Copyright © 2011 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
Non-linear response optimization with OptiStruct
Altair Engineering – 2011
Hans Gruber – Business Development Radioss
Copyright © 2011 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
OptiStruct and Nonlinearities…
Plasticity?
Contact
OptiStruct 7.0
Large Sliding?
Complex Material
models like rubber,
foam, ..?
Dynamic behaviour?
Large
Displacement?
Crash?
Copyright © 2011 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
OptiStruct and Nonlinearities…
Plasticity
OptiStruct 11.0
Contact
OptiStruct 7.0
Large Sliding
Complex Material
models like rubber,
foam, ..
OptiStruct 11.0
OptiStruct 11.0
Dynamic behaviour
Large
Displacement
OptiStruct 11.0
OptiStruct 11.0
Crash
OptiStruct 11.0
Copyright © 2011 Altair Engineering, Inc. Proprietary and Confidential. All rights reserved.
Content
Optimization capability overview
Solver integration
Methods for nonlinear response optimization
Examples
Topology Optimization of a gear box cover (contact)
Free shape Optimization connecting rod and a roll structure (geometric nonlinear)
Size/Shape Optimization of a bumper (crash)
Topology Optimization of a bumper (crash)
Topography Optimization of a automotive door (multi body dynamics)
Workflow (including live demo)
Summary
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Introduction - Optimization Disciplines
… with integrated
FEA solver
… generic study tool
for arbitrary solvers,
includes DOE and
Stochastics
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Introduction - Optimization Disciplines
•SIMP (truss)
•Shape Basis Vectors
•Free Size (shear
panel, composite)
(morphing technique)
•Shape Basis Vectors
•Continuous, Discrete
•Beadfraction Response
•PBARL optimization
•Free Shape
OptiStruct only
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Methods for Nonlinear Optimization – 10.0
Nonlinear Contact (geometric linear) OptiStruct
After solving the contact problem optimization is performed on a linear
equation
Sensitivity calculation wrt. design variables
Geometric Nonlinear (implicit and explicit) HyperStudy
Limitations
Long calculation times (many nonlinear function calls, depending on
the number of DV)
Topology-, Freesize, Topograhy and FreeShape Optimization are not
possible
No integrated approach
Advantage
Flexibility
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Solver integration (with optimization)
OptiStruct
RADIOSS
FEA
MBD
Geometric linear
Geometric non-linear
Rigid and flexible
bodies
Linear:
Non-linear:
Implicit:
Explicit:
• Kinematic
Static
Quasi-static
• Quasi-static
• Impact
• Dynamic
Dynamic
Plasticity
• Dynamic
• FSI
• Static
Buckling
Contact
• Post-buckling
• Thermal
• Quasi-static
• Materials
• Materials
• Contact
• Contact
Thermal
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Methods for Nonlinear response optimization
OptiStruct 11.0
Nonlinear Contact (NLSTAT)
After solving the contact problem optimization is performed on a linear
equation
Sensitivity calculation wrt. design variables
Geometric Nonlinear (NLGEOM, IMPDYN, EXPDYN)
Gradients can be very expensive or unavailable
Transferring the nonlinear problem into a series of linear problems is
more efficient (ESLM - Equivalent static load method)
For both methods, existing optimization techniques (for linear
problems) could be used
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Concept of Equivalent Static Load Method
Analysis
Dynamic Problem
Load time history
d
Optimization
Static Problem
Load
Design variables
Equivalent static loads
fteq = Kdt
t
• Originally developed to handle transient events (MBD) in optimization
• Modified for (geometric) nonlinear optimization
• Nonlinear implicit
• Nonlinear explicit
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Concept of Equivalent Static Load Method
• Sequential static response optimization with the equivalent static
loads
• Nonlinear analysis (outer loop), Static optimization (inner loop)
•
fteq = Kdt
will be determined in order to reach the same response
field as nonlinear analysis (including dynamic effects)
• Modified method to perform stress correction
Start
Nonlinear
Analysis
displacement
Calculate equivalent
static loads
Update design
variables
Time Step t0 t1 t2 L
Load set
Solve static response
optimization
No
feq0 feq1 feq2 L
tn time
feqn
Yes
Converged
Stop
Questions so far?
