(A) nodal density based topology optimization with continuous boundary

Abstract

Topology optimization is one of the structural optimization methodologies, which has been widely used in the conceptual design stage. In this thesis, in order to improve the boundary representation of the density based topology optimization, a new stiffness matrix is proposed by placing design variables at the nodes of the element. In the existing element density method, there is a limit to the boundary expression because of the characteristic that the density is constant in an element. Element density based method could provide smooth boundary with mesh refinement. In this proposed methodology, each node has density values which are linearly interpolated to divide the element at the threshold density by an iso-density line. The proposed stiffness matrix enables stable convergence using strain energy in sensitivity analysis. Verification of the proposed methodology was performed through several numerical examples in topology optimization.