Numerical Aspects of Element- and Nodal-Based Material Topology Optimization of Structures

Abstract

This study numerically compares the optimal solutions generated by element- and nodal-based material topology optimization of linear elastostatic structures. Both of these designs utilize a density distribution method for the design domain concept and produce optimal boundary representations on fixed grids. Since the nodal-based design utilizes material density redistributions for topologies and shapes which are based on nodal density averages, numerical instability is reduced. This instability often occurs as checkerboard patterns in classical material element-based topology optimization using design variables of element densities. Numerical examples are used to investigate numerical aspects of optimal solutions and convergences between element- and nodal-based designs, and demonstrate the efficiency of the nodal-based approach, which generates material boundaries with smooth shapes in the range of material topology optimization.