tosca structure 81 short seminar
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Simulia Tosca Structure Getting started with shape optimization
for reliable and durable designs
Dr. Claudia BANGERT SIMULIA Senior Portfolio Introduction Specialist
1. Shape optimization
2. Setup of the optimization task:
Model, design area, objective, constraint
3. Mesh smoothing
4. Restrictions on design variables
5. Demonstration
6. Durability and nonlinearities
Getting started with shape optimization for reliable and durable designs
45 minutes
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Shape optimization (1/8)
Modification of the surface of a design to improve its (dynamic and mechanical) behavior Change
a set of design variables (parameters describing the design) such that an objective (function evaluating the quality of the design) is maximized or minimized and necessary (design) constraints are satisfied
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Shape optimization (2/8)
Design variables
Problem
One DV = thickness
Two DV = thickness, angle
Several DV = variable thickness
Increasing shape flexibility
More design variables better solution Best design obtained by free (“non-parametric”) modification
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Shape optimization (3/8)
Parametric approaches Variation of diameters
Approaches considering
Morphing Shape basis vectors
Non parametric free form With SIMULIA Tosca Structure Including mesh smoothing
Increasing shape flexibility
100%
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Shape optimization (4/8)
Non parametric shape optimization Displacement of selected surface nodes Determination of the optimum contour of a component Consideration of all given boundary conditions
Motivation:
Easy setup (no parameterization required) Flexible result (maximum degree of freedom) Local stress reduction and durability increase
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Shape optimization (5/8)
Tosca Structure offers non-parametric structural optimization based on finite element analysis results in any CAE environment
Design proposals and design improvements are derived automatically
direct modification of the finite element model
No parametrization required!
Optimization with SIMULIA Tosca Structure
Abaqus ANSYS
MSC Nastran
CAE preprocessing
CAE postprocessing CAD CAD
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Shape optimization (6/8)
Example: Stabilizer bar link Problem
Stiffness requirements no longer fulfilled (changes to the front axle) Stress reduction of 25 % required!
Solution Parameter optimization (radius): Stress reduction only by 18 % Non-parametric optimization (Tosca): Stress reduction by 30 % New freeform contour approximated by circular segments
0%
20%
40%
60%
80%
100%
Weight Max. stressInitial design Optimization result
Images courtesy of
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Shape optimization (7/8)
Heuristic algorithms
Monte Carlo Genetic algorithms
Structural optimization
Optimality criteria
Fully stressed design
Kuhn Tucker
Other OC Tosca Structure
Mathematical programming
Direct methods SQP, MMFD, MFD, …
Penalty methods Newton, gradient based, ...
Approximation methods - SLP, SCP, …
Optimization strategies
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Shape optimization (8/8)
+ General applicability + Convergence speed independent of
number of design variables - Convergence speed depends on the type
of objective and the number of constraints - Effort in numerical implementation
+ Convergence speed independent of the number of design variables
+ Fast convergence + Solution independent of start value - No general approaches (very specific)
Mathematical programming
Optimality criteria
An optimized design is determined by an iterative algorithm which changes an initial design using sensitivities
Design variables are redesigned so they fulfill the optimality criteria
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Setup of the optimization task (1/8)
Model Definition of analysis model
1
Groups Node and element sets for further definitions
2
Design Area Area for modification with geometric restrictions
3
Stop Stop condition
6
Constraint Optimization restrictions
5
Objective Optimization target
4
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Good mesh
Setup of the optimization task (2/8)
Model for shape optimization Design space as finite element model Important:
Realistic models geometric details exact boundary conditions relevant load scenarios exact material models (e.g. non linear)
Mesh quality Not too fine, not too coarse
Quadratic vs linear elements
Too coarse
Too fine
Model Constraint Objective Stop Design Area Groups
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Setup of the optimization task (3/8)
Design area
Node group of surface nodes (design nodes) Node position can be modified Optimization displacement is calculated during optimization
Design variables are the displacement values of the design nodes
Positive: node “grows” out of the structure Negative: node “shrinks” into the structure
Model Constraint Objective Stop Design Area Groups
Optimization displacement
direction
Design nodes
Displaced design nodes
Optimization displacement
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Setup of the optimization task (4/8)
Input for the optimization: design responses Finite element analysis
Stiffness, stresses, eigenfrequencies, displacements, etc. For given load scenarios For given areas in the model
Model geometry
Weight, volume COG, inertia Position of nodes Element layout
Combine areas
Combine load scenarios
Extract values
Restrict Optimize
Model Constraint Objective Stop Design Area Groups
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Setup of the optimization task (5/8)
Targets: objective and constraints The objective is maximized or minimized
Maximize overall stiffness Minimize stresses …
The constraints are
geometrical manufacturing requirements or design limitations on structural responses from a FE analysis
Minimum
Maximum
Feasible Infeasible
Active constraint
Constraint
Model Constraint Objective Stop Design Area Groups
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Setup of the optimization task (6/8)
Some possible objectives Finite element solver:
Different stress criteria Strain density Nodal plastic strains (Abaqus, ANSYS) Different strain criteria (Abaqus) Nodal contact pressure (Abaqus) Maximizing the natural frequency
Fatigue results:
Damage Safety
Temp. [°C] High
Low
Plasticity / Fatigue
Max. contact pressure reduced by 50 %
Pin mounted as shrink fit
Model Constraint Objective Stop Design Area Groups
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Setup of the optimization task (7/8)
Constraint
restricts certain values dependent upon the design variables (design responses) only volume constraint with equality value defined on element groups admitted
Manufacturing restrictions and other geometric constraints independent of the optimization run can be defined as design variable constraints (later)
Model Constraint Objective Stop Design Area Groups
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Setup of the optimization task (8/8)
Global stop criterion Number of iterations Standard tasks 5-10
Local stop criterion
Change in certain variables, e.g. change of optimization displacement is smaller than 1% of previous iteration (see manual) not required, just resume your optimization with some more iterations
Model Constraint Objective Stop Design Area Groups
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Example (1/3)
LC 1
LC 2= 2*LC1
LC 2
LC 1
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Example (2/3)
Shape optimization by homogenization of the stresses
Update rule: Node stress > reference value → Growth in order to reduce stress Node stress < reference value → Shrinkage in order to increase stress Result: homogeneous stress distribution to the level of the reference value
Reference value is normally mean stress in design area Homogeneous stress distribution results in a minimization of the stresses in the design area.
