Multi-Material Design Optimization of Composite Structures

This PhD thesis entitled “Multi-Material Design Optimization of Composite Structures” addresses the design problem of choosing materials in an optimal manner under a resource constraint so as to maximize the integral stiffness of a structure under static loading conditions. In particular stiffness design of laminated composite structures is studied including the problem of orienting orthotropic material optimally. The approach taken in this work is to consider this multi-material design problem as a generalized topology optimization problem including multiple candidate materials with known properties. The modeling encompasses discrete orientationing of orthotropic materials, selection between different distinct materials as well as removal of material representing holes in the structure within a unified parametrization. The direct generalization of two-phase topology optimization to any number of phases including void as a choice using the well-known material interpolation functions is novel.
For practical multi-material design problems the parametrization leads to optimization problems with a large number of design variables limiting the applicability of combinatorial solution approaches or random search techniques. Thus, a main issue is the question of how to parametrize the originally discrete optimization problem in a manner making it suitable for solution using gradient-based algorithms. This is a central theme throughout the thesis and in particular two gradient-based approaches are studied; the first using continuation of a nonconvex penalty constraint to suppress intermediate valued designs and the second approach using material interpolation schemes making intermediate choices unfavorable through implicit penalization of the objective function. The last contribution consists of a relaxation-based search heuristic that accelerates a Generalized Benders' Decomposition technique for global optimization and enables the solution of medium-scale problems to global optimality. Improvements in the ability to solve larger problems to global optimality are found and potentially further improvements may be obtained with this technique in combination with cheaper heuristics.