Title page for ETD etd-10062005-140818

Type of Document Dissertation
Author Setoodeh, Shahriar
Author's Email Address shahriar@vt.edu
URN etd-10062005-140818
Title Optimal Design of Variable-Stiffness Fiber-Reinforced Composites Using Cellular Automata
Degree PhD
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Gürdal, Zafer Committee Chair
Batra, Romesh C. Committee Member
Hyer, Michael W. Committee Member
Jones, Robert M. Committee Member
Watson, Layne T. Committee Member
  • lamination parameters
  • Compliance Design
  • Cellular Automata
  • Tow-placed laminates
Date of Defense 2005-09-21
Availability unrestricted
The growing number of applications of composite materials in

aerospace and naval structures along with advancements in

manufacturing technologies demand continuous innovations in the

design of composite structures. In the traditional design of

composite laminates, fiber orientation angles are constant for each

layer and are usually limited to 0, 90, and ±45 degrees. To

fully benefit from the directional properties of composite

laminates, such limitations have to be removed. The concept of

variable-stiffness laminates allows the stiffness properties to vary

spatially over the laminate. Through tailoring of fiber orientations

and laminate thickness spatially in an optimal fashion, mechanical

properties of a part can be improved. In this thesis, the optimal

design of variable-stiffness fiber-reinforced composite laminates is

studied using an emerging numerical engineering optimization scheme

based on the cellular automata paradigm.

A cellular automaton (CA) based design scheme uses local update

rules for both field variables (displacements) and design variables

(lay-up configuration and laminate density measure) in an iterative

fashion to convergence to an optimal design. In the present work,

the displacements are updated based on the principle of local

equilibrium and the design variables are updated according to the

optimality criteria for minimum compliance design. A closed form

displacement update rule for constant thickness isotropic continua

is derived, while for the general anisotropic continua with variable

thickness a numeric update rule is used.

Combined lay-up and topology design of variable-stiffness flat

laminates is performed under the action of in-plane loads and

bending loads. An optimality criteria based formulation is used to

obtain local design rules for minimum compliance design subject to a

volume constraint. It is shown that the design rule splits into a

two step application. In the first step an optimal lay-up

configuration is computed and in the second step the density measure

is obtained. The spatial lay-up design problem is formulated using

both fiber angles and lamination parameters as design variables. A

weighted average formulation is used to handle multiple load case

designs. Numerical studies investigate the performance of the

proposed design methodology. The optimal lay-up configuration is

independent of the lattice density with more details emerging as the

density is increased. Moreover, combined topology and lay-up designs

are free of checkerboard patterns.

The lay-up design problem is also solved using lamination parameters

instead of the fiber orientation angles. The use of lamination

parameters has two key features: first, the convexity of the

minimization problem guarantees a global minimum; second, for both

in-plane and bending problems it limits the number of design

variables to four regardless of the actual number of layers, thereby

simplifying the optimization task. Moreover, it improves the

convergence rate of the iterative design scheme as compared to using

fiber angles as design variables. Design parametrization using

lamination parameters provides a theoretically better design,

however, manufacturability of the designs is not certain. The cases

of general, balanced symmetric, and balanced symmetric with equal

thickness layers are studied separately. The feasible domain for

laminates with equal thickness layers is presented for an increasing

number of layers. A restricted problem is proposed that maintains

the convexity of the design space for laminates with equal thickness

layers. A recursive formulation for computing fiber angles for this

case is also presented.

On the computational side of the effort, a parallel version of the

present CA formulation is implemented on message passing

multiprocessor clusters. A standard parallel implementation does not

converge for an increased number of processors. Detailed analysis

revealed that the convergence problem is due to a Jacobi type

iteration scheme, and a pure Gauss-Seidel type iteration through a

pipeline implementation completely resolved the convergence problem.

Timing results giving the speedup for the pipeline implementation

were obtained for up to 260 processors.

This work was supported by Grant NAG-1-01105 from NASA Langley

Research Center. Special thanks to our project monitor Dr. Damodar

R. Ambur for his technical guidance.

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