generative design with autodesk nastran topology optimization

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Generative Design with Autodesk Nastran Topology Optimization

Michael SmellProduct Manager, Simulation, [email protected]

David Weinberg Senior Software Architect, PDG-Digital Manufacturing [email protected]

© 2014 Autodesk

This class will introduce the basics of topology optimization in Autodesk Nastran and demonstrate some of the advanced features that empower designers to create better designs and modify existing ones, making them lighter and more efficient

This session features Autodesk Nastran and Fusion 360 Ultimate

Class Summary

© 2014 Autodesk

At the end of this class, you will be able to: Understand the basics of topology optimization in Autodesk

Nastran Learn how to modify an existing design to remove

unnecessary material and make it more efficient Understand the limitations of topology optimization Understand the workflow in setting up and performing a

topology optimization

Key Learning Objectives

© 2014 Autodesk

Nastran Topology Optimization Basic Theory

Autodesk Confidential© 2016 Autodesk

Shape optimization: Maintain the topology, change dimensions

Topology optimization: Determine layouts

Method with Finite Element Analysis Initial method…truss

Change member area and remove when area goes to zero

Discrete variables, predetermined nodal locations

Topology Optimization

?Shape Optimization Topology Optimization

? ?

?


For fixed mesh, determine density (xe) of each element

Structural volume

Element stiffness

SIMP = Solid Isotropic Material Penalization(Not limited to isotropic materials)

Exponent p: Reduce grey area, force zero or one

Typically, p = 3

Topology Optimization with Finite Element Analysis

xe = 0: voidxe = 1: material

Design variable

NE

e 0e 1

V( ) x v

x v0: volume of an element

pe e 0[ ] (x ) [ ]k k

1 xe

k0


Determination of optimal principal material distribution for a given problem

A powerful tool for concept design stage

Topology Optimization with Finite Element Analysis

Uniform (uneducated) initial guess Conventional (low-weight) design

Design Evolutionmaterial may be

added or removed from any location

0.6

0.7

0.8

0.9

1

1.1

1.2

0 10 20 30 40 50

Nor

mal

ized

Com

plia

nce

Iteration Number

Optimization History Plot

50% mass reduction 22% increase in stiffness


Objective – The goal of the design analysis

Design Constraint – Specific limits on results such as displacement at point, temperature, stress, etc.

Manufacturing Constraint – Specifies how a design region will be manufactured such as extruded along and axis or symmetric about a plane

Compliance – The inverse of stiffness

Volume Fraction – The ratio of full volume to reduced volume (effectively the same as mass fraction when density is constant in a design region)

Design Sensitivity - The gradient (change) of the objective (or constraint) with respect to the design variable (element density)

Definitions


Optimization algorithm searches for local minimum…global minimum is not guaranteed

Starting with different initial volume fractions and different mesh densities will result in different designs

Global Versus Local Minimum

Globaloptimum solution

Design

Objective Local optimum

Global optimum


Gradient-based MethodsWe do not know the function before optimizationWe can only evaluate the function and gradient at a given design

Optimum solution

Design

Objective

Start

MoveGradient

CheckGradient = 0

Stop

(Sensitivity)


How Constraints Play in Optimization?

Optimum solution

Design

Objective

Start

Move

Constraintviolated

Constraintsatisfied

Most cases, constraints determine optimal design

Single constraint example

Design 1

Design 2

Constraintviolated

Constraintviolated

Objectivedecreased

Constraint 1 = 0

Constraint 2 = 0

Optimum solution

Two constraints example


Topology Optimization Applications

Fixed leading edge wing ribs designs

White Magnolia Plaza Frame design(Skidmore Owings & Merrill)

Automotive door panel bead design

Automotive wheel design


Topology optimization results CAD model Requires expert’s opinion to interpret optimum results

