Topology optimization of truss-like continua with three families of members model under stress constraints

Abstract

A method to minimize structural volume under stress constraints subject to multiple load cases is presented. A new material model is developed and employed to simulate the constitutive relation of the truss-like continuum. It is assumed that there are infinite numbers of members with infinitesimal spaces along three orientations at any position. The densities and orientations of members at all nodes are taken as design variables. An iterative optimization method is presented. In one iteration step, design variables are optimized separately and independently. The orientations of three families of members at every node are optimized by mathematics program method. Fully stressed criterion is adapted to optimize member densities. In the every iteration step, member densities are adjusted to make their strains smaller than the permissible values while the stress states is assumed to keep unchanged. The densities and orientations of members at any point inside an element are obtained by their interpolating the corresponding values (i.e., the densities and orientations) at the nodes of the element. These values vary continuously inside an element and the intermediate values are not suppressed. By using this technique the optimal truss-like continuum is formed, which represents for member distribution field. Once parts of members are chosen, discrete truss can be constructed according to the continuous member distributive field. This discrete structure is a nearly optimal structure. In above process, there are no numerical instabilities such as checkerboard and mesh-dependency. Numerical examples are presented to demonstrate the effectiveness of the present method.