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© 2011 CAE Associates
Accelerate Your Nonlinear
Analyses for Structural Designs
Peter R. Barrett, P.E.
5/9/2011
2
Outline
Welcome
Efficient Creation and Meshing of Structural Finite Element Models
Advanced Material Modeling
Modeling Stick/Slip Connections
6:00 - 7:00 pm: Food, Refreshments and Networking
Realizing the Value of Multi-Core Computers
Time History Transient Analyses
Automated Design
3
Nicholas M. Veikos, Ph.D., President
Peter R. Barrett, M.S.C.E., P.E., Vice President
Michael Bak, Ph.D., Senior Engineering Manager
George Bauer, M.S.M.E., Engineering Manager
Kenneth W. Brown, Ph.D., Project Manager
Patrick Cunningham, M.S.M.E., Senior Engineering Manager
Steven Hale, M.S.M.E., Senior Engineering Manager
James Kosloski, M.S.M.E., Senior Engineering Manager
Michael Kuron, M.S.M.E., Project Manager
Zoran Dragojlovic , Ph.D., Project Engineer
Eric Stamper, M.S.M.E., Project Manager
Hsin-Hua Tsuei, Ph. D., CFD Manager
Lawrence L. Durocher, Ph.D., Associate
Richard Grant, M.B.A. , Business Development Manager
Christina Capasso, Marketing Coordinator
Tony Solazzo, M.S.Ch.E., Director of Sales
Anna Vincent, Business Manager
CAE Associates Staff Welcomes You!
4
CAE Associates, Inc.
» One of first 4 ANSYS
Channel Partners
Since 1985…
» Engineering Co.
Since 1981
5
CAE Associates, Inc.
CAE Associates, Inc. - Provides World Class services
6
Consulting Specialties
~ Structural Analysis
— Linear and Nonlinear
— Static and Dynamic
— Implicit and Explicit Dynamics
~ Thermal Analysis
— Linear and Nonlinear
— Steady-State and Transient
— Coupled Thermal-Flow
~ CFD
— Aerodynamics analysis, Flowfield analysis
— Turbo machinery, Propulsion
— Chemical reacting flows, Physical models
~ Custom Software Development
7
Software Technical Support
CAE Associates provides hotline support to 125 different companies,
including two of the world's biggest ANSYS users: United Technologies
and General Electric.
AE Firms: Parsons, AECOM, Weidlinger, Severud, Leslie E. Robertson,
Bechtel, AREVA, SGH, Enercon, Straam, Buro Happold
They have chosen us above all others because of our practical, technical
knowledge of both the software and their engineering applications.
We handle upwards of 95% of the questions ourselves with same day
response.
8
Finite Element Training
— CAE Associates is a world leader in
finite element training, providing
exclusive training for industry
leading companies, such as:
• General Electric (Aviation, Energy,
Nuclear, Global R&D)
• United Technologies (Pratt &
Whitney, Research, Sikorsky, Otis
Elevator, Hamilton Sundstrand, and
Carrier)
• U.S. Army Research Labs
• IBM Research Center
• Local AE firms in NY
CAE Associates Training and Mentoring
9
Seminars and Presentations
2010 Seminar: ―Advances in Simulation for the Engineering and
Construction Industry”
2011 Seminar: ―Accelerate Your Nonlinear Analyses for Structural
Designs”
NAFEMS World Congress 2011 - Boston
2012 ?
10
Earthquake Analysis
“Are We Prepared? Assessing Earthquake Risk
Reduction in the United States”
— Chris Poland P.E., S.E., FSEAOC, NAE - Chairman and
CEO of Degenkolb Engineers– April 7, 2011 - Hearing
before the Innovation and Technology Subcommittee of the
House Science, Space, and Technology Committee on
earthquake preparedness.
— NO!
— Need better performance-based earthquake engineering
design tools
— Need to develop the use of state-of-art performance standards
for existing critical structures
11
Seismic induced Collapses
12
Progressive Collapse
SEI Disproportionate Collapse Standards and Guidance (DCSG) Committee meeting in Las Vegas April, 2011 – Meeting Minutes
13
Current Technology can ..
