the constraint equation.

Riks Method and Its Variations

The displacement increment is limited by a constraint equation:

Equation 3-9.

where w is a scaling factor you specify with the SCALE parameter on the NLARCL bulk entry, andΔl is defined by

Equation 3-10.

You define the initial value of Δμ with the LDFACIN parameter on the NLARCL bulk entry. Theconstraint of Equation 3-9 has a disparity in the dimension by mixing the displacements with the loadfactor. For this reason, the scaling factor (w) is introduced so that you can scale μ to the appropriatedimension or delete the Δμ term. The default value of w is zero as demonstrated in Figure 3-4. Theiteration follows the path on the plane normal to the initial tangent as shown in Figure 3-1. Thereforethe subsequent iterations (i > 1) must satisfy


Subcase Types


Equation 3-11.

Recalling that the first iteration should result in

Equation 3-12.

Equation 3-11 may be reduced to

Equation 3-13.

from which the load factors for the subsequent iterations are determined by

Equation 3-14.

and

Equation 3-15.

Notice that the normal plane does not change during the iteration by Riks method. In addition, {ΔuP}remains constant if the iteration process is the modified Newton's method.

Alternatively, the normal plane may be updated at every iteration. If the normal plane is to be normalto the cumulative incremental displacements for the preceding iterations as shown in Figure 3-2, theorthogonality condition in Equation 3-11 should be modified to:

Equation 3-16.

The increment in the load factor for i > 1 is obtained by solving Equation 3-16,

Equation 3-17.



Subcase Types

This variation of Riks method has an advantage over the Crisfield method as it avoids the solution ofa quadratic equation.

Crisfield Method

Instead of iterating on the normal plane, the solution is sought on the surface defined by Equation 3-9with an arc-length of Δl as depicted in Figure 3-3,

Equation 3-18.

This constraint can be interpreted as keeping the incremental displacement constant, if w=0, asshown in Figure 3-4. Substituting Equation 3-8 into the preceding equation, we obtain a quadraticequation in terms of Δμ:

Equation 3-19.

where

Equation 3-20.

Since the Crisfield method leads to a quadratic equation, the selection of the proper root of thisequation becomes the most critical process for the success of this method. There are two roots toEquation 3-19,

Equation 3-21.

The root is chosen so that the angle between two vectors {ui-1 - uo} and {ui - uo} is less than 90degrees,

Equation 3-22.


Subcase Types


There are cases where no roots can be found. Such is the case when the trial solution is far from thetrue solution and stays outside the region covered by the arc-length. In this case, the trial solutionvector is scaled so that the direction vector intersects with the surface defined by Equation 3-18.

The wrong choice of the root could cause an unintentional loading path reversal, by which the solutionreturns to the previous state. Such cases can be detected by checking the orthogonality of theincremental displacements of the two successive solutions. If this case is detected, the root is chosenso that the angle between {ui - uo} and {ui - uo} is an acute angle.

Adaptive Arc-Length Method

It is difficult to estimate a proper arc-length for multi-degree-of-freedom problems. The initialarc-length for the Crisfield method can be determined by

Equation 3-23.

with

Δμ1 = μ1 = LDFACIN parameter on the NLARCL bulk entry.

You can define the maximum number of increments in the subcase with the MXINC parameteron the NLARCL bulk entry.

The arc-length should be continuously updated at every increment using the information gatheredduring the preceding increment. One method is to reduce the arc-length if it requires an excessivenumber of iterations to attain a converged solution,

Equation 3-24.

where Id is the desired number of iterations for convergence and defined with the DESITERparameter on the NLARCL bulk entry, and Imax is the number of iterations required for convergencefrom the preceding step.

The adaptive process should be based on the arc-length ratio,

Equation 3-25.

Combining two criteria, the new arc-length ratio is adapted to the nonlinearity by



Subcase Types

Equation 3-26.

In order to maintain the stability for the adaptive process, ALRATIO should also be bounded,

MINALR < ALRATIO < MAXALR

You can define the parameters MINALR and MAXALR on the NLARCL bulk entry, which have thedefaults of 0.25 and 4., respectively. If the adjusted ALRATIO falls outside the bounds, ALRATIOis reset to the limit. Then the arc-length is updated at the beginning of the next step based onALRATIO as follows:

Δlnew = ALRATIO * Δlold

In the unstable regime where the stiffness is negative, the load factor decreases with a forward step.When this happens, the sign of Δμ1 should be reversed. This possibility should be examined at thebeginning of each increment. The sign can be determined by the sign of a dot product,

Equation 3-27.