Challenge is systematic translator to CAD model

Lengthy process requiring most of the engineer’s time

Technical Challenges and Bottlenecks

Topology optimization results

Beam model for sizing optimization FINAL SEAT

Inte

rpre

tatio

n

Re-m

odel

ing


Nastran Topology Optimization Specifics

Autodesk Confidential© 2016 Autodesk CONFIDENTIAL

Objective Min/Max/EitherMultiple Load

CasesSolution Sequence

Compliance Min Yes LS

Compliance Index Min Yes LS

Max Displacement Component in Model Min No LS

Specific Grid Point Displacement Component Min No LS

Max Constraint Force Component in Model Min No LS

Specific Constraint Force Component Min No LS

Stress of a Specific TOPVAR Region Min No LS

Stress of all TOPVAR Regions Min No LS

Volume Fraction (Mass Fraction) of a specific TOPVAR Region Min Yes LS

Volume Fraction (Mass Fraction) of all TOPVAR Regions Min Yes LS

Thermal Energy of a Specific TOPVAR Region (Compliance) Min Yes LSSHT

Thermal Energy of all TOPVAR Regions (Compliance) Min Yes LSSHT

Average Temperature of a Specific Set of Nodes Either No LSSHT

Delta Temperature of a Specific Set of Nodes Either No LSSHT

Global Temperature of a Specific Set of Nodes Either No LSSHT

Normal Modes Frequency Max No NMNormal Modes Eigenvalue Max No NMBuckling Modes Eigenvalue (load factor) Max No LB

Nastran Topology Optimization Objectives

LS = Linear Statics, LSSHT = Linear Steady-State Heat Transfer, NM= Normal Modes, LB = Linear Buckling


Design Constraints RangeMultiple Load

CasesIndividual

Load CasesSolution Sequence

Compliance Range Yes Yes LS

Compliance Index Range Yes Yes LS

Max Displacement Component in Model Range Yes Yes LS

Specific Grid Point Displacement Component Range Yes Yes LS

Max Constraint Force Component in Model Range Yes Yes LS

Specific Constraint Force Component Range Yes Yes LS

Stress of a Specific TOPVAR Region < Upper Yes Yes LS

Stress of all TOPVAR Regions < Upper Yes Yes LS

Volume Fraction (Mass Fraction) of a specific TOPVAR Region < Upper Yes Yes LS

Volume Fraction (Mass Fraction) of all TOPVAR Regions < Upper Yes Yes LS

Thermal Energy of a Specific TOPVAR Region Range Yes Yes LSSHT

Thermal Energy of all TOPVAR Regions Range Yes Yes LSSHT

Average Temperature of a Specific Set of Nodes Range Yes Yes LSSHT

Delta Temperature of a Specific Set of Nodes Range Yes Yes LSSHT

Global Temperature of a Specific Set of Nodes Range Yes Yes LSSHT

Normal Modes Frequency Range No No NM

Normal Modes Eigenvalue Range No No NM

Buckling Modes Eigenvalue (load factor) Range No No LB

Nastran Topology Optimization Design Constraints

LS = Linear Statics, LSSHT = Linear Steady-State Heat Transfer, NM= Normal Modes, LB = Linear Buckling


Manufacturing ConstraintsCombinable

With

Non-Design Regions All

Symmetry All

Minimum Member Size All

Design for Extrusion Symmetry

Nastran Topology Optimization Manufacturing Constraints


Minimum Member Size Manufacturing Constraint

• Fixed at one end and edge loaded at the other end• Objective is minimize compliance (maximize stiffness)• Constraint is fixed volume fraction of 0.2 (reduce volume to

20% of its original)• Manufacturing constraints: minimum member size (prevents

non-designable feature generation)

Incr

easi

ng M

esh

Den

sity


Effect of Mesh Density and Volume Fraction Constraint

Mesh: 100x60 VF = 0.3 VF = 0.5 VF = 0.8

Mesh: 200x120 VF = 0.3 VF = 0.5 VF = 0.8

Mesh: 400x240 VF = 0.3 VF = 0.5 VF = 0.8

Objective: minimize compliance, Constraint: Volume fraction (VF)


Extrude and Symmetry Manufacturing Constraints

• Fixed at one end and symmetrically point loaded at the other end with 2 separate load cases

• Global max displacement design constraint limited to 0.3 in the direction of load in each load case

