Optimum structural topology design considering flexibility.

Abstract

In general structural design, the stiffest structure has been considered optimal. However, structures can provide higher performance or additional function if the flexibility is implemented in the appropriate portions in the structures. The purpose of this thesis is to develop the structural design method considering flexibility based on the homogenization design method. This method is applied to the designs of compliant mechanisms, automotive body structures, and flextensional actuators. First, the flexibility and the mutual stiffness are defined using the mutual energy concept. Their sensitivities with respect to a design variable are derived using variational calculus. The formulation of the flexibility is extended in the dynamic case and in the case where a domain is composed of the piezoelectric medium and the elastic material. Second, the multi-objective optimization problems for the three applications are formulated: the compliant mechanism, the automotive body structure, and the flextensional actuator. For the compliant mechanism design, four types of design optimization problems are introduced and formulated: the unconstrained single flexibility case, the constrained single flexibility case, the displacement constrained single flexibility case, and the multi-flexibility case. This formulation is extended to the dynamic case. For the automotive body structure design, the multi-objective function incorporating the multi-flexibility, stiffness, and eigen-frequency are formulated to achieve the design criteria. For the flextensional actuator design, the mean transduction, which is an extended concept of flexibility is utilized to formulate the optimization problem. Next, the new multi-objective functions are formulated for these applications. The Pareto optimality of these multi-objective functions are proved. Based on theses formulations, the optimization algorithm is constructed using the homogenization design method and sequential linear programming. Finally, several numerical examples and the applications of the topology configurations are presented. In these examples, the characteristics of the optimal configurations are examined, and the performance of the optimal configurations is verified. We confirmed that the structure design considering flexibility can be accomplished by the methodology presented here, and the implementation of flexibility in the structures can improve the performance or provide valuable additional functions.