2. 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
3. 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
4. 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
7. 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
8. 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
18 Review FEM using "basic FEM checklist"
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
36 Review FEM using "basic FEM checklist"
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. □
DATADEVELOPMENT
BASELINECONCEPTDESIGN
9. 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
10. 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)
11. 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
14. 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
• Execute the size optimization and post-process the
results
17. 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
18. 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
19. 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
• Execute the size optimization and
post-process the results
22. 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
24. 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
28. 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 Rb is either Rt or Rc )
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 AFT
kips 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
stress
ratios
1
1
..
22
sba RRR
SM
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 (in4
) 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 in2
2.922925
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
SECTIONAA
h_total
h
W
Region1
s
Reg.2
Reg.3
Reg.4
Region5
Y
X
12
3
_
bh
I locx
A
Ay
Ybar
AyYAyII barlocxxx
2
_
12
3
_
hb
I locy
AxXAxII barlocyyy
2
_
A
Ax
X 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^4 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
tEK
F c
bcr
2
2
2
112
b
tEK
F s
sscr
2
2
5.0
1
13
15.01
2
s
Ts
b
E
E
E
E
2
2
1
1
E
ES
S
29. 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
30. 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
31. 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
33. 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
34. 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
