Effect of self-weight on topological optimization of static loading structures

Abstract

Topological optimization is an approach for determining the optimal shape of a structure subjected to certain boundary and loading conditions without affecting the initial performance. Each structure has a certain weight which is also included in optimization. This paper presents the mathematical approach for topological optimization of structures subjected to self-weight condition. In this paper effect of self-weight on the topologies of structures, subjected to static loading conditions has been studied subjected to a variation of 200–10% of the value of static point load. Meshing of the structures is done with quadrilateral 4-node elements and for self-weight condition weight of an element is equally transferred to each node. MATLAB programming of proposed mathematical approach is done and compared with the conventional structural problems. SIMP method, which is a penalization scheme is used to determine the optimum distribution of material and void has been employed. Optimal criteria method is used to optimize the structures as per loading and boundary conditions. Different numerical examples have also been discussed to show the effect of self-weight on the static loading structures and the optimal topologies obtained by varying static loading in terms of self weight.