Perform detailed nonlinear time history earthquake simulation
on 3d continuum models
Perform integrated same-time code checking
Reduced solution times using parallel processing
Automate the interpretation and enveloping of time history
results.
Explicitly model a progressive collapse simulation
14
Types of Finite Element Analysis
Structural finite element analysis can include many advanced
types of analysis and features:
— Nonlinear: geometric, material, or element nonlinearities.
— Contact.
— Dynamics: modal, spectrum, harmonic, random vibrations.
— Buckling: linear and nonlinear.
— Submodeling.
— Substructuring.
— Optimization and sensitivity studies.
— Composites.
— Fracture mechanics.
— Probabilistic analysis.
— And combinations of all of the above.
15
What Finite Element Analysis Can Do
To achieve the goal of accurately predicting the behavior of a structure
subjected to loading, the following items must be included in the FEA
model and must closely represent the physical situation:
— Geometry.
— Loading and boundary conditions.
— Nonlinear effects, if required.
— Appropriate element type.
— Material properties, including nonlinear properties if required.
— Accurate mesh.
16
Creation and Meshing of FEA Models
Wizards and Templates
Translation Software
Parametric Scripting
CAD Model Simplification
Simplified Modeling
17
Templates for Automation
Standard and User Defined Sections & Wizards
Tri-cell box section definition
a1
p11
b1
a2
t 22 t 21
t 11
p21p22
s31
1
1
p121
11
t 31
hL
vL
y
z
vCL
hCL
hCU
vCU
t 41
vU vUr
hU hUr
a /20
vCUr
hCUr
hCLr
vCLr
18
Example SAP to ANSYS Model Conversion
SAP2000
ANSYS Modal Analysis
y
z
SAP ANSYS
19
Automated Geometry & Meshing from Scripts
Very Simple Freedom Tower Demo
Scripted Input using Parameters
Example Parameters:
— s_h=1776*12 ! Spire height
— t_h=1368*12 ! Tower height
— width=200*12 ! Width
— b_ht=65*12 ! Base Height
— sp_dia1=25 ! Spire Top Dia.
— sp_dia2=100 ! Spire Base Dia.
Change width to 500’
— One line edit
— Auto generate new model
Parameters can be:
— Geometry, Materials, Loads,
— Mesh, etc.
Optimization can be performed
— Minimize Wt meeting Strength & Displ. Criterion
20
Automated Meshing From Script
21
Interesting Fact: Static Displacement
Maximum displacement located at the perfect octagon shaped floor
22
Shell Elements – Surface Extraction
Extract the surface bodies from the solid.
Mid-plane extraction tool
— Top and bottom surfaces of the shell are paired.
Thin Solid Surfaces
23
Shell Elements – Shell Thickness
Shell element idealization of the thin solid structure as surface bodies.
Mid-plane extraction tool will determine and assign the thicknesses
automatically or the user can define them manually.
T=0.175
T=0.1
T=0.15T=0.125
T=0.175
T=0.2T=0.12
T=0.12
Uniform thicknesses
24
Shell Elements – Variable Thickness
Mid-plane or offset sections are possible
Shell elements with thickness displayed
25
Mid-Surface Tool
―Surface Extension‖ can be used to adjust geometry at the joints between
surface bodies (created after mid-plane operation).
Mid-Surface Tool Surface Extension Tool
26
Solid-Shell Elements
Another option for modeling thin structures is the Solid-Shell approach.
The Solid-Shell element has the following characteristics:
— It has the geometry of an 8-noded brick element.
— It performs like a shell in bending with only one element through the thickness.
— It can be meshed with large aspect ratios
— Contact is automated based on external surfaces
27
Method #1 – Forming Parts
Examples:
— Parts composed of bodies with a common sweep direction can be swept with
solid-shell elements.
Shared nodes in the T connection
28
Method #1 – Forming Parts
Examples:
— T connections on parts composed of shell bodies present no problem for the
quad shell mesher.
