TOPOLOGICAL OPTIMIZATION OF CONTINUUM STRUCTURE WITH STRESS AND DISPLACEMENT CONSTRAINTS UNDER MULTIPLE LOADING CASES
多工况应力和位移约束下连续体结构拓扑优化

ICM (Independent Continuous Mapping) methodology is used to establish an optimization model for continuum structure in which the formulation is identical to skeleton structure's. The model minimizes the structural weight with stress and displacement constraints for multiple loading cases. The topological variable is independent so that it doesn't attach to the sectional or shape variable any longer. Moreover, the topological variable is continuous instead of discrete because of the use of a filter function. The filter function can also recognize element weight, stiffness and allowable stress and it is the key to construct ICM model. Inverse mapping from the continuous variable to the discrete variable is implemented using an adaptive threshold. In each iteration, stress topology variables and displacement topology variables are obtained using the zero order and the first order approximate models respectively and the later is the solution of a quadratic programming that is a second order approximation of the dual programming corresponding to the primal problem with displacement constraints under multiple loading cases. A multiple--level strategy and a weight factor are used when the loads are of different order of magnitude whose state is called as ill loading case in the paper. Typical topology optimization examples of both two and three dimension show that the method is successfully extended from the skeleton structure to the continuum structure.