Topology Optimization Of Compliant Mechanisms Based On Meshless Methods

The continuum topology optimization is an effective method for designing compliant mechanisms. Currently, almost all the research works about topology optimization of compliant mechanisms are based on the finite element method(FEM). However, in some instances, the use of FEM to model some kinds of problems, such as the large deformation, may be confronted with the difficulty caused by the distortion and inconsistent of mesh grids. The meshless method is typically processed by evaluating the approximate solutions only in terms of a set of nodes scattered in the design domain, and no inter-relationship of the nodes is needed indeed. It can provide us with much convenience to effectively handle problems which may experience numerical difficultly when the standard FEM is employed. Therefore, the basal theories of meshless methods and topology optimization are studied deeply in this work. Then, the element-free Galerkin method(EFGM) is introduced into the topology optimization of compliant mechanisms, and the relevant key technologies are studied systemically.EFGM is studied systemically in this dissertation. The method to enforce the essential boundary conditions by using Lagrange multipliers is predigested, but it is characterized with high accuracy and easy implementation. The relationship of the matrix singularity between shape function and the nodal distribution is discussed. In order to avoid the matrix singularity, the method for choosing the node's domain of influence is proposed. The load is classified according its character, and then the load is enforced by the corresponding method according its class. The predominance of EFGM for solving the geometrical nonlinear problem is demonstrated by numerical examples.The meshless method is introduced into the continuum topology optimization method. The structural response analysis and sensitivity analysis are carried out using EFGM, with linear and geometrical nonlinear structures considered. The process of structural stiffness optimization is treated as an example to describe the flowchart of the topology optimization based on the meshless method.Optimal design of compliant mechanisms is studied by using the topology optimization based on meshless methods. In the process of optimization, the structural response analysis is carried out using EFGM. Comparing FEM with EFGM for topology optimizations of geometrical nonlinear compliant mechanisms, the processes and results demonstrate the advantage of EFGM. Well studied numerical examples have been applied to demonstrate the non-linear EFGM can obtain the better topologies than the linear EFGM to design compliant mechanisms. The limitation of spring model is analyzed, which is corrected by applying stress constraints. In this manner, the more actual compliant mechanisms can be gotten. The discontinuous scattered points in optimal topologies are disappeared by using the method of the sensitivity filtering of Gauss points. This method is very efficient to get rid of intermediate densities and can get transparent topologies.According to the topologies designed by linear and nonlinear meshless methods, two kinds of compliant mechanisms are manufactured by wire-electrode cutting. The non-linear EFGM is necessary for designing large-displacement compliant mechanisms, which is demonstrated by testing those compliant mechanisms about the performance of load-displacement response.The topology optimization based on meshless methods is extended to design thermomechanical compliant mechanisms. The processes of topology optimization for thermal structures and thermomechanical coupling mechanisms are studied, which exploits the apply domain of meshless methods.