• Objective is minimize mass/volume• Manufacturing constraints: extrusion, symmetry,

symmetry + extrusion

Extrude Only

Extrude+Symmetry

Symmetry OnlyDesign Region

Non-Design Region


Examples an Objective and Constraints Objective Design Constraint(s) Manufacturing Constraint(s) Solution Type

Minimize mass • Max displacement in a direction below• Stress below• Reaction force at a constraint below

• Symmetry• Min member size

Linear Statics

Minimize mass • Compliance index below• Stress below

• Symmetry,• Extrudable

Linear Statics

Minimize compliance • Mass/volume fraction below• Stress below

• Extrudable,• Minimum member size

Linear Statics

Maximize frequency • Mass/volume fraction below • Minimum member size Normal modes

Minimize mass • Frequency above • Symmetry• Minimum member size

Normal modes

Maximize buckling load factor • Mass/volume fraction below • Minimum member size Normal modes

Minimize mass • Buckling load factor above • Symmetry• Minimum member size

Normal modes

Minimize temperature at a point • Mass/volume fraction below • Symmetry• Minimum member size

Linear Steady-State Heat

Maximize global temperature • Mass/volume fraction below • None Linear Steady-State Heat

Minimize mass • Maximize global temperature above • Symmetry• Extrudable

Linear Steady-State Heat

Autodesk Confidential

Traditional: Optimization engine calls FEA (inefficient)

FEA-controlled: FEA calls optimization engine (efficient)• Allows pre-calculation of all information required in optimization

• Repeated operations can be scaled or skipped entirely

Topology Optimization Framework

Optimization Engine

Finite Element Analysis

DesignVariables Responses

Traditional Framework

Optimization Engine

Finite Element Analysis

DesignVariablesResponses

FEA-based Framework


Standard preprocessing of Nastran Bulk Data file including specific optimization objectives, constraints, and parameters

Additional preprocessing of optimization specific data such as adjacency, distances, manufacturing constraint dependency, initial VF, etc.

First iteration calculates stiffness and mass matrixes and all subsequent are scaled

Optimization engine simply decides new design variables (scaled stiffness and mass) and determines if to continue or stop

Topology Optimization FrameworkModel Input Translation

Topology Optimization Setup

Geometry ProcessorAssemble [K] and [M]

Solution ProcessorAssemble User and Adjoint Loads

and Solve for Displacements

Results ProcessorCalculate Responses [K]{d} and

Stresses

TO EngineOCM/MAM

Converged?OCM/MAM

ExitOCM/MAM

Generate Converged Design Geometry

New DesignScale/Assemble [K] and [M]


Optimality Criteria Method (OCM)• Do not need information from previous iteration (minimum information

stored)• Good with a single objective and single constraint (mostly used with

compliance objective with volume fraction constraint)

Moving Asymptotes Method (MAM)• Need to store 5 x number of design variables (NTOELEM) information• No need to store Hessian information• Can handle multiple constraints• Many user-controlled and internal parameters (need to tune these

parameters for fast convergence and stability)

Optimization Design Engine


OCM scales better than MAM• OCM 16 CPUs between 8x – 11x speed

up in TO engine

• MAM 16 CPUs between 2x – 4x

• OCM is the default for compliance/VF models

MAM performance more problem dependent

Parallelization of Optimization Engine

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10 15 20 25 30 35

Scal

e Fa

ctor

Number of CPUs

L-Bracket Model with 25 Constraints

MAM TO Engine

Total Analysis


Regions are identified by PSHELL and PSOLID (element property) Nastran Bulk Data entries

TOPVAR entry for each region• Can have different volume fraction• Can have different minimum member size• Can have different manufacturing constraints• Model dependent defaults• Adaptive P

Stress constraints can be defined overentire regions or over individualregion

Region 1

Region 2

Region 3

Non-design Region

Region-Based Topology Optimization


Additive Design Space Can Produce a More Efficient Design

• Boundary Condition: Fixed at one end• Loading: Uniform shear loaded at free end• Design constraint: Max. displacement at the free end limited to 0.25 in the direction of load• Objective: Minimize mass/volume• Manufacturing Constraint: Extrusion

