TOPOLOGY OPTIMIZATION FOR ELASTIC STRUCTURES WITH FINITE DEFORMATION USING HMPS METHOD AND IESO METHOD

Abstract

 The topology optimization method using voxel finite element method is an effective method to create various morphologies from rectangular parallelepiped design domain. Fujii et al. [1, 2] created morphologies of building structures using such method. Also, Fujii et al. [3] applied such method to create link mechanisms that amplify input displacement such as toggle damping device. However, these link mechanisms increase manufacturing cost and maintenance cost as the number of links increases. Therefore, it is desirable to develop compliant mechanisms that amplify input displacement by elastic deformation. However, almost topology optimization methods to create these compliant mechanisms [4, 5] are based on the infinitesimal deformation theory. Therefore, in this paper, we develop a topology optimization method considering finite deformation in order to develop a vibration control device using compliant mechanism.

 In this paper, we use a particle method instead of finite element method, because when using finite element method, the computation time becomes enormous, and the convergence solution often cannot be obtained because the calculation becomes unstable by the large distortion of elements. Manabe and Fujii [6] have proposed a method that using CA-ESO method for topology optimization and MPS method [11] for particle method. Also, Manabe et al. [7] have developed amethod using Level Set method for topology optimization. However, these methods target two-dimensional problems, and methods for three-dimensional problems have not been developed yet. Therefore, the purpose of this study is to extend this approach to three-dimensional problem.

 The proposed method in this paper is an extension of the proposed method in ref. [6]. That is, HMPS (Hamiltonian Moving Particle Semi-implicit) method [12-14] is used instead of MPS method [11], and IESO (Improved Evolutionary Structural Optimization) method with finishing algorithm is used instead of CA-ESO method.

 In Section 2, the formulation of HMPS method is shown so that our created program can be understood. In Section 3, the outline of IESO method with finishing algorithm using HMPS method is explained. In Section 4, we verify the effectiveness of the proposed method by numerical examples in which jumping buckling occurs. In Section 5, the above results are summarized.

 The conclusions are as follows.

 (1) In the analysis of infinitesimal deformation range, the solutions of the proposed method almost agree with the solutions of the method using voxel finite element method.

 (2) In the analysis of finite deformation, the solutions corresponding to buckling cannot be obtained by IESO method alone. However, the solutions obtained by IESO evolve into solutions corresponding to the buckling by the finishing algorithm (CA+IESO method). Also, the two-dimensional solutions have the same topology as the solutions in ref.[7], [9]. And, the shapes of two and three dimensional solutions change according to the magnitude of the load. Furthermore, the solutions of two-dimensional problem and three-dimensional problem show similarities in topology.

 In addition, the proposed method is very robust and the computation time does not become enormous. Therefore, the proposed method can be practically implemented as a three-dimensional topology optimization method that can consider finite deformation.

 In the next step, we plan to apply the proposed method to the topology optimization problem of compliant mechanisms.