Multi-material topology optimization using isogeometric method based reaction–diffusion level set techniques

Abstract

This work presents a new approach to multi-material topology optimization (MMTO) using Isogeometric Analysis (IGA) based reaction–diffusion equation (RDE) level set method. Level set based topology optimization, frequently used for achieving clear material boundaries and avoiding checkerboard patterns in topology optimization problems is further augmented by RDEs which enhance numerical stability of the solver. The multi-material formulation uses a blended combination of different level-set functions to ensure that each point in the domain corresponds to a single material. In this work, isogeometric analysis (IGA) is used for the first time in RDE-based level set for solving MMTO problems. The same Non-Uniform Rational B-Splines (NURBS) basis function is used for approximating state variables, geometry modeling and level set function, thus facilitating seamless coupling between analysis and product design. Using the IGAFEM toolbox (Nguyen et al., 2015), MMTO is performed for a few benchmark problems for varying material composition and mesh sizes. Results indicate that satisfactory distribution of material is achieved in all the MMTO examples and bi-quadratic element based IGA is a competent tool to be applied in RDE-based level set method for topology optimization. Future work will focus on using the same IGA framework for further shape optimization of the designed structures to produce fabrication ready CAD models.