A new topology description function based approach for structural topology optimization

In the present paper, a new approach for structural topologyoptimization based on implicit topology description functions (TDF) isproposed. TDF is used to describe the shape/topology of the structure, whichis approximated in terms of its nodal values. Then a relationship isestablished between the element stiffness and the values of the topologydescription function on its four nodes. In this way and with some non-localtreatments of the design sensitivities, not only the shape derivative butalso the topological derivative of the optimal design can be incorporated inthe numerical algorithm in a unified way. Numerical experiments demonstratethat by employing this approach, the computational efforts associated withTDF (level set) based algorithms can be saved. Clear optimal topologies andsmooth structural boundaries free from any sign of numerical instability canbe obtained simultaneously and efficiently.