A Structure Topology Optimization with the First-Order Saddlepoint Approximation

Abstract

In practical engineering, uncertain loads usually cause the variations of structure stiffness to affect the security of the structure. To enhance the reliability and find the optimum structure in engineering, a topology optimization method is developed for the optimization of structural stiffness in this paper. The first-order saddle point approximation method is introduced into the topology optimization process. A multi-constrained stiffness optimization model considering uncertain loads is proposed. The corresponding sensitivity mathematical formula for stiffness is also given. The complete optimization iteration process is given. The structural stiffness optimization problems with the joint constraints of volume and displacement are solved here to illustrate the application of the proposed method. In the examples, a U-shape groove in different working situations is considered which includes the single node displacement constraint and the multi-node displacement constraint. The corresponding optimization results of different working situations are compared, and the results accord with the law of engineering.