Topology optimization using a mixed formulation: An alternative way to solve pressure load problems

A shortcoming of the traditional density based approach to topology optimization is the handling of design dependent loads that relate to boundary data, such as for example pressure loads. Previous works have introduced spline and iso-density curves or alternative parametrization schemes to determine the load surfaces. In this work we suggest a new way to solve pressure load problems in topology optimization. Using a mixed displacement–pressure formulation for the underlying finite element problem, we define the void phase to be an incompressible hydrostatic fluid. In this way we can transfer pressure loads through the fluid without any needs for special load surface parametrizations. The method is easily implemented in the standard density approach and is demonstrated to work efficiently for both 2D and 3D problems. By extending the method to a three phase (solid/fluid/void) design method we also demonstrate design of water containing dams.