Shared nodes in the T connections are visible in the mesh.
29
Method #2 - Bonded Contact
Bonded contact is often the fastest and easiest method for defining part
connections:
— Dissimilar meshes across the interface can be used.
— Element types with different DOF can be connected via contact regions (no
extra consideration of the shell rotational DOF is needed when connecting to
solid elements).
— Contact regions in many cases are created automatically.
30
Method #2 - Bonded Contact
Bonded contact can be automatically generated and used for:
— Solid to Solid connections (including Solid Shells)
— Solid to Shell connections (including Solid Shells)
— Shell to shell connections
Shell edge to
Shell surface
Shell edge to
Solid-Shell
Shell surface to
Solid-Shell
Solid-Shell to
Solid-Shell
31
Meshing Approaches – Example Shells
Shell mesh with offset sections.
All elements connected with shared nodes
Extract mid-plane geometry
Shell mesh (with thickness shown)
32
Meshing Approaches – Example Shells
Shell mesh: constant thickness surfaces assumed.
All elements connected with shared nodes
Extract mid-plane geometry
Shell mesh (with
thickness shown)
33
Meshing Approaches – Example Solid-Shell
Solid-Shell mesh: accounts for variable part thickness.
Bonded contact used to connect adjacent surfaces.
Extract sweepable geometry
Solid-shell
mesh
34
Advanced Material Modeling
Steel Structures
— Plasticity, Creep, Cyclic Loading, Fatigue, Fracture Mechanics, Ratcheting
Concrete Structures
— Cracking, Creep, Construction sequence
Soils
— Pore-Pressure DOF
— Cap Drucker Prager
— Mohr-Coulomb
— Hoek & Brown
— Seepage
— Slope Stability
— Initial Stress
Rubber / Plastics
— Hyperelastic
t
Secondary
Tertiary
Primary
RuptureTftfffcr 4321
35
Steel Plasticity / Fracture Mechanics
Plasticity Models
36
Steel Plasticity / Fracture Mechanics
Fracture Mechanics
— Create both 2-D crack tip and 3-D crack front singular elements.
— Automated commands are available for pre- and post-processing.
— Crack Tip Elements: - The stress intensity factors are automatically computed
from a fit of the nodal displacements in the vicinity of the crack.
— Automated features for performing the J-integral calculation.
37
Concrete Cracking
38
Concrete Material
Advanced Concrete Modeling
39
Concrete Cracking – Static Loading
40
Reinforced Concrete
Types of Body Interactions
— Reinforcement
• Used to apply discrete reinforcement to solid bodies
— Line body elements scoped to the object, contained
within any solid body in the model, are converted to
discrete reinforcement elements / nodes
— Reinforcing beam nodes are constrained to stay at the
same parametric location within the solid element they
reside during element deformation
41
Reinforced Concrete
Types of Body Interactions
— Reinforcement
42
Reinforced Concrete
Plot Damage (User Defined Result)
— The range of DAMAGE will always lie between 0.0 and 1.0.
— DAMAGE = 0.0: material is entirely intact.
— DAMAGE = 1.0: material is completely damaged and cannot carry tension or
shear.
