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

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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

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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

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Constraint Optimization restrictions

5

Objective Optimization target

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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

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Example (3/3)

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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

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Node position (Theta=[0°,90°])

Initial design

Loadcase 1 Loadcase 2

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Path for stress distribution

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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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