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 it reflects the inn ate characteristics of topology optimization as a combinatorial optimizatio n 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 inclu ding two kinds of variables is solved directly by using the relative differ ence quotient algorithm. The computational results are satisfactory and som e new topologies and better solutions are obtained.