Structural Component Design Optimization for Additive Manufacture

TEACHING AEROSPACE DESIGN

OPTIMIZATION

Robert M. Taylor

Optimal Structures

David Durocher

Altair Product Design

Robert Yancey

Altair Engineering

Project Objective

• Develop training curriculum to

transfer knowledge in application of

optimization technologies in design

of aerospace structures

• Move beyond typical training module

prescriptive approach to using OptiStruct

with simple parts

• Leverage knowledge base in optimization

application

• Teach application of optimization

technologies to typical aerospace design

scenarios

• Aerospace Optimization Academy

Approach • Develop optimization knowledge,

skills, and experience

• Practical, real-world applications

• Hands-on exercises

• Self-paced

• Modular

• Accessible online

• Assignments leading to certification

• Approximately 120 hours in 2 hour sections

• Students can be assigned an Altair mentor for questions, guidance, and general assistance

• Certification for Course Completion

Typical Student Profile

• The Aerospace Optimization Academy student

will have

• 2-3 years aerospace structural analysis

experience

• Basic finite element analysis skills & tool familiarity

• Limited optimization knowledge, experience

• Prerequisites

• Intro CAE

• HyperMesh & HyperView

• OptiStruct

• Intro Aero Concepts

• Aero Structural Analysis

• Materials

• Intro Composites

• Intro to Structural Optimization

AOA Modules—Overview Title Number of Exercises Status

1 Optimization Overview 0 Ready

2 Project Management 0 Ready

3 Basic Optimization 4 Ready

4 Spreadsheet-driven Optimization 4 Future

5 Finite Element-driven Optimization 4 Ready

6 Optimization with Composites 4 2/4 Ready

7 Optimization with Joints 1 Ready

8 Optimization with DaDT constraints 1 Future

9 Structural Concept Comparison 2 Future

10 Loads 1 Future

11 Structural Optimization Exercises 2 Future

12 Advanced Concepts ? Future

AOA Modules—Ready 1 Optimization Overview

2 Project Management

3 Basic Optimization

5 Finite Element-driven Optimization

6 Optimization with Composites

7 Optimization with Joints

AOA Module 1—Optimization Overview • Objective: Develop familiarity with

• Optimization methods, tools, and processes used in aerospace applications • What is optimization—goals, why and when to use

optimization

• Overview of topology, shape, size, and combined optimization

• Elements of optimization problem formulation • Design variables, objective function, constraints, and

other terminology

• Basic theoretical concepts of optimization algorithms • Unconstrained minimization

• Constrained optimization

• Optimality criteria and dual methods

• Approximation techniques

• Sensitivity analysis

• Case studies illustrating tools, methods, and applications

• No Exercises

AOA Module 2—Project Management • Objective: Develop

familiarity with optimization process, including tasks, models, data flow, and potential issues

• Optimization Project Checklist • Data Development

• Baseline Assessment

• Concept Design

• Design Refinement

• Deliverables

• No Exercises

Item Description Milestone Meetings ECD Actual Delivery

1

Create project schedule and process flow chart, deliver to owner of

structure

2 Gather project data: □ CAD □ FEM □ Loads □ Materials □ Design Space

3

Project kick off meeting. Agenda: Project schedule, Review project data

set, solicit baseline displacements/stress, equilibrium forces, preferred

modeling assumptions, bcs, loading, find out if stress is allowed to follow

plastic stress/strain for Ftu for usage of Neuber. □

4

Design Space Given? □ yes □ no, If no, submit design space proposal using

Design_Space_Documentation_Template.ppt

5 Design Space review □

6 Constraints Document □

6 Baseline assessment:

7 If baseline is available:

8 Convert baseline FEM (if available) to OptiStruct

9 Run Analysis

10

Compare displacements/stress/buckling results to requirements or

baseline strength check notes

11 Review FEM using "basic FEM checklist"

12

Is the OptiStruct displacement/stress similar to the previous analysis

work? (if available)

13 If baseline is not available:

14

Before meshing CAD, decide whether to partition geometry for topology

efficiency (nondesign/design).

