NLSDP Algorithms For Confidence Structural Robust Design And Optimization

The study of optimal design and optimization under uncertainty has gained more and more attention in recent years and has become a hot topic in the field of structural optimization.In the present paper, confidence robust design and optimization of truss structures under static and dynamic cases with stiffness and load uncertainties are considered under WCDO (Worst Case design and Optimization) framework. The considered problems can be formulated as NonLinear Semi-Definite Programming (NLSDP) problems and solved with NLSDP algorithms.In order to improve the capacity and efficiency of the NLSDP algorithms for the solution of large scale problems, in this paper, a modified NLSDP algorithm is proposed based on the Augmented Lagrange algorithm developed by Sun et al. In our algorithm, a single nonlinear semidefinite constraint matrix is decomposed into multiple sub-equivalent constraint matrices and the nonlinear constraints are dealt with BFGS method separately. In this way, the computational effort involved in the solution of NLSDP problems can be reduced greatly. A large number of numerical examples illustrate the quick convergence speed, high precision and the effectiveness of the proposed modified NLSDP algorithm.