Evaluating Topological Optimized Layout of Building Structures by Using Nodal Material Density Based Bilinear Interpolation

Abstract

This study presents a boundary representation of Eulerian-type in order to achieve conceptual structural layouts of building structures by relieving material discontinuities of structural topology optimization in comparison with classical ones. According to the partition of unity concept, a bilinear interpolation can be employed by nodal densities and shape functions with the use of discretization of four-node square elements and then material properties, i.e. here, densities in finite elements are not constant but variational values. As a result, the improvement of material continuity can be established as optimal topologies, and numerical singularity and zigzag material boundaries which may occur in classical topology optimization design are relieved. Numerical applications verify the efficiency of this method by evaluating this conceptual structural layout approach for designing building structures.