15

If shape opti is planned, the mesh should be built such that it

suitable for shape perturbations

16 Build OptiStruct FEM from CAD

17 Run Analysis


19 Communicate baseline assessment □

20

Use free body loads for optimization □ yes □ no. Free body loads are

sometimes appropriate for optimization work in cases where loads to the

structure aren't expected to change, where a large portion of non-design

structure can be removed from the FE model to reduce iteration time, etc.

21 If yes, data in free body model and non-free body must be identical.

22 Verify free body contains expected applied and reacted loads

23 □ yes □ no

24 Verify that stresses are identical to the original model.

25 □ yes □ no

26 Write .spcf file, verify spc forces are negligible.

27 □ yes □ no

28

Non-linear gaps solutions only: Use non-linear gap status (by way of

GAPPRM,HMGAPST,YES) and GAP-to-MPC macro for optimization □ yes □ no. This

can reduce optimization cpu time by representing the non-linear gap status

by means of MPC equations in a linear analysis. An initial non-linear

analysis must be run to generate the status file. Expected percentage

reduction in cpu time is 75%.

29

If yes, Verify, using the Free Body Forces tool, that reaction forces

at the gap locations are identical in the non-linear gap model and the

MPC'd linear model.

30 □ yes □ no

31 Optimize structural layout using conceptual design tools

32 □ topology □ free size □ topography

33 □ shells □ hexas □ 1st order tets

34

Run analysis with 100% material fraction (topology) or thickness (free

size) to see if any responses violate constraints and cannot be

rectified.

35 Run optimization jobs


37 Design interpretation of conceptual design results

38

Design interpretation of topology results can be enhanced by running

topology optimization on individual load cases. These results can

then be compared to the combined topology run. Structural features

should become more meaningful. Load path analysis should become

clearer.

39

□ Consider producibility in the interpretation, minimum gauge, common

radii, cutting tools, undercuts, etc.

40

Secondary conceptual design (if appropriate). Sometimes running a secondary

topology using the interpreted design can help refine the design quicker

than going directly to shape optimization. The main goal of this secondary

conceptual work is to pinpoint where inefficient structure exists.

41 □ topology □ free size □ topography

42 □ shells □ hexas □ 1st order tets

43 Concept design analysis

44 □ Weight reduction compared to baseline

45 □ Allowable violations (if any)

46 Communicate concept design. Agenda: Producibility, assembly. □

DATA DEVELOPMENT

BASELINE

CONCEPT DESIGN

AOA Module 3—Basic Optimization • Objective: Develop familiarity with basic

model construction for typical optimization methods used in aerospace applications • Optimization using spreadsheet analysis

model

• Preprocessing in Hypermesh

• Finite element cards used in optimization

• Exercises 1. Analytic model optimization

(HyperStudy/Excel)

2. Basic size optimization

3. Basic shape optimization

4. Basic topology optimization

• Short review for candidates that have completed OptiStruct training

AOA Module 5—Finite Element-driven

Optimization • Objective: Develop familiarity with

optimization of metallic structural

components for stiffness, strength,

and stability using OptiStruct size,

shape, and topology optimization

• Model development

• Loads

• Design interpretation

• Exercises

• Compact Fitting—Door Hinge

(Exercise 1)

• Stiffened Metallic Skin (Exercises 2-4)

AOA Module 5—Exercise 1 Compact

Fitting—Door Hinge • Objective: Design a door hinge fitting

within a given package space that includes cutouts for stay-out zones • Optimization tools: topology, size

• Criteria: Strength, stiffness

• Loading: Point loads

• Model details: contact (gap elements), z-offsets, 2D and 3D elements

• In this exercise the student will • Setup topology optimization for the body region

of the hinge tetrahedral element model

• Execute the topology optimization and post-process the results

• Define a shell element size optimization model based on the topology optimization results

