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Optistruct Optimization 90 Vol1 Manual

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OptiStruct OptimizationConcept Design and Structural Optimization Volume I

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Trademark and Registered Trademark Acknowledgments Listed below are Altair HyperWorks applications. Copyright Altair Engineering Inc., All Rights Reserved for: HyperMesh 1990-2008; HyperCrash 2001-2008; OptiStruct 1996-2008; RADIOSS 1999-2008; HyperView 1999-2008; HyperView Player 2001-2008; HyperStudy 1999-2008; HyperStudy DSS 2002 2008; HyperGraph 1995-2008; HyperGraph 3D 2005-2008; MotionView 1993-2008; MotionSolve 2002 2008; HyperForm 1998-2008; HyperXtrude 1999-2008; FEModel 2004-2008; Process Manager 20032008; HyperDieDynamics 2007-2008; Templex 1990-2008; Data Manager 2005-2008; MediaView 1999-2008; Batch Mesher 2003-2008; TextView 1996-2008; Manufacturing Solutions 2005-2008.

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HyperWorks 9.0

Table of ContentsConcept Design and Structural Optimization Volume I

OptiStruct Optimization

Chapter 1: Introduction to OptiStruct ................................................................... 1 Chapter 2: Topology Optimization ...................................................................... 15 Chapter 3: Topography Optimization................................................................ 121

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II

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HyperWorks 9.0

Chapter 1: Introduction to OptiStruct

Chapter 1

Introduction to OptiStructWhat is OptiStruct?Altair OptiStruct is a finite element and multi-body dynamics software which can be used to design and optimize structures and mechanical systems. OptiStruct uses the analysis capabilities of RADIOSS and MotionSolve to compute responses for optimization.

Structural Design and OptimizationStructural design tools include topology, topography, and free-size optimization. Sizing, shape and free shape optimization are available for structural optimization. In the formulation of design and optimization problems, the following responses can be applied as the objective or as constraints: compliance, frequency, volume, mass, moment of inertia, center of gravity, displacement, velocity, acceleration, buckling factor, stress, strain, composite failure, force, synthetic response, and external (user defined) functions. Static, inertia relief, nonlinear gap, normal modes, buckling, and frequency response solutions can be included in a multi-disciplinary optimization setup. Topology, topography, size, and shape optimization can be combined in a general problem formulation.

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OptiStruct Optimization 1

Chapter 1: Introduction to OptiStruct

WHAT IS ALTAIR HYPERWORKS?A World Class Suite of CAE Tools

HyperMesh

HyperView HyperWeb HyperView Player

HyperViewPlayer HyperWeb HyperGraph HyperStudy HyperView MotionView OptiStruct MotionSolve HyperForm Altair HyperWorks HyperMeshHyperGraph HyperStudy

HyperForm MotionView Altair Proprietary and Confidential Information MotionSolve

OptiStruct

Copyright 2008 Altair Engineering, Inc. All rights reserved.

What is OptiStruct An Optimizer with a Finite Element and Multi-body dynamics solver integrated Used for the design, analysis and optimization of structures and mechanical systems OptiStruct Structural Optimization solutions: Topology Topography Shape and Size Free Size and Free Shape

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HyperWorks 9.0

Chapter 1: Introduction to OptiStruct

Optimization Definitions: Topology: is a mathematical technique that optimized the material distribution for astructure within a given package space

Free Size: is a mathematical technique that produces an optimized thicknessdistribution per element for a 2D structure.

Topography: Topography optimization is an advanced form of shape optimizationin which a design region for a given part is defined and a pattern of shape variablebased reinforcements within that region is generated using OptiStruct .

Shape: is an automated way to modify the structure shape based on a predefinedshape variables to find the optimal shape.

Size: is an automated way to modify the structure parameters (Thickness, 1Dproperties, material properties, etc) to find the optimal shape.

Free Shape: is an automated way to modify the structure shape based on set ofnodes that can move totally free on the boundary to find the optimal shape.

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Optimization Terminology: Design Variables: System parameters that are varied to optimize system performance. Design Space: selected parts which are designable during optimization process. For example, material in the design space of a topology optimization Response: Measurement of system performance. Objective Function: Any response function of the system to be optimized. The response is a function of the design variables. Ex. Mass, Stress, Displacement, Moment of Inertia, Frequency, Center of Gravity, Buckling factor, and etc. Constraint Functions: Bounds on response functions of the system that need to be satisfied for the design to be acceptable. Feasible Design: One that satisfies all the constraints. Infeasible Design: One that violates one or more constraint functions. Optimum Design: Set of design variables along with the minimized (or maximized) objective function that satisfy all the constraints.Altair Proprietary and Confidential Information Copyright 2008 Altair Engineering, Inc. All rights reserved.

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OptiStruct Optimization 3

Chapter 1: Introduction to OptiStruct

Structural Optimization ConceptsThe Optimization Problem Statement: Objective (What do I want?) min f(x) also min [max f(x)] Design Variables (What can I change?) XiL gj(x) Xi XiU i =1,2,3,N 0 j = 1, 2, 3, , M Design Constraints (What performance targets must be met?)

Note: The functions f(x), gi(x), can be linear, non-linear, implicit or explicit, and are continuous Example: Explicit y(x) = x2 2x Implicit y3 y2x + yx x=0

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Optimization Problem Example A cantilever beam is modeled with 1D beam elements and loaded with force F=2400 N. Width and height of cross-section are optimized to minimize weight such that stresses do not exceed yield. Further the height h should not be larger than twice the width b.

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HyperWorks 9.0

Chapter 1: Introduction to OptiStruct

Optimization Problem Example Objective Weight: min m(b,h)

Design Variables Width: Height: bL < b < bU, hL < h< hU, 20 < b < 40 30 < h < 90

Design Region:

All beam elements

Design Constraints: (b,h) max, with max = 160 MPa (b,h) max, with max = 60 MPah 2*bAltair Proprietary and Confidential Information Copyright 2008 Altair Engineering, Inc. All rights reserved.

Optimization Problem ExampleMathematical Design Space

Beam height, h (mm)

Beam width, b (mm)

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OptiStruct Optimization 5

Chapter 1: Introduction to OptiStruct

Interpreting the Results Objective Did we reach our objective? How much did the objective improve?

Design Variables Values of variables for the improved design

Constrai

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