A Thermal-Solid–Fluid Method for Topology Optimization of Structures with Design-Dependent Pressure Load

Abstract

For the topology optimization of structures with design-dependent pressure, an intuitive way is to directly describe the loading boundary of the structure, and then update the load on it. However, boundary recognition is usually cumbersome and inaccurate. Furthermore, the pressure is always loaded either outside or inside the structure, instead of both. Hence, the inner enclosed and outer open spaces should be distinguished to recognize the loading surfaces. To handle the above issues, a thermal-solid–fluid method for topology optimization with design-dependent pressure load is proposed in this paper. In this method, the specific void phase is defined to be an incompressible hydrostatic fluid, through which the pressure load can be transferred without any needs for special loading surface recognition. The nonlinear-virtual thermal method (N-VTM) is used to distinguish the enclosed and open voids by the temperature difference between the enclosed (with higher temperature) and open (with lower temperature) voids, where the solid areas are treated as the thermal insulation material, and other areas are filled with the self-heating highly thermally conductive material. The mixed displacement–pressure formulation is used to model this solid–fluid problem. The method is easily implemented in the standard density approach and its effectiveness is verified and illustrated by several typical examples at the end of the paper.