• Execute the size optimization and post-process the results

AOA Module 5—Exercise 1 Sample

AOA Module 5—Exercises 2-4 Stiffened

Metallic Skin • Objective: Design a multi-bay aft fuselage panel

with a circular cutout • Optimization tools: size

• Criteria: Strength, stability

• Loading: up bending, down bending, and torsion conditions combined with pressure

• Model details: 1D and 2D elements

• Optimize design using three methods • Exercise 2—Global model

• Exercise 3—Carve-out—balanced freebody loads

• Exercise 4—Static Condensation—DMIG reduced model

• In these exercises, the student will • Define a size optimization model comprised of shell and

bar elements in a region of a global model


AOA Module 6—Optimization with

Composites • Objective: Develop familiarity with optimization of

composite structural components using for stiffness, strength, and stability using OptiStruct composites tools

• Tools, processes, and methods unique to composites • Failure criteria

• SMEAR and SMCORE idealizations

• Composite free-size optimization to shape plies

• Ply-based analysis and design variables

• Two approaches for bolted joint bearing/bypass strength—simplified curve fit equation and externally calculated margin of safety (e.g. BJSFM)

• Manufacturing rules—ramp rate, ply percentage limits, stacking sequence, zone continuity

• Core

Module 6—Exercises • Exercise 1—Preliminary Sizing Optimization

• 2 spar, 3 rib wing optimization

• Triangular pressure distribution

• Up Bending, down bending, twist load conditions

• 27 laminate designs—PCOMP with SMEAR, [0,90,45,-45] laminate family

• Max strain failure criterion

• Exercise 2—Detail Panel Optimization • Skin panel with cutout

• Carveout model with balanced freebody loads

• Ply thickness optimization of constant thickness laminate

• Strength, stiffness, stability, manufacturing constraints

• Exercise 3—Detail Panel Optimization (Future) • Skin panel with cutout

• Carveout model with balanced freebody loads

• Ply shape optimization of variable thickness laminate

• Strength, stiffness, stability, manufacturing constraints

• Exercise 4—Detail Panel Optimization with Bearing/Bypass Constraint (Future) • Apply bearing/bypass constraints at bolted joints using two methods:

simplified analysis and external tool (e.g. BJSFM)

• Repeat optimization of both constant thickness and variable thickness laminates

Module 6—Exercise 1—Wing Skin

Preliminary Sizing • Problem Statement

• Objective: minimize mass

• Constraints: Maximum strain, buckling eigenvalue

• Design variables: • Composite shell element

thicknesses—skin panels

• Metallic shell element thicknesses—spars, ribs

• Beam element dimensions—spar caps

• In this exercise, the student will: • Define a size optimization model

comprised of 2D shell and 1D beam elements, including 1D offsets


Module 6—Exercise 2—Detail Panel

Optimization • Problem Statement

• Objective: minimize mass

• Constraints: Maximum strain, buckling eigenvalue

• Design variables:

• Composite ply shapes

• Composite ply thicknesses

• In this exercise, you will: • Create a carve-out model from a global model

• Generate balanced free-body loads

• Refine mesh and create cutout on detail panel

• Define and execute composite optimization models comprised of composite shell elements

• Free size optimization to determine ply shapes

• Size optimization to determine ply thicknesses

• Shuffle optimization to determine ply stacking sequence

• Post-process the results

AOA Module 7—Optimization with Joints

• Objective: Develop familiarity with optimization of joint placement, joint number and joint size • Joints loads based on elasticity

• Exercise 1—Overview of Joint Analysis and Optimization • Joint modeling—hole detail, fastener elements,

fastener end conditions, fastener length, plate offsets

• Data analysis—bearing loads, bypass loads, plate stresses

• Plate gauge and fastener optimization

• Joint fatigue details: reference stress, bearing stress, bypass stress, bearing load, fastener diameter, plate thickness and t/D ratio

• Exercise 2—Joint Optimization with Bearing Bypass Stress Calculation Using an External Function • Repeat exercise 1 using calculations from DRESP3

external function defined in HyperMath

AOA Modules—Future 4 Spreadsheet-driven Optimization

8 Optimization with DaDT constraints

9 Structural Concept Comparison

10 Loads

11 Structural Optimization Exercises

12 Advanced Concepts

AOA Module 4—Spreadsheet-driven

Optimization • Objective: Develop familiarity with optimization of metallic

structural components for stiffness, strength, and stability using spreadsheet-driven classical analysis methods