Additional Design Region

Design RegionNon-Design Region

Non-Design Region


Additive Design Space Can Produce a More Efficient Design

Vertical Displacement Vertical Displacement

INITIAL MASS = 3.666E-02FINAL MASS = 2.763E-02MASS REDUCTION = 24.6%

INITIAL MASS = 9.165E-02FINAL MASS = 1.109E-02MASS REDUCTION = 69.7%(Based on Design Region Mass)


Nastran Bulk Data File Structure for Topology Optimization

Objective (minimize mass)

Constraint (displacement/compliance index less than)

Topology Optimization Solution

Design Region (elements, manufacturing constraints)

Design Responses (defines objective and constraints)

Design Constraints (references a design response)


Nastran Topology Optimization Examples


Non-Design Region

Non-Design Region

Design Region

Topology Optimization Example

• Boundary Condition: Fixed at bottom corners

• Loading:• Static: Point load in vertical and

shear directions, thermal gradient load from HT solution

• Heat Transfer: Internal heat generation at base and convection on free surfaces

• Design constraints: • Stress limit• Compliance index• Lowest buckling load factor• Lowest frequency• Max temperature

• Objective: Minimize mass/volume• Manufacturing constraint: Symmetry


Linear Statics

Results of Individual Topology Optimization SolutionsLinear Buckling

Normal Modes Linear Steady-State Heat Transfer

Mass Reduction: 79.0%Design Constraints: Stress < 400MPa (reduced allowable factors in 1.25 design margin and 200 °C)Compliance Index < 5.0(stiffness > 1/5 initial stiffness)Loading: 2 load cases, point and thermal loads

Mass Reduction: 74.9%Design Constraints: Lowest buckling load fact > 1.0Loading: same as linear statics load case 1

Mass Reduction: 91.0%(all material in designable region removed)Design Constraints: Lowest frequency > 20.0Hz

Mass Reduction: 88.9%Design Constraints: Maximum temperature in design region < 200 °C


Effect of Point Mass on Modal TO Example

• Boundary Condition: Fixed bottom corners

• Design constraint:• Lowest frequency greater than

20Hz• Objective: Minimize mass/volume• Manufacturing constraint: Symmetry• Original model (left) achieves the

design constraint with just the non-design region (all material removed)

• Updated model (right) adds a point mass on the free edge which drives down the lowest modal frequency resulting in added material in design region

Point Mass AddedOriginal Model


Results of Multi-Module Topology Optimization Solutions Without Heat Transfer (Compliant Design)

• Linear statics, normal modes, and buckling are run simultaneously to produce a compliant design

• Mass Reduction: 76.5%• Objective and Design constraints:

same as individual TO solutions• Loading: point loads only (no thermal

loading)• Design dominated by linear static

solution• Stresses are well below 400MPa limit

(below 10MPa in design region)• Note: stress constraints only apply to

design regions and are not controlled in non-design regions


Design Evolution of Multi-Moddule Topology Optimization Solutions With Heat Transfer (Compliant Design)

• All four solution types are run simultaneously to produce a single compliant design

• Loading now included thermal loads in the linear statics solution which results in higher stresses

• Heat transfer solution drives the overall design resulting in a heavier structure (57.5% versus 76.5% mass reduction)


Nastran Multi-Module Topology Optimization Linear Statics Normal Modes Linear Buckling Linear Steady-State Heat Transfer


Results of Multi-Module Topology Optimization Solutions With Heat Transfer (Compliant Design)

• Mass Reduction: 57.4%• Stresses are well below 400MPa limit

(below 10MPa in design region)• Temperature in design region below

200°C• Lowest frequency above 20Hz• Lowest buckling load factor above 1.0


Verification Analysis Using Original TO MeshLinear Statics: von Mises stress < 400MPa

Linear Buckling: lowest load factor > 1.0 Normal Modes: Frequency > 20Hz Heat Transfer: Temperature < 200 °C