An adaptive bisection algorithm is also incorporated to cope with divergent cases. If the iterativeprocess using the arc-length method tends to diverge, the arc-length is bisected. The bisection iscombined in concert with the stiffness matrix update strategy. The bisection procedure continuesuntil the iterative process is stabilized and a converged solution is found. However, the number ofcontiguous bisections is limited by the parameter MAXBIS on the NLCNTL bulk entry. The variablearc-length at every increment invokes the recovery from the bisection process once the difficulties inconvergence are overcome.


Subcase Types


Figure 3-1. Riks Method

Figure 3-2. Modified Riks Method



Subcase Types

Figure 3-3. Crisfield Method - Arc-length in terms of Combined Variables

Figure 3-4. Crisfield Method - Arc-length in terms of Displacements


Subcase Types

Chapter 4: Element support

4.1 Element OverviewThe following summarizes all of the elements and materials supported in SOL 401.

• The 3D solids elements CTETRA, CHEXA, CPENTA and CPYRAM are supported for linear,geometric nonlinear, and material nonlinear analysis.

• The axisymmetric elements CQUADX4, CQUADX8, CTRAX3, CTRAX6, the plane strainelements CPLSTN3, CPLSTN4, CPLSTN6, CPLSTN8, and the plane stress elements CPLSTS3,CPLSTS4, CPLSTS6, CPLSTS8 are supported for linear, geometric nonlinear, and materialnonlinear analysis.

The grid points on these elements must all lie in either the XZ plane, or all in the XY plane of thebasic coordinate system. The software automatically determines the orientation.

When axisymmetric elements are defined on the XZ plane, X is the radial direction, and Z is theaxial direction. The grid points defining these elements must have X ≥ 0.

When axisymmetric elements are defined on the XY plane, Y is the radial direction, and X is theaxial direction. The grid points defining these elements must have Y ≥ 0.

• A special, generalized plane strain formulation is available using the CPLSTN3, CPLSTN4,CPLSTN6, and CPLSTN8 element types. See Generalized plane strain analysis.

• The chocking element is available. The chocking elements is a special type of axisymmetricelement that are used to model regions in an axisymmetric analysis that can carry a compressivehoop stress, but cannot carry a tensile hoop stress. See Chocking elements.

• The cohesive element is available to model adhesively bonded interfaces. Cohesive elements canaccount for compliance in the connection and damage in the material. See Cohesive elements.

• The bar and beam elements defined with the CBAR and CBEAM entries are available. Theysupport large displacements and rotations when large displacements are requested withPARAM,LGDISP,1.

• The shell elements CTRIAR, CQUADR, CTRIA6, and CQUAD8 entries are supported. CQUAD4and CTRIA3 elements are also supported as inputs and the software will treat them as CQUADRand CTRIAR elements.

• The spring elements CELAS1, CELAS2, CBUSH1D, and CBUSH are supported.

• The RBE2 and RBAR rigid elements are supported with optional large displacement effects andthermal expansion. The RBE3 rigid element is also supported, but it does not support the largedisplacement effects or thermal expansion. See Rigid element support.

• The mass elements CMASSi and CONMi are supported.



• The PSOLID or the PCOMPS bulk entries define the element properties. The PCOMPS isoptionally used to define a layered solid composite property.

You can model progressive ply failure in solid composites. See Progressive failure analysisin solid composites.

• The supported material types include the following.

The MAT1 and MATT1 (temperature dependent) bulk entries define isotropic materials.

The MAT3 and MATT3 (temperature dependent) bulk entries define isotropic materials.

The MAT9 and MATT9 (temperature dependent) bulk entries define anisotropic materials.

The MAT11 and MATT11 (temperature dependent) bulk entries define orthotropic materials.

Plastic and creep materials can optionally be assigned to the 3D solid elements, axisymmetricelements, the plane stress elements, and the plane strain elements. You can enable one or bothplasticity/creep in all subcases, or in specific subcases. See Support for plasticity analysis andSupport for creep analysis.

Externally computed, user defined material models are supported. You can define a materialmodel by developing and compiling an external routine. See User defined materials.

• You can request stress norm, stress error norm, strain energy norm, and strain energy errornorm output. The output is computed and stored on an individual element basis. The Pre/Postapplication uses the output for adaptive meshing. See Error estimator for mesh refinement.

• You can compute and output the j-integral in a crack simulation. The j-integral output canbe requested and used by third-party software like Zencrack to perform a fracture mechanicsanalysis. The CHEXA bulk entry allows for a collapsed element definition. See Crack simulation.

4.2 Elements in nonlinear analysisIn nonlinear finite element analysis, lower-order elements are often preferred over higher-order onesbecause of their robustness and reasonable accuracy at reduced costs. The software supports linearelements, rather than quadratic or cubic elements, to process nonlinearity. When using lower-orderelements, quadrilateral and hexahedral elements are generally preferred over triangular, pentahedralor tetrahedral elements. Triangular and tetrahedral elements can exhibit excessively stiff behavior,and caution is needed when using these elements.