Growth Shrinkage s
σ
σref
100%
0%
100%
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Example (3/3)
0
1
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Von
Mis
es S
tres
s (m
pa)
Node position (Theta=[0°,90°])
Initial design
Loadcase 1 Loadcase 2
100%
0%
Path for stress distribution
100%
0%
0
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Von
Mis
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tres
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pa)
Node position (Theta=[0.90°])
Optimized design
Loadcase 1 Loadcase 2
Start model Optimized design
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Mesh smoothing (1/3)
Displacement of the surface nodes due to the local stresses Strongly distorted elements on the surface layer Quality of the finite element analysis is affected
Smoothing of the mesh of the internal structure (MESH_SMOOTH)
the optimization displacement is passed to the inner nodes Performed on an user defined element group (mesh smooth area) All design nodes must be at surface of mesh smooth area Element qualities are considered during mesh smoothing
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Mesh smoothing (2/3)
Layer Automatic definition of the mesh smooth area Starting on a surface node group All elements in the defined number of element layers are grouped The MESH_SMOOTH area should contain at least 4-6 element layers.
The mesh smooth element group should be as large as necessary but as small as possible to guarantee:
The best possible mesh quality The lowest possible calculation time
Design_nodes
Element layers
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Mesh smoothing (3/3)
FREE_SF Automatic fixation of free surface nodes Free surface nodes are all nodes, that
are not design nodes are not fixed due to another restriction (DVCON_SHAPE)
The number of transition nodes that are used for mesh adaption has to be defined
Transition nodes Design nodes
No transition
With transition
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Restrictions on design variables (1/5)
Non parametric shape optimization generates freeform surfaces
processing in CAD systems may take some time complex surfaces are not always producible external constraints often require additional restrictions
Restrict the movement of nodes to
avoid the change of border areas to other components ensure the ability to manufacture the component control the design and look of the part
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Restrictions on design variables (2/5)
Displacement restrictions
Restricting the absolute optimization displacement amount
Restricting the displacement direction
Variation and restriction areas
Element groups
Minimum/Maximum member size
FIX FREE
my_cs
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Restrictions on design variables (3/5)
Coupling restrictions
Symmetry Demolding Stamping Drilling Turning
Part
Mold
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Design area
Symmetrical meshing
Restrictions on design variables (4/5)
Without symmetry link
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Restrictions on design variables (5/5)
Y
Z X
Symmetry plane
With symmetry link
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Live demo (1/2)
Wind turbine hub model Objective function
Minimize maximum stress within the design area
Design and manufacturing driven constraints:
Cyclic symmetry constraint (120° degree) Frozen area constraint (Exclusion of certain nodes from the design area)
Tosca Structure wind hub example is provided with each Tosca Structure installation
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Live demo (2/2)
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Durability and nonlinearities (1/5)
Shape optimization improves already existing designs:
Quality of optimization result depends on quality of analysis model Avoid time-consuming and error-prone linearization Exploit the full optimization potential through realistic models No safety margin required
Nonlinear behaviour and durability aspects need to be considered in the optimization!
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Durability and nonlinearities (2/5)
Static loading Superimposed von Mises equivalent stress (max – function)
Cyclic loading Damage distribution after durability analysis
Determination of the equivalent stress for optimization
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Durability and nonlinearities (3/5)
σ0 = 100 %
Shape optimization based on cyclic loading
Shape optimization based on static loading
σmax = 0.7 σ0
dmax = 0.13 d0
dmax = 5.6 d0
If the location of maximum damage and maximum stress are not matching, fatigue life simulation should always be included in the optimization loop.
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SIMULIA Tosca Structure
Abaqus ANSYS
MSC Nastran
Durability and nonlinearities (4/5)
Directly supported durability solvers fe-safe Femfat
Customization required: ncode Designlife MSC Fatigue LMS Virtual.Lab Durability FE-fatigue FEMSite
SIMULIA Tosca Structure
Abaqus ANSYS
MSC Nastran
Fatigue solver
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Durability and nonlinearities (5/5)
Abaqus ANSYS MSC Nastran
Geometrical nonlinearities YES YES YES
Contact YES
(including nonlinear responses)
YES YES
Constitutive material laws in design area ALL ALL ALL
(no strain responses)
Constitutive material laws outside design
area ALL ALL ALL
Tooth of gear wheels (contact, material)
Exhaust manifold (plastic strain)
Torque support (rubber material)
Thank you!
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Recording will be available in the Simulia Learning Community
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