エネルギー原理および数理計画法を用いた非線形骨組構造物の最適化に関する研究

抄録

This paper describes unified and efficient new optimum design methods for plane frame structures with nonlinear materials. The structural analysis problem with material nonlinearity is formulated as the total complementary energy minimization problem subject to equilibrium equations, and the necessary conditions for nonlinear analysis problem are derived. Then the primal optimum design problem is reformulated considering both the primal design constraints and the necessary conditions for analysis problem. Furthermore the unknown member end forces for each member elements and the displacements at the free nodes are also dealt with as the design variables in addition to the primal sizing and configuration variables. The reformulated optimum design problem is solved efficiently by using the gradient projection method. The advantages, rigorousness, efficiency and reliability of the proposed optimum design method are demonstrated by comparing the results obtained by the dual method in which the behavior sensitivities are used.