• Link HyperStudy with existing spreadsheet analysis methods

• Define design variables inside spreadsheet

• Exercise

• Optimize multi-section beam using classical analysis from spreadsheet

Variables: Equations:

faxial = axial stress along beam = (P/A)

fsweb = shear stress in the web = (V/A) (where R b is either R t or R c )

fscord = shear stress in cords = (V/A)

fbtxx = tensile stress at top of I-beam (from bending about x-axis)

fctxx = compressive stress at bottom of I-beam (from bending about x-axis) Procedure:

fbty y = tensile stress from bending about y-axis 1. calculate all stress values based on geometry and load inputs.

fcty y = compressive stress from bending about y-axis 2. combine stress values to obtain total stress at each of the four corners of the I-beam.

fb1,2,3,4 = total applied stress at point 1,2,3,or4 (fbtxx + fctxx) 3. calculate the stress ratios for bending and shear

Ftu = ultimate tensile stress (for bending, consider both tensile & compressive stress as well as ultimate and yield for allowable limits)

Fcy = compressive yield stress 4. calculate M.S. using stress ratios

Fsu = ultimate shear stress

Rt = (applied tensile stress) / (allowable tensile stress) References:

Rc = (applied compressive stress) / (allowable compressive stress)

Rs = (applied shear stress) / (allowable shear stress) 18.028

Ra = (applied axial stress) / (allowable compressive stress) ( stress ratio, margin of safety definition, interaction equations: see page C1.7-C1.8, and C3.11 )

1,2 3,4 1,3 2,4

TOP BOTTOM FWD AFTkips kips in kips kips in kips psi psi psi psi psi psi psi psi psi psi psi psi psi psi

Section LGB Station A A_web A_cords h_total y_bar h - y_bar w_total x_bar w-x_bar Ixx Iyy Paxial Vy Mxx Vx Myy faxial fs web fs cord fbtxx fbcxx fbty y fbcy y fb1 fb2 fb3 fb4 Ftu Fcy Fsu Rt Rc Rs Section

AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 AA

BB 72.000 11.466 2.768 9.196 12.750 6.375 6.375 6.000 3.000 3.000 357.089 27.596 BB

CC 120.000 17.725 3.278 15.319 13.250 6.625 6.625 6.000 3.000 3.000 576.476 45.968 CC

DD 168.000 25.994 3.458 23.967 13.750 6.875 6.875 6.000 3.000 3.000 854.329 71.910 DD

EE 216.000 36.878 3.726 35.362 14.250 7.125 7.125 6.000 3.000 3.000 1166.462 106.094 EE

FF 264.000 47.842 4.282 46.603 14.750 7.375 7.375 6.000 3.000 3.000 1441.337 139.816 FF

1,2 3,4 1,3 2,4

SUBCASELoad Case Independent Margins TOP BOTTOM FWD AFT

Section LGB Station A A_web A_cords h_total y_bar h - y_bar w_total x_bar w-x_bar Ixx Iyy Paxial Vy Mxx Vx Myy faxial fs web fs cord fbtxx fbcxx fbty y fbcy y fb1 fb2 fb3 fb4 Ftu Fcy Fsu Raxial Rt Rc Rs Section

1 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 -10.000 -15 -360 0 0 -1502 5580 0 12399 -12399 0 0 12399 12399 -12399 -12399 130000 126000 80000 0.01 0.10 0.10 0.07 6.66 AA

2 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 10.000 -15 -360 -10 -240 1502 5580 2390 12399 -12399 57308 -57308 69708 -44909 44909 -69708 130000 126000 80000 0.01 0.54 0.55 0.07 0.76 AA

3 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 -10.000 15 360 -10 -240 -1502 5580 2390 -12399 12399 57308 -57308 44909 -69708 69708 -44909 130000 126000 80000 0.01 0.54 0.55 0.07 0.76 AA

