TOSCA Structure 81 Short Seminar

Simulia Simul ia Tosc Tosc a Struc Structur tur e Getting Ge tting started with sh ape optimization optimization for reliable and and d urable designs

Dr. Claudia BANGERT SIMULIA Senior Portfolio Introduction Specialist

Getti Ge tti ng starte st arted d wit h shape opti mization for r eliable and durable designs

1. Sh Shape ape optim optimiza izati tion on 2. Setup Setup of the the optimiz optimizatio ation n task: task: Model, design area, objective, constraint 3. Me Mesh sh sm smoot oothin hing g 4. Res Restri trictio ctions ns on design design variab variables les 5. De Demo monst nstra rati tion on 6. Dur Durabil ability ity and and nonlinea nonlinearit rities ies 45 minutes

Getti Ge tti ng starte st arted d wit h shape opti mization for r eliable and durable designs

1. Sh Shape ape optim optimiza izati tion on 2. Setup Setup of the the optimiz optimizatio ation n task: task: Model, design area, objective, constraint 3. Me Mesh sh sm smoot oothin hing g 4. Res Restri trictio ctions ns on design design variab variables les 5. De Demo monst nstra rati tion on 6. Dur Durabil ability ity and and nonlinea nonlinearit rities ies 45 minutes

Shape opti mization (1 (1/8 /8))

L1.3

Modification of t he surface of a design design to improve its (dynamic and mechanical) behavior Change a set of design variables (parameters describing the design) such that s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

an objective objective (function (function evaluating the quality of the design) is maximized or minimized and necessary (design) constraints constraints are are satisfied

L1.4

Shape opti mization (2/8)

Design variables

One DV = thickness

Problem s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Two DV = thickness, angle

I n c r e a s i n g

s h a p e

Several DV = variable thi ckness

More design variables  better solution Best design obtained by free (“non-parametric”) modification

f l e x i b i l i t y

L1.5

Shape opti mization (3/8) Parametric approaches Variation of diameters Approaches considering s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Morphing Shape basis vectors Non parametric free form With SIMULIA Tosca Structure Including mesh smoothing

I n c r e a s i n g s h a p e

f l e x i b i l i t y

100%

0%

Shape opti mization (4/8) Non parametric shape optimization Displacement of selected surface nodes

s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

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

L1.6

L1.7

Shape opti mization (5/8) Tosca Structure offers non-parametric structural optimization based on finite element analysis results in any CAE environment


CAD

CAE preprocessing

Optimization with SIMULIA Tosc a Struc tur e

CAE postprocessing

Ab aqu s ANSYS MSC Nastran

Design proposals and design improvements are derived automatically direct modification of the finite element model No parametrization required!

CAD

L1.8

Shape opti mization (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 %

100% 80% 60%

Non-parametric optimization (Tosca): Stress reduction by 30 % New freeform contour approximated by circular segments

40% 20% 0%

Weight Initial design

Max. stress Optimization result Images courtesy of

L1.9


Optimization strategies

Heuristic algorithms Monte Carlo


Genetic algorithms

Mathematical programming Direct methods SQP, MMFD, MFD, … Penalty methods Newton, gradient based, ... Approx im ation m ethods - SLP, SCP, …

Optimality criteria Structural optimization

Fully stressed design Kuhn Tucker Other OC Tosca Structure


L1.10

Mathematical programming + General applicability


+ Convergence speed independent of number of design variables - Convergence speed depends on the type of objective and the number of constraints

An optimized design is determined by an iterative algorithm which changes an initial design using sensitivities

- Effort in numerical implementation Optimality criteria + Convergence speed independent of the number of design variables + Fast convergence + Solution independent of start value - No general approaches (very specific)

Design variables are redesigned so they fulfill the optimality criteria

L1.11

Setup of the opt imization t ask (1/8) 6 Stop Stop condition

5 s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Constraint Optimization restrictions

1 4

Model Definition of analysis model

Objective Optimization target

2 3 Design Area Area for modification with geometric restrictions

Groups Node and element sets for further definitions

L1.12

Setup of the opt imization t ask (2/8) Model for shape optimization

Too coarse

Design space as finite element model Important: s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Realistic models

Too fine

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

Good mesh

L1.13

Setup of the opt imization t ask (3/8) Desig n area Node group of surface nodes (design nodes)

Displaced design nodes Design nodes

Node position can be modified s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

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

Optimization displacement Optimization displacement direction

L1.14

Setup of the opt imization t ask (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

Extract values

Combine load scenarios

Combine areas

COG, inertia Position of nodes Element layout

Restrict

Optimize

L1.15

Setup of the opt imization t ask (5/8) Targets: objective and constraints

Maximum

The objective is maximized or minimized Maximize overall stiffness s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Minimize stresses … Minimum

