© 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.

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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 ?

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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

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Seismic induced Collapses

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Progressive Collapse

SEI Disproportionate Collapse Standards and Guidance (DCSG) Committee meeting in Las Vegas April, 2011 – Meeting Minutes

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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

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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

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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

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Automated Meshing From Script

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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

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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

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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.

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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)

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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)

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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

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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

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Steel Plasticity / Fracture Mechanics

Plasticity Models

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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.

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Concrete Cracking

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Concrete Material

Advanced Concrete Modeling

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Concrete Cracking – Static Loading

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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

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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

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Elastomeric Bearing Detailed Model

Rubber(Hyperelastic)

Steel (Elastic)

Lead (Elastic Plastic)

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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

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Elastomeric Bearing Simplified Model

Plastic Strain in Lead – Beam Model

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Elastomeric Bearing Simplified Model

52

Elastomeric Bearing Single Element Model

Single Truss Element

— Bilinear Isotropic Hardening Material Law

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Elastomeric Bearing Single Element Model

3D model ran in over 5000 sec’s / Single Element model ran in 75 sec’s

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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

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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