A density gradient approach to topology optimization under design-dependent boundary loading

Abstract

The paper proposes a density gradient based approach to topology optimization under design-dependent boundary loading. Since there is no explicit boundary representation in density-based topology optimization, the design-dependent boundary loads are implicitly imposed through a domain integration of spatial gradient of the density field. The density gradient based loading is formally derived and justified based on the smoothed boundary method for numerical solution of PDE. The Heaviside projection, density filtering and local refinement are combined to efficiently control the thickness of the loading interface and the number of elements within it. For problems with both loading and non-loading boundary, an auxiliary density field is introduced to keep track of the loading boundary. Both 2D and 3D heat conduction problems, linear elasticity problems and coupled thermoelastic problems under design-dependent boundary loading are presented to illustrate the effectiveness and efficiency of the method.