Optimal design of variable-stiffness fiber-reinforced composites using cellular automata

Growing number of applications of composites materials in aerospace and naval structures along with advancements in manufacturing technologies demand continuous innovations in 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, optimal design of variable-stiffness fiber-reinforced composite laminates was studied using an emerging numerical engineering optimization scheme based on cellular automata paradigm. Cellular Automata (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 was derived, while for the general anisotropic continua with variable thickness a numeric update rule was used. Combined lay-up and topology design of variable-stiffness flat laminates was performed under the action of in-plane loads and bending loads. Optimality criteria based formulation was used to obtain local design rules for minimum compliance design subject to a volume constraint. It was shown that the design rule splits into a two-step application. In the first step an optimal lay-up configuration was computed and in the second step the density measure was obtained. The spatial lay-up design problem was formulated using both fiber angles and lamination parameters as design variables. A weighted average formulation was used to handle multiple load case designs. Numerical studies were conducted to investigate the performance of the proposed design methodology. It was shown that 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 were free of checkerboard patterns. The lay-up design problem was 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 the in-plane and also for the bending problem 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, and provides a theoretically better design; however, manufacturability of the designs are not certain. Cases of general, balanced symmetric, and balanced symmetric with equal thickness layers were studied separately. The feasible domain for laminates with equal thickness layers was presented for an increasing number of layers. A restricted problem was proposed which maintains the convexity of the design space for laminates with equal thickness layers. A recursive formulation for computing fiber angles for this case was also presented. On the computational side of the effort, a parallel version of the present CA formulation was implemented on message passing multi-processor clusters. It was shown that a standard parallel implementation does not converge for an increased number of processors. Detailed analysis revealed that the convergence problem was due to a Jacobi iteration scheme, and a pure Gauss-Seidel 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