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Examples
Contact, linear Geometry, implicit solution method
Topology Optimization
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Nonlinear Optimization
Contact Analysis
Topology Optimization of a Gearbox Cover
Bolted flange transfers
forces from housing to
gearbox
Flange (Design Space)
Gearbox
Reduce mass of flange
Contact modeled between
housing, flange and
gearbox
Displacement Plot
Force
Bearing housing
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Nonlinear Optimization
Contact Analysis
Topology Optimization of a Gearbox Cover
Design Results:
Contact modeled
with linear spring
elements
Contact modeled
with nonlinear
GAP elements
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Nonlinear Optimization
Contact Analysis
Speedup for nonlinear sub iterations during optimization
•
•
•
•
•
Gap status will be taken as initial conditions for next iteration
Contact is solved in every optimization iteration
Less nonlinear iterations if material distribution doesn’t change much
Example ZF: Topology Optimization of a Gearbox Cover
Reduction of Nonlinear iterations of about 74%
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Examples
Plastic Material, nonlinear Geometry, implicit solution method
FreeShape Optimization
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Free Shape Optimization of a Connecting Rod
• Analysis Type: Geometric Non-Linearity (NLGEOM)
• Material: Johnson-Cook Elastic-Plastic Material
• Loading: Bearing Pressure (causing bending about the Z-axis)
• Problem Formulation:
• Objective Function: Minimize Volume
• Design Constraints: Element Strain ≤ 0.08
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Free Shape Design Variable Grids
• With 1-plane Symmetry Manufacturing Constraint
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Optimization Results – Shape
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Optimization Results – Plastic Strain
Max plastic strain reduction: 0.14 to 0.007
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Roll Structure Optimization
• Analysis Type: Implicit, quasi-static, nonlinear geometry
• Optimization model
Min (mass)
s.t. displacement and stress (based on requirements)
• Shape Change:
• Mass was reduced by > 16%
• 5 outer loops (nonlinear function calls)
© Force India Formula One Team Ltd
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Roll Structure Optimization
• Comparison final shape: nonlinear vs. linear
Displacements differ by 3,4%
Stresses differ by 7% - 15%
• Underestimation of stresses would lead to additional mass
• Additional design cycles are necessary
• One step solution with ESL
© Force India Formula One Team Ltd
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Examples
Dynamic problem, nonlinear Geometry, explicit solution method
Size&Shape Optimization
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Size and Shape Optimization of a Bumper
• Analysis Type: Explicit Dynamics (EXPDYN)
• Analysis Setup:
Moving wall velocity = 2.5 m/s
Rigid wall mass = 1000 Kg
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Size and Shape Optimization of a Bumper
Baseline Design Results
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Optimization Formulation
• Design Variables:
Gauge:
Bumper backing plate: 1.5 ≤ 2.0 ≤ 3.0
Bumper top and bottom sections: 2.0 ≤ 2.5 ≤ 3.5
Shape
Thickness design variables
5 Bumper section shape variables
• Design Constraints:
Maximum allowable mass ≤ 14 Kg
Baseline design mass ~ 12 Kg
• Objective Function:
Shape design variables
Minimize bumper intrusion
Objective function
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Size and Shape Optimization of a Bumper
Optimized Design Results
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Design Comparison
Baseline Design
Optimized Design
Backing plate thickness = 2 mm
Bumper sections = 2.5 mm
Mass = 12 Kg
Intrusion = 100%
Backing plate thickness = 3 mm
Bumper sections = 3.04 mm
Mass = 14 Kg
Intrusion = 87%
Bumper intrusion improved by ~ 13%
10 nonlinear function calls (outer loops)
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Examples
Dynamic problem, nonlinear Geometry, explicit solution method
Topology Optimization
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Topology Optimization of a bumber
• Introduction of rips as topology design space (connected by tied contact)
• Objective is max (d1-d2)
• S.t. m < mtarget
Topology design space inside profile
Deformation due to crash loading
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Topology Optimization of a bumber
Optimization Results
• Objective was improved by 43%
• Mass is unchanged
Density result
Deformation before optimization
Deformation after optimization
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Examples
Multi Body Dynamics
Topography Optimization
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Topography Optimization for Door Slam
Objective Function:
*Geo Metro Model from the NHTSA website
Minimize (Max) Compliance
from the inner panel
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Optimized Bead Pattern
*Geo Metro Model from the NHTSA website
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Max Deflection under Door Slam
~ 19% Displacement Reduction
*Geo Metro Model from the NHTSA website
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Topography Optimization using ESLM
Current Design
Optimized Design
Proposal
Topography Optimization
Results
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RADIOSS - Speed up solutions
Hybrid MPP version
•
•
•
Hybrid version combines the benefit of booth
Radioss parallel versions SMP & SPMD inside
an unique code with enhanced performance.