The constraints are geometrical manufacturing requirements or

Constraint Feasible

Infeasible

design limitations on structural responses from a FE analysis

Active constraint

L1.16

Setup of the opt imization t ask (6/8) Some poss ible objectives

Temp. [ °C] High

Finite element solver: Different stress criteria s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Low

Strain density

Plasticity / Fatigue

Nodal plastic strains (Abaqus, ANSYS) Different strain criteria (Abaqus) Nodal contact pressure (Abaqus) Maximizing the natural frequency

Pin mounted as shrink fit

Fatigue results: Damage Safety

Max. contact pr essure reduced b y 50 %

Setup of the opt imization t ask (7/8)

L1.17

Constraint restricts certain values dependent upon the design variables (design responses) only volume constraint with equality value defined on element groups admitted s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Manufacturing restrictions and other geometric constraints independent of the optimization run can be defined as design variable const raints (later)

Setup of the opt imization t ask (8/8)

L1.18

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

L1.19

Exampl e (1/3)

LC 1 LC 2 s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

LC 2= 2*LC1

LC 1

L1.20

Exampl e (2/3) Shape optimization by homogenization of the stresses

100%

100%

0%

0%

Update rule: s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

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

σ

σref

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

L1.21

Exampl e (3/3) Optimized d esign

Start model


Path for stress distribution

100%

100%

0%

0%

Initial design ) a7 p m 6 ( s5 s e r 4 t S s3 e2 s i M 1 n o0 V 8

Optimized design ) 8 a7 p 6 m (

1

2

3

4

5

6

7

8

9

10 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1

Node posi tion (Theta=[0°,90°])

s5 s4 e r t 3 S s2 e s1 i 0 M n o V

1

2

3

4

5

6

7

8

9

10

11

12

13 1 4 1 5 1 6 1 7 1 8 1 9

Node p ositi on (Theta=[0.90°])

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

L1.22

L1.23

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

Design_nodes

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

Element layers

L1.24

Mesh smoot hing (3/3) FREE_SF Automatic fixation of free surface nodes Free surface nodes are all nodes, that

No transition

are not design nodes s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

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

With transition

Restr icti ons 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 s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

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

L1.25

L1.26

Restr icti ons on design variables (2/5) Displacement restrictions Restricting the absolute optimization displacement amount s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Restricting the displacement direction Variation and restriction areas

my_cs

FIX

Element groups Minimum/Maximum member size

FREE

L1.27

Restr icti ons on design variables (3/5) Coupling restrictions Symmetry


Demolding Stamping Drilling Turning

Part Mold

L1.28

Restr icti ons on design variables (4/5) Design area Without symmetry link


Symmetrical meshing

L1.29

Restr icti ons on design variables (5/5)

With symmetry link Symmetry plane s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Y Z

X

Live demo (1/2) Wind turbine hub model Objective function


Minimize maximum stress within the design area Design and manufacturin g driv en 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

L1.30

Live demo (2/2)


L1.31

Durability and no nlinearities (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 s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Exploit the full optimization potential through realistic models No safety margin required

Nonlinear behaviour and durability aspects need to be considered in the optimization!

L1.32

L1.33

Durability and no nlinearities (2/5) Determination of the equivalent stress for optimization


Static loading

Superimposed von Mises equivalent stress (max – function)

Cyclic loading

Damage distribution after durability analysis

L1.34

Durability and no nlinearities (3/5)

σmax


= 0.7 σ0

d max = 5.6 d 0

Shape opt imization based on static loading

d max = 0.13 d 0

= 100 %

σ0

Shape opti mization based on cyclic loading

If the location of maximum damage and maximum stress are not matching, fatigue life simulation should always be included in the optimization loop.

L1.35

Durability and no nlinearities (4/5) Directly supported durability solvers fe-safe

SIMULIA Tosca Structure

Femfat


Customization required:

Abaqus ANSYS MSC Nastran

ncode Designlife MSC Fatigue LMS Virtual.Lab Durability FE-fatigue FEMSite

Fatigue solver

L1.36

Durability and no nlinearities (5/5)

Ab aqus

ANSYS

MSC Nastran

YES 

YES 

YES 

(including nonlinear responses)

YES 

YES 

Constitutive material laws in design area

ALL 

ALL 

Constitutive material laws outside design area

ALL 

ALL 

Geometrical nonlinearities s e m è t s y S t l u a s s a D © | m o c . s d 3 . w w w

Torque support (rubber material)

YES  Contact

ALL  (no strain responses)

Exhaust manifold (plastic strain)

ALL 

Tooth of gear wheels

TOSCA Structure 81 Short Seminar

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