ITO for Structures with Stress-Minimization

Abstract

In Chaps. 2 and 3, the classic stiffness-maximization design problems are concerned in the discussions of the effectiveness and efficiency of the proposed ITO and M-ITO methods, due to the corresponding positive features, like the stable convergence and quickly arrive at the expected values. In practical use, the stress is a more critical factor in the design of engineering structures, where stress concentrations are mostly occurred in the practical use, rather than the lower stiffness. However, the considerations of the stress in the topology optimization will introduce several numerical difficulties in the optimization due to the special features of the stress, namely the highly nonlinear behavior, the local naturality and the singular topologies during the optimization. Hence, the stress-related topology optimization poses more challenge than the known compliance-minimization topology optimization designs. In the current chapter, the main intention is to develop a stress-related ITO formulation for the minimization of the global stress to eliminate the occurrence of stress concentrations in structures, which is applied to show the effectiveness and efficiency of the proposed ITO method on the design of stress-related optimization problems. In the ITO method for the stress-related designs, the critical aspects should be considered: (1) how to develop an IGA model to replace the traditional finite element method for stress computation to improve numerical precision; (2) how to develop a stress evaluation model to ensure the computational accuracy of the global stress by aggregating all local stress in the design domain; (3) how to develop the ITO formulation for the stress-minimization designs. The ITO formulation for the stress-minimization also contains some similar aspects: (1) the material description model using the DDF to represent structural topology; (2) the NURBS-based IGA. Meanwhile, in the current chapter, the main intention is to show the effectiveness and efficiency of the ITO method on the stress-minimization design problems, and the related positive features or merits of the ITO on the stress-related design problems have been already submitted to the journal.