An application of relative difference quotient algorithm to topology optimization of truss structures with discrete variables

In this paper, the definitions of cross-sectional variable and topological variable are advanced, and a mathematical model of topology optimization of truss structures with discrete variables including two kinds of variables is developed. The model has considered the coupling relations between cross-sectional variables and topological variables, so that is reflects the innate characteristics of topology optimization as a combinatorial optimization problem. Moreover, problems such as limit stress and singular solution of structural optimization can be overcome by using this model. The model of topology optimization of truss structures with discrete variables including two kinds of variables is solved directly by using the relative difference quotient algorithm. The computational results are satisfactory and some new topologies and better solutions are obtained.