Composite Plate Optimization with Practical Constraints

Copyright © 2015 by Robert TaylorCopyright © 2015 by Robert Taylor
COMPOSITE PLATE OPTIMIZATION WITH
PRACTICAL DESIGN CONSTRAINTS
Robert Taylor
University of Texas at Arlington
2015 ATCx Conference
Houston, TX
October 8, 2015

Introduction
• Composite optimization technology
enables optimal design of ply shapes and
thicknesses
• Highly tailored components
• Increased complexity, cost
• Objective: characterize value of composite
ply shape optimization using realistic
design criteria and constraints
• Background
• Methodology
• Study
Taylor, R., Admani, M., Strain, J, “Comparison of Methodologies for Optimal Design of a
Composite Plate under Practical Design Constraints,” 55th AIAA/ASME/ASCE/AHS/SC
Structures, Structural Dynamics, and Materials Conference, National Harbor, Maryland, 2014

Background
Composite Structural Optimization
• Mature, robust methods for design synthesis based on
finite element models
• Weight minimization
• Accelerated design maturation
• Commercial tools: increased accessibility, usability,
integration
• Isotropic: 2 phase process—topology optimization followed by sizing
optimization
• Composite: 3 phase process—free size (ply shape), ply size, stack shuffle
• Zhou, et al

Copyright © 2015 by Robert Taylor
Composites Optimization
General Composites Optimization
• Phase 1—Concept level optimization
• Determine ply shape
• PCOMP with SMEAR
• Structural criteria—stiffness
• Phase 2—System level optimization
• Determine ply group thickness
• PCOMP (or PCOMPP, STACK, and PLY) with
SMEAR
• Structural criteria—strength, stiffness, and stability
• Phase 3—Detail optimization
• Determine ply sizing and laminate stacking
sequence (shuffle)
• Structural criteria—strength, stiffness, and stability
• Manufacturing and design criteria—minimum gage
limits, stacking constraints, ply percentage limits,
ply termination/continuation restrictions

Background
Composite Design Criteria
• Structural Constraints
• Strength
• Failure theory—max strain
• Stability
• Finite element eigenvalue extraction
• Damage Tolerance
• CSAI strain level for laminate design and structural configuration
• Bearing and bypass at bolted joints
• Empirical equations
• Simple cutoffs from test data—Grant and Sawicki
• Encapsulated in semi-empirical tool
• Fracture mechanics basis—LM IBOLT tool—Eisenmann & Rousseau
• Stress basis—Bolted Joint Stress Field Model (BJSFM)—Garbo & Ogonowski
• Not included in this study
• Stiffness (displacement)
• Natural frequency
𝐹 = 𝑚𝑎𝑥
𝜺1
𝑋
,
𝜺2
𝑌
,
𝜸 𝟏2
𝑆

Background
Composite Design Criteria
• Manufacturing/Design Constraints
• Minimum Gage
• Stacking sequence
• Consecutive plies
• Adjacent angles
• Ply percentage limits
• Ply termination, ramp rate
• Ply continuity
• Fiber placement minimum tow length
• Knowledge-based criteria
• Requires rules integrated in finite element optimizer or knowledge-
based tool to drive optimization

Methodology
• Design Study—minimize mass of composite plate with
hole
• Three processes
• Constant thickness plate—ply size optimization
• Three zone plate—ply size optimization
• Optimized zone plate—ply free size optimization followed by ply
size optimization
• Model Formulation
• Geometry
• Material
• Acreage Strength Criteria
• Bearing-Bypass Criteria
• Design Criteria

Model Formulation
Geometry
• [0º/45º/-45º/90º] laminate family
• 10 x 20 inch plate
• 1.75 inch diameter hole
• Loads
• Distributed point loads at fasteners
• Spaced assuming 0.25 inch fasteners at
5d pitch
• Tension, compression
• 2000 lbs/inch (20 kips total on short edge)
• Shear
• 1000 lbs/inch (20 kips total on long edge,
10 kips total on short edge)

Model Formulation
Material
• MAT8 orthotropic material in
OptiStruct
• Generic material system
• Unidirectional tape
• Like carbon fiber/epoxy
• Laminate definition
• PCOMP—constant thickness and
three zone models
• Ply-based laminate definition via
PCOMPP , PLY, and STACK—
free-size optimized model
Property Value
E1 20,000,000 psi
E2 1,000,000 psi
G12 800,000 psi
G23 500,000 psi
12 0.30
tply 0.01 in
 0.06 lb/in3

