composite plate optimization with practical design constraints

Copyright © 2015 by Robert Taylor Copyright © 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 = 𝑚𝑎𝑥𝜺1

𝑋 ,

𝜺2

𝑌 ,

𝜸𝟏2

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, 𝜖𝐵𝑦𝑝𝐶 4.2·10-3 in/in

Bearing cutoff stress, 𝐹𝐵𝑟𝑔 80 ksi

linear interaction strain, 𝜖𝑖𝑛𝑡 2.9 ·10-3 in/in 𝜖𝐵𝑦𝑝𝑇 = 𝑃𝑒𝑟𝑐45° − 𝑃𝑒𝑟𝑐0° ∙ 𝑚 + 𝑏

𝜖𝑙𝑖𝑚 =𝜖𝑖𝑛𝑡 − 𝜖𝐵𝑦𝑝𝑇

𝐹𝐵𝑟𝑔∙ 𝜎𝑏𝑟𝑔 + 𝜖𝐵𝑦𝑝𝑇

𝜖 𝐵𝑦𝑝𝑇


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


Optimization Results 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


Optimization Results 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


Optimization Results Optimized Ply Shape Laminate

• 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%


Optimization Results Optimized Ply Shape Laminate—Pressure Load 1.0, tply 0.010

• Repeat with 1.0 psi

pressure load • Increase buckling resistance

in ply shapes

• Step 1—Free size

optimization to determine

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

• Buckling constraint • 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



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

• Step 1—Free size

optimization to determine

optimal ply shapes

• Objective: Min

compliance • 40% volume fraction

constraint

• Added bearing land

region ply shape




thicknesses



thickness

• Symmetric SMEAR



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



• 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 design constraints

Engineering