4 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 0.000 -15 -360 0 0 0 5580 0 12399 -12399 0 0 12399 12399 -12399 -12399 130000 126000 80000 0.00 0.10 0.10 0.07 7.29 AA

5 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 10.000 30 720 -10 -240 1502 11161 2390 -24799 24799 57308 -57308 32509 -82107 82107 -32509 130000 126000 80000 0.01 0.63 0.65 0.14 0.47 AA

6 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 10.000 30 720 10 240 1502 11161 2390 -24799 24799 -57308 57308 -82107 32509 -32509 82107 130000 126000 80000 0.01 0.63 0.65 0.14 0.47 AA

7 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 0.000 30 720 10 240 0 11161 2390 -24799 24799 -57308 57308 -82107 32509 -32509 82107 130000 126000 80000 0.00 0.63 0.65 0.14 0.50 AA

8 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 -10.000 -10 -240 10 240 -1502 3720 2390 8266 -8266 -57308 57308 -49042 65575 -65575 49042 130000 126000 80000 0.01 0.50 0.52 0.05 0.87 AA

9 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 -10.000 -30 -720 -10 -240 -1502 11161 2390 24799 -24799 57308 -57308 82107 -32509 32509 -82107 130000 126000 80000 0.01 0.63 0.65 0.14 0.47 AA

10 AA 24.000 6.657 2.688 4.185 12.250 6.125 6.125 6.000 3.000 3.000 177.830 12.564 0.000 30 720 0 0 0 11161 0 -24799 24799 0 0 -24799 -24799 24799 24799 130000 126000 80000 0.00 0.19 0.20 0.14 3.15 AA

Lowest Margin for Section is 0.47

MS

Bending

Bruhn, E.F., Analysis & Design of Flight Vehicle

Structures

Rbending

Rbending

str

ess

ratios

1

1..

22

sba RRRSM

Variables:

W width of region

h height of region

A area of region

In moment of inertia of region about it's own centroid

Ixx moment of inertia of entire beam about x-axis

Iy y moment of inertia of entire beam about y-axis

Aweb area of web (reg2+reg3+reg4+part of reg1 +part of reg5)

Acords area of cords (reg1+reg5)

Ybar y-distance from bottom of I-beam to centroid of I-beam

Xbar x-distance from left edge of I-beam to centroid of I-beam

Equations (Flabel, J.C., Practical Stress Analysis for Design Engineers , p.658)

Region W (in) h (in) A (in2) x (in) Ax (in3) Ax2 (in4) y (in) Ay (in3) Ay2 (in4) Ix_loc (in4) Iy _loc (in

4) Aweb: 2.687944 in2

1 6.000 0.349 2.092 3.000 6.277 18.830 12.076 25.265 305.096 0.021 6.277 Acoords: 4.185 in22.922925

2 0.308 0.527 0.163 3.000 0.488 1.463 11.638 1.892 22.013 0.004 0.001 Ybar: 6.125 in

3 0.205 10.498 2.148 3.000 6.444 19.331 6.125 13.156 80.578 19.727 0.007 Xbar: 3 in

4 0.308 0.527 0.163 3.000 0.488 1.463 0.612 0.100 0.061 0.004 0.001 Ixx 177.830 in4

5 6.000 0.349 2.092 3.000 6.277 18.830 0.174 0.365 0.064 0.021 6.277 Iyy 12.564 in4

totals: 6 12.250 6.657 19.972 40.777 407.812 19.777 12.564

SE

CT

ION

AA

h_total

h

W

Region 1

s

Reg. 2

Reg. 3

Reg. 4

Region 5

Y

X

12

3

_

bhI locx

A

AyYbar

AyYAyII barlocxxx

2

_

12

3

_

hbI locy

AxXAxII barlocyyy

2

_

A

AxX bar

Variables

Fcr critical buckling stress (compression)

Fscr critical buckling stress (shear)

fs applied shear stress

fc applied compressive stress (bending about x-axis)

