Topology optimization of structural systems using convex approximation methods.

In this dissertation, three topics are presented aiming at increasing the efficiency and applicability of structural topology optimization methods. Convex approximation methods are improved. The efficiency of the convex approximation methods depends on the choice of internal program parameters, such as values of moving asymptotes. In this dissertation, two strategies are proposed to determine the moving asymptotes in the Method of Moving Asymptotes, and a new algorithm is introduced. The algorithm preserves the nature of the method as a first order one, while increasing approximation accuracy. In addition, a new, more general, formulation for convex approximation methods is proposed that offers more flexibility in generating approximation problems. Finally, it is pointed out that convex approximation methods can use any intermediate variables. Through this idea, new formulations of convex approximation methods may be derived in the future. Topology optimization is advanced from a single component level to a system level. The topology of connections between the components of a structural system strongly affects its performance. The topology of connections is defined and a new classification for structural optimization is introduced that includes topology optimization of connections. A convex approximation method using analytical gradients is used to solve a mathematical programming formulation of the connection problem. As an example, this methodology is applied to the optimal design of spot-welds and adhesive bond patterns and locations. A technique to add multiple constraints to the topology optimization model with homogenization is introduced. The direct solution of optimality criteria in the homogenization method restricts the optimization model to have only one constraint. It is shown that in the homogenization formulation the iteration procedure derived from the optimality criteria method has strong similarity with the one derived from the convex approximation methods. Therefore, multiple constraints can be included in the homogenization-based topology optimization model solved by convex approximation methods. The inclusion of multiple constraints increases the range of applicability of homogenization-based approaches. As an example, the multipurpose topology optimization problem is formulated and solved.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105103/1/9635540.pdfDescription of 9635540.pdf : Restricted to UM users only