Ordered multi-material SIMP approach applied to 3D topology optimization

Abstract

This paper presents a topology optimization framework for multi-material 3D structures to be used in mechanical load carrying applications. This framework is an extension of an ordered multi-material interpolation scheme originally proposed in 2D to the 3D minimum compliance problem implemented in MATLAB. The algorithm starts by using the Young’s moduli and cost of the selected materials, then picks binary combinations with ordered densities to interpolate the value for the current iteration. Following these interpolations, the next step of the design is the solution of the mechanical compliance problem until the desired minimum compliance is met subject to volume and cost constraints. The solution scheme is based on Optimality Criteria Method and standard density filtering schemes. The main contribution of this paper is that the proposed design scheme implemented in MATLAB is an easy-to-use 3D topology optimization scheme with multi-material constituents based on a modified SIMP interpolation. Results show that the 3D code is able to deliver similar design results when compared with the existing 2D version. This effectively expands the topology optimization based design capability to many practical 3D engineering problems in a standard topology optimization setting and easy-to-use implementation in MATLAB.