SC
43
Elastomeric Bearing with Lead Plug
44
Elastomeric Bearing Detailed Model
Rubber(Hyperelastic)
Steel (Elastic)
Lead (Elastic Plastic)
45
Elastomeric Bearing Detailed Model
Couple all nodes on
top face
Symmetry
46
Elastomeric Bearing Detailed Model
Lateral Displacement
47
Elastomeric Bearing Detailed Model
Force vs. Displacement @ Top of Bearing
— Increased magnitude of cyclic +/- displacement loops
Stress vs. Displ. in Rubber
48
Elastomeric Bearing Simplified Model
5 Beams (lead) and 5 Solids
(Rubber and Steel)
49
Elastomeric Bearing Simplified Model
Couple Lead to Steel
50
Elastomeric Bearing Simplified Model
Plastic Strain in Lead – Beam Model
51
Elastomeric Bearing Simplified Model
52
Elastomeric Bearing Single Element Model
Single Truss Element
— Bilinear Isotropic Hardening Material Law
53
Elastomeric Bearing Single Element Model
3D model ran in over 5000 sec’s / Single Element model ran in 75 sec’s
54
Detailed-to-Simplified Finite Element Model
55
Modeling Stick / Slip Connections
Contact Elements
— Beam-to-Beam
— Beam-to-Shell
— Shell-to-Shell
— Shell-to-Solid
— Solid-to-Solid
Lateral Resistance
— Friction and Cohesion
Applications
— Expansion Joints
— Soil-Structure Interaction
— Base Isolators
— Roller Bearings
— Bolted Connections
— Post-tensioning tendons
56
Expansion Joints with Sliding Contact Model
Friction coefficient vs velocity
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.00 2.00 4.00 6.00 8.00 10.00
velocity
fric
tio
n c
oef
fici
ent
Friction coefficientvs velocity
3d Modeling Input
— Gap
— Friction
Surface mesh does not have to
match on joining surfaces
57
Local Pin Pullout Model
Description of Assembly:
— Clevis assembly consists of an upper clevis with 2 lugs, a lower clevis with 3
lugs and a cylindrical pin. The geometry and mesh of the clevis assembly is
shown below:
Upper Clevis
Lower Clevis
Pin
58
Problem Description
Kinematic Assessment
— Sequential Loading
• Normal tension to yield pin
• Torque required to rotate pin 180 degrees
• Force required to remove the pin from the assembly
Rotate
Pin
Remove
Pin
59
Problem Setup
The clevis assembly was created in CAD
Parameters were setup in CAD to control the dimensions of each feature
and enable parametric updates to the assembly.
CAD geometry and parameters are linked to FEA allowing for parametric
changes to be made within the FEA environment.
Pass CAD
geometry and
parameters into
FE Analysis
60
Problem Setup
Analysis information is categorized in an outline tree.
The named bodies from CAD are imported along with their associated
parameters.
Contact pairs are automatically detected and created between bodies.
Bodies from CAD
Automatic Contacts
61
Problem Setup
Meshing
— Mesh controls allow for:
• Automatic brick meshing of clevis without any geometry modifications (i.e. slicing).
• Bolt hole surface refinement
• Initial element size
• Higher order elements
Nodes = 25,967
Elements = 5,434
62
Supports
— The bottom surface of the lower clevis is held throughout the analysis with a
Fixed Support.
Problem Setup
Fixed Support
63
Problem Setup
Normal Load
— The upper clevis normal load
was imposed on the model with a
preloaded ―spring‖.
• The spring was used to maintain
the preload in the clevis during
the rotation.
• The spring spans between the
top of the upper clevis surface
and the centerline of the pin.
64
Pin rotation and extraction
— A Remote Displacement boundary condition was applied to the end surface of
the pin, which allowed for a translation and rotational displacement. The
specified values of displacement are input in a table.
Problem Setup
Remote
support
Remote support
values
65
Example Results (6x Displacement Scale)
40,000 lbs normal load
Equivalent Stress Accumulated Plastic Strain
After normal load is released (to 100 lbs)
Equivalent Stress Residual Deformation (vertical)
66
Foundation Sliding
One World Trade Center
— Simple Example
67
Foundation Sliding
Soil – Foundation Interface modeled with contact elements
Static Pressure
All Sticking
68
Foundation Sliding
Contact elements – Seismic Response @ 5.9 seconds
Status Pressure
Sliding
69
1993►1st general-purpose parallel CFD with
interactive client-server user environment
2001 - 2003►Parallel dynamic moving/deforming mesh►Distributed memory particle tracking
A History of HPC Performance
1980
2010
1990► Shared Memory Multiprocessing for structural simulations
1994►Iterative PCG Solver Introduced for large structural
analysis
1999 - 2000►64bit large memory addressing►Shared memory multiprocessing (HFSS 7)
2004►1st company to solve 100M structural
DOF
2007 - 2008► Optimized performance on
multicore processors►1st One Billion cell fluids
simulation
2009►Ideal scaling to 2048 cores (fluids)►Teraflop performance at 512 core
(structures)►Parallel I/O (fluids)►Domain Decomposition introduced
(HFSS 12)
1998-1999►Integration with load management systems►Support for Linux clusters, low latency
interconnects►10M cell fluids simulations, 128 processors
2005 - 2006►Parallel meshing (fluids)►Support for clusters using Windows HPC
© 2008 ANSYS, Inc. All rights reserved.