Hybrid version means high flexibility : adapt to
customer’s needs and hardware their
resources & evolution.
Perfect Repeatability
Multi Domain
•
•
The global model is replaced by physically
equivalent sub domains (no limitations)
Significant reduction of the CPU time with
same accuracy
Nehalem 2.80 GHz Cluster
Neon 1 million elements
Speedups
16 SPMD domains vs # SMP threads
8 ms simulation
6
Advanced Mass Scaling
•
•
New technology based on a modification of the
mass matrix to increase the time step
Applicable to full models
5,08
5
Speedups
3,65
4
3,8
3
2,9
1,95
2
RADIOSS
competitor*
1,88
1
1
11
2
3
4
5
#threads
6
7
8
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Workflow for optimization with ESL
FEM/CAD
Models
• Unchanged workflow (vs. linear optimization)
• Analysis Model setup
• Set up of nonlinear load case(s) using bulk syntax
• Definition of the optimization model (design variables, objective,
constraints)
• ESL parameter
Demo
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Optimization Methods
OptiStruct
RADIOSS
FEA
MBD
Geometric linear
Geometric non-linear
Rigid and flexible
bodies
Linear:
Non-linear:
Implicit:
Explicit:
• Kinematic
Static
Quasi-static
• Quasi-static
• Impact
• Dynamic
Dynamic
Plasticity
• Dynamic
• FSI
• Static
Buckling
Contact
• Post-buckling
• Thermal
• Quasi-static
• Materials
• Materials
• Contact
• Contact
Thermal
Direct sensitivities
ESL
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Summary – Nonlinear response optimization with
OptiStruct
OptiStruct could be applied on a wide range of nonlinear application
All optimization disciplines are supported
ESL is a effective and efficient approach for MBD and nonlinear
response optimization
Various analysis solution methods are possible: quasi static/dynamic implicit or
explicit
Integrated solver and optimization environment
Optimization could performed on multiple load cases (MDO)
Unchanged workflow
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References
1. Altair OptiStruct, Users Manual v11.0, (2011), Altair Engineering inc., Troy MI.
2. Byung Soo Kang,YawKang Shyy, Design of Flexible Bodies in Multibody Dynamic
Systems using Equivalent Static Load Method, American Institute of Aeronautics and
Astronautics
3. David Mylett, Dr. Simon Gardner Force India Formula One Team Ltd., Principal Roll
Structure Design Using Non-Linear Implicit Optimisation in Radioss, 7th Altair CAE
Technology Conference, UK
4. Gruber H.; Schuhmacher, G.;Förtsch, C.; Rieder, E., Optimization assisted structural
design of the rear fuselage of the A400M, a new military transport aircraft, *Altair
Engineering, NAFEMS Seminar: “Optimization in Structural Mechanics”, April 27-28, 2005,
Wiesbaden Germany
5. Hans Gruber, Warren Dias, Dennis Schwerzler, Altair Engineering; Structural Optimization
in Automotive Design, automotive CAE Grand Challenge 2011, 19th – 20th March, 2011
6. Prof. Dr. Lothar Harzheim, Adam Opel AG –ITDC, The Challenge of Shape and Topology
Optimization, automotive CAE Grand Challenge 2011, 19th–20thMarch, 2011
7. Ki-Jong Park and Gyung-Jin Park, Structural Optimization for Non-Linear Behavior Using
Equivalent Static Loads, 16th World Congresses of Structural and Multidisciplinary
Optimization, Rio de Janeiro, 30 May - 03 June 2005, Brazil
8. Uwe Schramm, Optimization Processes for Aerospace Structures, 8th World Congress on,
Structural and Multidisciplinary Optimization, June 1 - 5, 2009, Lisbon, Portugal