Node-Wise Topological Shape Optimum Design for Structural Reinforced Modeling of Michell-Type Concrete Deep Beams

Abstract

This study presents an associated structural design to continuous material topology optimization and a particular case of shape optimization using node-wise densities as design parameters. The generation of optimal shapes and topologies represented in this study is based on a three-dimensional density function bilinearly interpolated by element shape functions and nodal densities. The material interface between void and solid regions is described by a specific 0.5 cut-off level of continuous and smooth iso-lines of the nodal density function on a fixed mesh. This approach allows us to perform a simultaneous node-wise topology and shape optimization, which can be easily implemented by existing gradient-based optimization codes. Contrary to those of conventional material topology optimization methods, these optimal solutions are similar to ideal optimal solutions from analytical optimization techniques. Numerical examples for structural reinforced modeling of Michell-type concrete deep beams are used to demonstrate the efficiency and superiority of the resolutions of the present method.