ANSYS, Inc. Proprietary
1980’s► Vector Processing on Mainframes
1994 - 1995►Parallel dynamic mesh refinement and
coarsening►Dynamic load balancing
2005 -2007►Distributed sparse solver►Distributed PCG solver►Variational Technology►DANSYS released►Distributed Solve (DSO) HFSS 10
2000
1990
70
Product Design Challenges
71
FEA Benchmark Problem
Bolted Flange with O-Ring
Nonlinear material properties
(Hyperelastic O-Ring)
Large Deformation
Nonlinear Contact
1 Million Degrees of Freedom
72
High End Desktop Workstation
SuperMicro 4U Tower Black SATA 5.25
Bays 8 Hotswap EATX3 800W RPS
Dual Hex Core (12 cores total)
— Intel® XEON 5650 2.66GHz Processors
24 GB RAM
— (4) 6GB (3 x 2GB) – 1333MHz
DDR3/PC3-10600 – Non-ECC – DDR3
SDRAM – 240-Pin DIMM
Four 300GB Toshiba SAS 15,000 RPM
16MB 3.5IN drives in RAID 0.
One 500GB SATA Hard Drive for the
Operating System
Nvidia Quadro FX 1800 Video Card
LG DVD/RW
73
FEA Benchmark Performance
0
1
2
3
4
5
6
7
0 2 4 6 8 10 12 14
Solv
er
Spe
ed
Up
# Cores
Single Machine - SMP vs. MPP DSPARSE
SPARSE
DSPARSE
Example: 1.5 hrs vs. 9 hr single processor solution
74
GPU Computing
GPUs are an attached accelerator to an x86 CPU
— GPUs cannot operate without an x86 CPU present
— Attached via PCI Express Slots
Use of GPU acceleration is user-transparent
— Jobs launch and complete with no additional user steps
Schematic of a CPU with an attached GPU accelerator
— CPU begins/ends job, GPU manages heavy computations
Schematic of an x86 CPU with a GPU accelerator
- FEA job will launch on CPU
- During solver phase FP ops are
sent to GPU for processing
- GPU sends results back to CPU
-FEA job completes as normal
75
FEA Speedup with GPU Workstation
0
100
200
300
400
500
600
700
800
900
4-Core 4-Core w/GPU 6-Core 6-Core w/GPU 8-Core 8-Core w/GPU
830
690
593
426411 390
FE
A T
ime
s in
Se
co
nd
s
Number of Cores and Tesla GPU
Xeon 5560 2.8 GHz Nehalem (Dual Socket) Xeon 5560 2.8 GHz Nehalem + Tesla C2050
Lower
Is
Better
49%
34%40%
76
Large Scale Time History Results in a Day!
Compute Times on a Desktop Workstation
— 340,372 DOF & 6400 Cumulative Iterations
— 1.8x speed improvement with GPU and more processors
CPU Time 182 Hours 209 hours
Wall Clock 27.8 Hours 51 hours
GPU Accelerated
12 cores
No GPU -
7 cores
Share
Memory
77
Dynamics Analysis
The more general form of equilibrium, referred to as dynamic equilibrium, can be expressed using the following equations:
These equations are time-dependent and represent the case where all structural forces are included to satisfy equilibrium. In this case, the applied loads are balanced by a combination of the inertia, damping, and elastic forces.