Caution is also needed when different element types are combined in a model, and if theseelements are incompatible. In such cases, some provision (e.g., appropriate constraints) may benecessary at the interface boundary. Modeling the joints (such as bolted, riveted, or welded) isparticularly difficult. For lack of better information, the joints are usually modeled as rigid or free incertain degrees-of-freedom. If improved accuracy is required at such joints, the characteristics ofthe joint (stiffness and/or damping) may have to be identified from experiments or the local analysisof a detailed model at the joint. Modeling of the boundary conditions at the supports poses similardifficulties. Ideal boundaries are represented as free, clamped, pinned, roller or ball joints. Thereality tends to be in smeared condition.

Elements become actively nonlinear if the parameter LGDISP is tumed. As for geometric nonlinearity,the software does not currently support large strain capability. However, large displacement is treatedeffectively by computing element stresses and strains in the updated element coordinates.



Element support

4.3 Shell elementsSolution 401 supports shell elements defined with the CTRIAR, CQUADR, CTRIA6, and CQUAD8entries. CQUAD4 and CTRIA3 elements are also supported as inputs, and the software will treatthem as CQUADR and CTRIAR elements.

The shell elements are supported in the subcase types STATIC, PRELOAD, and MODAL. They arenot supported in the BUCKLING, CYCLIC and FOURIER subcase types.

The PSHELL property entry is supported. In addition, the PCOMPG1 property entry is available todefine a composite property which allows for a different failure theory for each layer.

The shell element using the PSHELL bulk entry supports geometry nonlinear conditions (largedisplacement, large rotation, and contact) and material nonlinear (plasticity and creep). When youuse a nonlinear plastic or creep material, the NLAYERS parameter is supported to define the numberof integration points through the thickness. The NLAYERS parameter supports 3, 5, 7, and 9 pointsthrough the thickness.

A composite shell element using the PCOMPG1 property bulk entry supports the geometry nonlinearconditions, but does not support material nonlinear.

The ZOFF field on the element entry is supported to offset the element reference plane.

PSHELL property

• The MID1, MID2, and MID3 are all required. MID1 and MID2 must be explicitly defined, and theMID3 field defaults to the MID2 value.

• MID4 is optional. If MID4 is defined, MID1 and MID2 must be defined. MID4 is applied withrespect to the element plane regardless if ZOFF is defined or not. A ZOFF definition on theelement entry produces a coupling independent of the MID4. As a result, defining both MID4 andZOFF together will create two independent sources of coupling. If you define both MID4 andZOFF, the MID4 should represent an additional coupling which is unique to the ZOFF coupling.

• When plastic or creep nonlinear materials are defined, the MID1, MID2, and MID3 must allbe the same, and MID4 must be undefined.

• The Z1 and Z2 fields on the PSHELL, which define fiber distances for stress calculations in othersolution types, are not supported by SOL 401.

PCOMPG1 property

• The PCOMPG1 property entry is available to define a composite property which allows for adifferent failure theory for each layer.

• The MATFT defines the failure theory allowables for both shell and solid composites. MATFT isrequired to define allowables with the MAT9 and MAT11 material entries. If you are using theMAT1 material entry, you can optionally define the allowables with the MATFT, or you can specifythem on the MAT1 entry directly. For shell composites, only FT = HILL/HOFF/TSAI/STRN aresupported (NO FT = STRS/TS), and the transverse material properties are ignored for shells:

FT = HILL/HOFF: Zt, Zc, S13, S23 are ignored.

FT = TSAI: Zt, Zc, S13, S23, F13, F23 are ignored.

FT = STRN: Zet, Zec, Se13, Se23 are ignored.


Element support


• When a composite property is used, the software does not create a smeared, homogeneous shellrepresentation using classical lamination theory. Instead, an integration scheme similar to what isused for solid composites is used.

• Failure index and strength ratio output are supported for all failure indices.

Material support

• The MAT1 and MATT1 bulk entries define isotropic materials for any shell and composite property.

• The MAT2 and MATT2 bulk entries define anisotropic materials for any shell and compositeproperty.

• The MAT8 and MATT8 bulk entries define orthotropic materials for any shell and compositeproperty.

• The MAT9 and MATT9 bulk entries define anisotropic materials for any shell and compositeproperty.

• The MAT11 and MATT11 bulk entries define orthotropic materials for any shell and compositeproperty.

• The nonlinear plastic and creep material are only supported for the PSHELL.

• User defined materials defined with the UMAT external program are only supported for thePSHELL property.

Material coordinate systemThe material coordinate system is used to define the orientation of material properties whenorthotropic or anisotropic materials are selected. In addition, stress and strain results are alwaysoutput in the material coordinate system. The material coordinates are updated when large rotationoccurs.

The X-axis of the material coordinate system for the shell elemen

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