# Topology Optimization of Multi-Materials Compliant Mechanisms
## 1 Introduction
However, current research on compliant mechanisms is mainly focused on single materials, which determine that the design results are difficult to meet the requirements of compliant mechanisms applications. In order to maximise the design potential of topology optimisation, it is necessary to develop from the traditional design using single materials to match materials and properties, i.e., topology optimisation of multi-material compliant mechanisms. [PERSON] carried out the research on topology optimization of two materials based on the homogenization method for the first time [37]. [PERSON] proposed that the material properties of a multi-material can be described in terms of a single variable through a peak function interpolation model [38]. [PERSON] et al. proposed a microscopic multi-material optimisation design model [39]. The design of a multi-material compliant actuator was investigated by [PERSON] et al. through a level set approach [40]. Topology optimization of thermal expansion compliant mechanisms using two materials were carried out by [PERSON] et al. [41; 42]. [PERSON] proposed a solution strategy for multi-objective topology optimization under thermal structural coupling [43; 44]. [PERSON] et al. proposed an element exclusion strategy for multi-material compliant mechanisms to achieve the arrangement of each material in the design domain with different addition and deletion criteria of element materials [45; 46]. [PERSON] et al. used the method of moving asymptotes to solve the problem of variables in multi-material topology optimization [47]. [PERSON] et al. proposed topology optimization of discrete variable structures under multi-material cost constraints [48]. [PERSON] proposed an Allen-Cahn projection gradient multi-material topology optimization method based on the SIMP model [49]. [PERSON] et al. studied the topology optimization design of multi-material laminates [50]. [PERSON] controlled the length scale by the Heaviside projection method in the topology optimization of multi-material [51]. [PERSON] presents a systematic design method for a 2-degrees-of-freedom compliant parallel mechanism with decoupling performance, input coupling is reduced by resorting to a flexure-based decoupler [52]. In order to save computational resources, [PERSON] et al. proposed simple models to simulate the fluid-dynamic behaviour and to predict the instability operating range [53; 54]. At present, the design theory of multi-material compliant mechanisms is basically extended from the single material, but the number of design variables is multiplied, and the existing material interpolation models are not efficient. At the same time, due to the introduction of multi-material, the numerical instability of single node hinge and checkerboard is more prominent. In this paper, based on the generalized SIMP material interpolation model, taking the least square difference between the actual displacement and the target displacement of each output index point as the optimization objective, the mathematical model for topology optimization of multi-material compliant mechanisms is established. The polygonal mesh is used in the finite element solution process to avoid single node hinge. The remainder of the paper is organized as following. Section 2 is the main part of this work, the topology optimization model for multi-material compliant mechanisms, as well as the main idea of the proposed method is given. In Section 3, two benchmark numerical examples are provided to illustrate that our method is validity. Section 4 gives some conclusions.