)(tuM
)(tuC
Inertial Forces
Damping Forces
tFtuKtuCtuM )()()(
78
Dynamic Analysis Methods
Modal Analysis
— Pre-Stressed with linear perturbation
— Response Spectrum
— Random Vibrations
Harmonic Analysis
— Full and Mode Superposition
Rigid Body Dynamics
— Fixed, Revolute, Cylindrical, Translational, Universal, Spherical, Bushing Joints
Nonlinear Implicit Dynamics
— Time Domain, nonlinear geometry , nonlinear materials, contact
Nonlinear Explicit Dynamics
— Wave propagation, shock, impact, very large strains, plasticity, hyperelasticity,
material failure etc.
Fluid-Structure Interaction
— CFD – FEA or Explicit Dynamics
79
Solvable Dynamics Problems
Modal (natural frequencies and mode shapes).
— Prestressed structures.
— Spectrum loadings.
Harmonic or frequency response.
— General loading conditions.
— Prestressed structures.
Transient dynamics.
— General loading conditions.
— Material nonlinearities.
— Geometric nonlinearities.
80
Case Study
Example Concrete Arch Bridge Analysis
— Nonlinear Implicit Dynamics
— Detailed Analysis Sequence
— Example Analysis Results
— Example Design Evaluation
— Benchmark HPC Computing
81
Brick / Shell / Beam Model
Brick
Shell
Beam
82
Boundary Conditions
Initially fixed large lumped mass
Base of bridge / piles couples to large mass
Gravity acceleration for static loading
Acceleration loads for earthquake applied to lumped
mass
83
Analysis Sequence
Fix lumped ―earth‖ mass in all directions
Apply gravity and initial conditions with time integration
turned off
Run two load steps to create zero velocity response
Turn on time integration effects
Convert fixed constraint to force loading by deleting
constraint and applying equal and opposite reaction
force loads
Apply acceleration history to large mass
84
Combined Damping
Contact Elements with Friction
Elastomeric Bearings
Mass Proportional (alpha)
Stiffness Proportional (Beta)
Numerical (Newmark or HHT for example)
85
Detailed Analysis Sequence
Earthquake Time History Input Motion
— Solution at each time point
-3.00E-01
-2.00E-01
-1.00E-01
0.00E+00
1.00E-01
2.00E-01
3.00E-01
4.00E-01
0 2 4 6 8 10 12 14 16 18 20
Acc
lera
tio
n (g
's)
Time (seconds)
20 Second Earthquake Input of the 1940 Imperial Valley Earthquake
El Centro 1940 North - South Record
86
Example Displacement Response
87
Displacement Response History
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.00E+00 2.00E+00 4.00E+00 6.00E+00 8.00E+00 1.00E+01 1.20E+01 1.40E+01 1.60E+01 1.80E+01 2.00E+01
Dis
pla
cem
en
t (m
ete
rs)
Earthquake Time History (Seconds)
Bridge seismic displacment at deck center and abutment
Deck center - vertical
Deck center - along span
Deck center - transverse to span
Abutment - vertical
Abutment - along span
Abutment - transverse to span
88
What Information is Obtained?
Displacements, reactions, strains, stresses.
Maximum values, distribution over entire model.
Contour plots, path plots, vector plots.
Animations.
89
For Beams – Ex. Column Bending Moments
90
How do we deal with all this data?
Example: Brick Model Seismic analysis with 100,000 nodes and 1000 time
points
Displacements = 300,000,000 unique values
Component Stresses & Invariants = 900,000,000 unique values
Nodal Forces = 300,000,000 unique values at each node. No moments or
total section forces.
What do we do with this data?
How can we possibly efficiently use this data in design?
91
Existing Tools & Design Specs
Calculation Sheets
Spreadsheets
Experimental Data
None of these methods leverage detailed analysis data!
92
AASHTO Guide for Seismic Design
Analytical Methods
— Equivalent Static Analysis
— Elastic Dynamic Analysis
— Nonlinear Time History Method
Use the NL Time History Method When…
— Seismic isolation is present
— Comprehensive analysis method to consider inelastic behavior
— Structures with long periods or large damping ratios (effective
stiffness/damping inadequate)
93
Leveraging Advanced FE Models in Design
Envelope Results
— Perform Code Checks
• Check the section
• Check the amount of reinforcement
• Check buckling requirements, etc.
