OPTIMIZATION OF MINIMIZING COMPLIANCE UNDER MULTIPLE LOAD CASES BY THREE MEMBERS TRUSS-LIKE MATERIAL MODEL

A method to minimize the compliance of structures under multiple load cases is studied. A three member truss-like material model is presented. The stiffness matrix and its sensitivities are derived. The member distributed field is optimized to form a truss-like continuum. In most topology optimization method, structural topology is expressed by ‘existence’ and ‘nonexistence’ of elements. Rough outlines with zigzag lines are not avoided. This problem is overcome thoroughly. The member densities and orientations at the nodes are taken as design variables. The member densities and orientations at any point in an element vary continuously. For intermediate densities being not suppressed, no numerical instabilities exists at all. Since there is an explicit relation between a truss-like continuum and a member structure, it is easy to transfer a truss-like continuum to a member structure rationally. Parts of members in the truss-like continuum, which are formed according to the member distribution, are chosen to form the nearly optimal member structure. Furthermore if the positions of the nodes and the cross sectional areas of the members are optimized, the final topological optimal structures are established.