Model Formulation
Acreage Strength Criteria
• Static Strength constrained using
max strain criteria
• Arbitrary values for generic material
• Stability constraint
• Omitted first pass
• Buckling eigenvalue lower limit
Allowable Value
XT 2.5·10-3 in/in
XC 2.5·10-3 in/in
YT 0.2·10-3 in/in
YC 0.4·10-3 in/in
S 0.4·10-3 in/in

Model Formulation
Bearing-Bypass Criteria
• Constraints enforced at fastener locations
• Checked at two end-of-run locations—peak
loads
• Could tailor fastener land thickness by adding
more locations
• Use interaction curve fits—Grant & Sawicki
• Arbitrary values for generic material
• Tension bypass interaction
• Tension pure bypass failure strain function of
laminate stack
Allowable Value
Compressive bypass strain, 𝜖 𝐵𝑦𝑝𝐶 4.2·10-3 in/in
Bearing cutoff stress, 𝐹𝐵𝑟𝑔 80 ksi
linear interaction strain, 𝜖𝑖𝑛𝑡 2.9 ·10-3 in/in
𝜖 𝐵𝑦𝑝𝑇 = 𝑃𝑒𝑟𝑐45° − 𝑃𝑒𝑟𝑐0° ∙ 𝑚 + 𝑏
𝜖𝑙𝑖𝑚 =
𝜖𝑖𝑛𝑡 − 𝜖 𝐵𝑦𝑝𝑇
𝐹𝐵𝑟𝑔
∙ 𝜎𝑏𝑟𝑔 + 𝜖 𝐵𝑦𝑝𝑇
𝜖𝐵𝑦𝑝𝑇

Model Formulation
Manufacturing/Design Criteria
• Constraints—composite design rules of thumb and laminate
producibility
• 0º and 90º within 20%-60% of total laminate stack at all locations
• Balanced 45º and -45º plies at all locations
• Symmetric laminate stack
• Single ply thickness 0.01 inch thick
• Ply counts based on this thickness
• Discrete optimization
• Future work
• Ply drop-off constraints not included in current study
• Some thickness step not achievable—ramp region would be longer for a
greater step change—affects 3 zone and optimized ply shape models
• Global search option (DGLOBAL ) used
• Discrete composite sizing optimization susceptible to local minima
• Automatically start at 20 different starting points

Optimization Results
Constant Thickness Laminate
• Upper bound weight for
comparison
• Design variables: 0º, 45º, -45º,
and 90º total thickness
• Symmetric SMEAR option
used
• Effectively homogenize ply
angle distribution through
laminate thickness
• Remove stacking sequence
from laminate preliminary
design
• Final laminate 0.22 inch thick
• Buckling eigenvalues large
Max strain failure
criterion results
Buckling mode results F = 1.56 (C), F = 3.88 (S)
Final
thickness
distribution

Three Zone Laminate
• Three zones defined by
engineering judgment
• Design variables: 0º, 45º,
-45º, and 90º total
thickness in each zone
• Symmetric SMEAR option
used
• Buckling constraint
• Buckling eigenvalue lower
limit constraint on second
run
• Slight weight increase to
satisfy
Max strain failure
criterion results
Final
thickness
distribution

Optimized Ply Shape Laminate
• Step 1—Free size
optimization to determine
optimal ply shapes
• 0º, 45º, -45º, and 90º plies
• 4 shapes per angle
• No sizing yet—next step
• Objective: Min compliance
• Volume fraction constraint
• 30%, 35%, 40% checked—
decreasing detail
• 40% yielded lighter weight
design
• Added human-defined
bearing land region ply shape
• Small disconnected element
groups around fasteners
Bearing land region ply
shape
Unedited ±45º ply
shapes
Edited 0º ply shapes Edited ±45º ply shapes
Edited 90º ply shapes Max Thickness

• Step 2—optimize ply shape
thicknesses
• Design variables: 0º, 45º, -
45º, and 90º ply shape
thickness
• Symmetric SMEAR
Max strain failure
criterion results
Final
thickness
distribution,
no buckling
constraint

Final
thickness
distribution,
no buckling
constraint
• Buckling eigenvalue lower
limit constraint on second run
• Significant weight increase to
satisfy
• Reduced stiffness around
cutout
• In-plane stiffness-tailored ply
shapes
• Mode shape changes
• Ply shapes not tailored to
resist buckling deformation
• Optimized design not efficient