— Perform Design
• Compute amount of reinforcement required
Smart Combinations
— Scale factors on live on dead loads
Design of Experiments
— Develop design sensitivities
Design Optimization
— Example: Minimize weight while meeting design functions
Local Submodeling
— Example: Local plate buckling evaluation
94
Pseudo Shells for Design
n+1 n+1yi yi-1xi xi-1
x x i-1 y i-1d
i =2 i =2
N = dt d N = d 2 2
Automate the process of converting stresses to member forces and moments
95
Solid to Shell Data Mapping
Convert 3D solid element results to shells
Integrates the stresses of prismatic sections and convert them into
forces and moments.
Converts 3D solid elements assuming a laminar structure into the
forces and moments needed to evaluate a code or standard
96
Solid to Shell Data Mapping
Required input data: element and node components (no geometry
required)
97
Solid to Shell Data Mapping
Nodes are used as a basis to create surface elements
Surface elements will be transformed into shell elements at centerline of
the section
98
Solid to Shell Data Mapping
Illustrated nodes and shell elements generated from updated surface with
element shape turned on to illustrate shell thickness.
99
1 xy xz
G
i yx 2 yz
zx zy 3
= i = 1, Npts E T E
i i = C C
n+1 n+1yi yi-1xi xi-1
x x i-1 y i-1d
i =2 i =2
N = dt d N = d 2 2
n+1 n+1yi i yi-1 i-1xi i xi-1 i-1
x x i-1 y i-1d
i =2 i =2
ξ ξ ξ ξM = . dt = d M = d
2 2
n+1 n+1zyi zy i-1zxi zx i-1
zx zx i-1 zy i-1d
i =2 i =2
τ ττ τT = τ dt d T d
2 2
n+1xyi xy i-1
xy xy i-1d
i =2
τ τN = τ dt d
2
n+1 n+1
xyi i xy i-1 i-1zxi i zx i-1 i-1xy zx i-1 zx i-1
di =2 i =2
τ ξ τ ξτ ξ τ ξM = τ ξ dt d M = d
2 2
Solid to Shell Data Mapping
Methodology - Theory
100
Solid to Shell Data Mapping
Also valid for tetrahedral elements
101
Solid to Shell Data Mapping
Solution Results and Design Results
102
Steel Area Requirements
103
Code Checking / Design Options
— Code checking• Checks the structure with initial amount
of reinforcement and shows the safety factor of each element.
— Code design• Checks the structure and multiplies the
scalable reinforcement until obtaining a safety factor (1/criterion) as closer as possible to 1.00.
104
Code Checking Capabilities
Steel Reinforce Concrete Seismic
Pre-Stress Concrete
105
Solid to Shell Data Mapping
Postprocessing & Code Checking
— ACI 349 & ACI 359
— Wood Armer
— CEB-FIP method
— Orthogonal Directions method
— Most Unfavorable Direction method
106
Solid to Shell Data Mapping
Post-processing Tools
107
Concrete Interaction Diagram
108
Load Combinations
The most critical condition may occur when one or more loads are not
acting.
Example load combinations and the corresponding load factors can be
investigated:
109
Design of Experiments
A Design of Experiments, or DOE, method determines how many and
which design points should be solved for the most efficient approach to
optimization
110
Design Optimization
Do you want to:
— Minimize your Structures weight?
— Maximize column stiffness?
— Maximize girder spacing?
Design Optimization performs these tasks using:
111
Submodel Calculation
ARCH-TIE CONNECTION NODE:
112
Submodel Calculation
DIAPHRAGMS ON TIE CONNECTION:
113
Summary
Better performance-based nonlinear engineering design analysis
tools exist today!
More robust solutions include 3d continuum models with material,
geometric and contact nonlinearities
Code checking can be integrated into a high fidelity analysis process
Leveraging multi-processors and graphics accelerator cards results
in faster throughput