A node moving-based structural topology optimization method in the body-fitted mesh

Abstract

The work presents a node-moving algorithm for topology optimization (NMTO) in the arbitrarily shaped design domain. Also, we further enhanced a body-fitted mesh generation algorithm to express smooth boundaries more efficiently. In each optimization iteration, a narrowband offset from the structural profile is established, based on which a signed-distance function is constructed to determine the node-moving direction. At the same time, the magnitude of node velocity is derived from the shape derivative of the objective function - the sum of mean compliance and mean curvature. After the signed-distance function is updated based on the new position of the nodes within the narrowband with the abovementioned velocity, boundaries implicitly represented by its zero-level contour are obtained naturally. Such a forward Euler updating scheme is much more efficient than the well-known upwind algorithm for the body-fitted mesh as it avoids the interpolation of triangular nodes to the rectangular nodes and a small time step. Compared with other methods, benchmark numerical examples demonstrate that the proposed method can produce elegant structures with smoother boundaries and better objective functions for optimization problems seeking maximal stiffness or displacement at a prescribed node. In addition, the proposed approach prevents, to a large extent, useless void parts from being included in the time-consuming finite element analysis.