• Buckling-tailored Ply Shapes
• Not compatible with minimum compliance objective
• Can’t simultaneously include
• Separate free size optimization for each buckling load case
• Objective: maximize buckling eigenvalue
• Constraint: 40% volume fraction
• Added 24 additional ply shapes to sizing optimization
• 3 ply shapes generated per 4 ply angles and 2 buckling load cases
• Material scattered in a patchwork—manual editing to make manufacturable
• Buckling feasible design weight results comparable to 3 zone model
±45º ply bundles generated for shear buckling

Results Comparison
Weight in lbs
Constant
Thickness
Three
Zone
Optimized Ply
Shape
No buckling constraint 2.65 2.00 1.62
With buckling constraint
(without buckling optimized shapes)
2.65 2.05 2.32
(with buckling optimized shapes)
- - 2.08
Weight Reduction
(% Constant Thickness Weight)
Three
Zone
Optimized Ply
Shape
No buckling constraint 24.5% 38.9%
(without buckling optimized shapes)
22.6% 12.4%
(with buckling optimized shapes)
- 21.5%

Optimized Ply Shape Laminate—Pressure Load 1.0, tply 0.010
• Repeat with 1.0 psi
pressure load
• Increase buckling resistance
in ply shapes
optimal ply shapes
• Objective: Min
compliance
• 40% volume fraction
constraint
• Added bearing land
region ply shape
0º plies
±45º plies
90º plies
Bearing land region
ply shape included
at all angles
Unedited ply shapes Edited ply shapes

thicknesses
thickness
• Symmetric SMEAR
• F > 1.02
• Optimized Mass = 2.11 lbs
Max strain failure
criterion results
Buckling mode results F = 1.02 (C), F = Large (S)
Final thickness
P = 1.0 psi
tply = 0.010 in

• Repeat with tply = 0.005 in
thicknesses
thickness
• Symmetric SMEAR
• F > 1.02
Max strain failure
criterion results
Final thickness
P = 1.0 psi
tply = 0.005 in

0º plies
±45º plies
90º plies
Bearing land region
ply shape included
at all angles
Unedited ply shapes Edited ply shapes
• Repeat with 0.5 psi
pressure load
• Soften ply shapes, maintain
some buckling resistance
optimal ply shapes
• Objective: Min
compliance
• 40% volume fraction
constraint
• Added bearing land
region ply shape

thicknesses
thickness
• Symmetric SMEAR
• F > 1.02
Max strain failure
criterion results
Final thickness
P = 0.5 psi
tply = 0.010 in

• Repeat with tply = 0.005 in
thicknesses
thickness
• Symmetric SMEAR
• F > 1.02
• Stack shuffle optimization Max strain failure
criterion results
Final thickness
P = 0.5 psi
tply = 0.005 in

Results Comparison
Weight in lbs
Constant
Thickness
Three
Zone
Optimized
Ply Shape
Reduction
(fr. Const. Thick)
No buckling constraint 2.65 2.00 1.62 38.9%
No buckling optimized shapes 2.65 2.05 2.32 12.4%
Buckling optimized shapes - - 2.08 21.5%
Pressure optimized shapes
(P = 1.0, tply = 0.010)
2.11 20.4%
(P = 1.0, tply = 0.005)
2.06 22.3%
(P = 0.5, tply = 0.010)
2.04 23.0%
(P = 0.5, tply = 0.005)
2.01 24.2%

Conclusion
• Composite free size optimization can be used to optimally
shape plies based on loading environment prior to sizing the
plies
• Meaningful weight improvement for strength-driven design
• Balance against increase in complexity and manufacturing cost
• Can adjust ply shapes for manufacturability where needed
• Weight result equivalent to knowledge-based zone configuration for
buckling-driven design
• Must include buckling resistant ply shapes to produce weight efficient design
• Pressure loading can improve buckling resistance of ply shapes
• Buckling resistance may be better optimized through structural
configuration if possible
• Stiffeners
• Frame spacing
• Isogrid/orthogrid

Future Work
• Improved optimization processes to design
buckling resistant composite components
• Topology optimization for stiffener placement
• Global vs. local stiffening concepts
• Sensitivity of ply shapes and sizing to edge
support conditions
• Out-of-plane loading
• Stiffener design—orthogrid/isogrid
• Additional manufacturing considerations
• Ply drop-off constraints
• Fiber placement minimum tow length
• Laminate built-up from one side—design for one
side smooth

Composite Plate Optimization with Practical Constraints

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