Rb } stress ratios

Rs }

a panel width

b panel height

t panel thickness

Kc compression buckling coefficient

Ks shear buckling coefficient

v 0.33 poissons ratio

E 1.65E+07 Young's modulus

Es = 0.7E 1.16E+07 (secant modulus)

ET=0.85E 1.40E+07 refer to Ramsberg/Osgood equation, Bruhn, pp B1.8

Equations

(compression due to bending)

(shear)

Reference

Bruhn, E.F , pp C5.1-C5.10

pp B1.8

Sect a b t a / b Kc Ks ƞb ƞs Fcr (Bruhn) Fscr X Ybar Ybar_aux1 Ixx Mxx Vy

in in in ksi ksi in in in in 4̂ in kips kips

AA 15.00 10.50 0.20 1.43 36.00 11.25 0.58 0.56 121.66 36.60 0.88 6.13 5.25 177.83

BB 15.00 10.12 0.19 1.48 36.00 11.00 0.58 0.56 111.81 32.89 1.32 6.38 5.06 357.0886

CC 15.00 9.55 0.21 1.57 36.00 10.75 0.58 0.56 156.19 44.90 1.85 6.63 4.78 576.4758

DD 15.00 8.57 0.19 1.75 36.00 10.50 0.58 0.56 152.50 42.82 2.59 6.88 4.28 854.3288

EE 15.00 7.12 0.15 2.11 36.00 10.00 0.58 0.56 137.96 36.90 3.56 7.13 3.56 1166.462

FF 15.00 5.71 0.13 2.63 36.00 9.75 0.58 0.56 165.10 43.05 4.52 7.38 2.85 1441.337

Bruhn, Bruhn,

fig. C5.15 fig. C5.11

pp C5.7 pp C5.7

a

x

b

Y_bar

Y_bar_aux1

t

a

b

b

2

2

2

112

b

tEKF c

bcr

2

2

2

112

b

tEKF s

sscr

2

25.0

1

1315.01

2

s

Tsb

E

E

E

E

2

2

1

1

E

ESS

AOA Module 8—Optimization with DaDT

constraints • Objective: Develop familiarity with optimization of metallic

structural components with DaDT stress allowable constraints • Two approaches for DaDT stress allowable calculation: simplified

curve fit equation and externally calculated margin of safety

• DaDT analysis considerations: loading spectrum, control points, stress concentrations, design rules

• Exercise • Optimize DaDT critical structural component for service life stress

constraints

AOA Module 9—Structural Concept

Comparison • Objective: Develop familiarity with methods and tools for truss and

shear web optimization • Topology optimization setup and parameters for truss or stiffener configuration

• Effect of topology parameter settings

• Free size optimization for shear web thickness configuration

• Comparison of designs and methods

• Exercises • Topology optimization of structural component

• Free-size optimization of structural component

AOA Module 10—Loads

• Objective: Develop familiarity with internal loads model

concepts and how they affect structural optimization

• Critical load surveys

• Carveout model development

• Global-local modeling issues

• Freebody loads

• Analysis issues (e.g. buckling)

• Modeling details

• Load inconsistencies

• Exercise

• Load survey and carveout exercise

AOA Module 11—Structural Optimization

Exercises • Objective: Execute complete design cycle for structural

component: loads, topology, size, shape, margin

calculation

• Exercises

• Metallic part design optimization

• Composite part design optimization

AOA Module 12—Advanced Concepts

• Objective: Develop familiarity with advanced optimization

concepts

• Possible topics include

• Mesh refinement

• Cross section checks through DRESP3

• Failsafe using MPC

• Multi-objective

• Multidisciplinary

• Robust

• Nonlinear

Conclusion

• Aerospace Optimization Academy

• Teach application of optimization technologies to typical aerospace

design scenarios—

• Develop broader application knowledge, skills, and experience

• Practical, real-world applications

• Hands-on exercises

• Self-paced

• Modular

• Initial modules available for training

• Future modules developed based on demand

Structural Component Design Optimization for Additive Manufacture

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