• Models generated from .BDF files exported automatically (elements with density greater than 0.5)

• Geometry is not smoothed which can affect stress accuracy


Verification Analysis Using Smoothed and Refined TO Mesh

Linear Statics: von Mises stress < 400MPaManually Smoothed and Refined Model

Linear Buckling: lowest load factor > 1.0 Normal Modes: Frequency > 20Hz Heat Transfer: Temperature < 200 °C


Max stress constraint:• Discontinuous and oscillating

• Occurs at a localized small number of elements

Global stress constraint:• Continuous but different from local

max stress

Applicability of global stress

Global Stress Constraint

GPN is accurate…Uniform stress

GPN is not accurate…Variable stress…Local max stress


Global Stress Subdivisions

5

20

87365

1523

2000 elements Divided Over 5 Subregions

Subdivision/Constraint Number of Elements1 52 203 874 3655 1523

Divide domain into a user defined number of subdomains or sub-regions

Number of elements in each sub-region starts small and increases rapidly with higher stress elements in smaller sub-regions

Use a sub-region update strategy to allow design convergence

The number of sub-regions used is a tradeoff between performance and accuracy


L-Bracket Test Case – Max Allowable Stress = 1.2

Density

Eqv. Stress


L-Bracket Test Case – Max Allowable Stress = 2.0

Density

Eqv. Stress


L-Bracket Test Case

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0 10 20 30 40 50

Erro

r (%

)

Number of Sub-Regions

Stress Error

Variable Sub-Region, Smax=1.2

Constant Sub-Region, Smax=1.2


50

55

60

65

70

75

80

0 10 20 30 40 50

Mas

s R

educ

tion

(%)

Number of Sub-Regions

Mass Reduction


Constant Sub-Region, Smax=1.2



Commonly Used Topology Optimization Parameters

Parameter Description Default Suggested Range

Remarks

MAXTOPTITER Limits the number of design iterations

200 100 - 300 Increase when iteration limit exceeded

NTOPTSTRESSDIV Number of stress sub-divisions 10 1 - 20 Reduce for better performance/increase for better accuracy

TOPTELEMEXTTOL Tolerance for extrusion manufacturing constraint

1.0E-02 < 1.0 Increase if elements are not linked

TOPTELEMSYMTOL Tolerance for symmetry manufacturing constraint

1.0E-02 < 1.0 Increase if elements are not linked

TOPTDESIGNTOL Tolerance for MAM/OCM internal iterations

1.0E-13 < 1.0E-06 Reduce for better accuracy/increase for better performance

TOPTITERTOL Tolerance for overall design iteration tolerance

5.0E-03 < 1.0E-02 Reduce for better accuracy/increase for better performance


Shape Optimization with Fusion 360 Ultimate

© 2016 Autodesk© 2016 Autodesk

Workflow in Fusion 360 Ultimate

Develop Design Space

Define Simulation

Settings

Define Optimization

Settings

Review Results

Promote Result to

Model Workspace

Update Design

and Validate


Problem Definition

Optimize shape for Aircraft Elevator

Hinge based on the following: Defined design space envelope

Material – Ti 6Al 4V

Minimum FOS – 1.2

Maximum Displacement – 0.55mm

6 multi-directional load cases @ 1.5x

operating loads


Review Results of Multiple Mass Targets


Review Results of Single vs. Multiple Load Cases


Promote Result to Model Workspace


Redesign


Redesign Validation – FOS & Displacement


Ready for Additive MFG


The Future… Stress & Displacement Constraints

+Displacement & Stress

+DisplacementMass Target Only


The Future… Automatic Mesh to BREP


The Future… Lattice Workflows


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How Did We Do?

Autodesk is a registered trademark of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries. All other brand names, product names, or trademarks belong to their respective holders. Autodesk reserves the right to alter product and services offerings, and specifications and pricing at any time without notice, and is not responsible for typographical or graphical errors that may appear in this document. © 2016 Autodesk, Inc. All rights reserved.© 2016 Autodesk. All rights reserved.

generative design with autodesk nastran topology optimization

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