Engineering Application And Numerical Method Research Of Shape Optimization Based On EFG Method

Shape optimization has played a very important role in the engineering application. It is a task of structural shape optimization that the performance of structure is improved by changing the geometry shape of structure, in which it is more to minimizing stress concentration of structure and/or to improve the stress-distributing status. The most advantage of meshless method is that it can alleviate the mesh constrained of node, and the distortion of mesh presented in the process of structural shape optimization can be completely avoided by integrating the meshless method into the shape optimization. In many meshless methods, the element-free Galerkin (EFG) method is one of the most promising and well-developed method for engineering application.The selection of the weight function and its parameter are studied firstly in moving least square (MLS) method in this paper. The relation between value of shape function and size of influence domain of a node is discussed by means of error analysis. The influence of weight function on shape function and its derivatives is studied by using uniform and irregular nodal arrangement. The advice on selecting weight function and its parameter in MLS method is presented by analyzing the influence of weight function curve on the precision of computational result on the basis of energy norm proposed. A numerical method for discreteness-based shape design sensitivity analysis (DSA) using EFG method is presented by using direct differential method on the discrete Galerkin control equilibrium equation, and the essential boundary condition is imposed by employing Lagrange-multiplier method. The derivative of shape function with respect to design variable is obtained by utilizing the ideas of direct differential approach and semi-analytical method, and the accuracy and consistency, computational cost and implementations effort of building approaches is discussed. The result obtained in the numerical test show that this approaches can meet demand of engineering application.However the EFG method is marked by some shortcoming, where the primary one is that there is much more computational cost and it is difficult in imposing the essential boundary condition. The advantage in both finite element (FE) method and EFG method can be developed by integrating coupled FE-EFG method into structural shape optimization. A collocation approach is introduced to couple firstly FE and EFG method in isoparametric quadrangle interface element between EF and meshless regions, and the interpolation function for the displacement at the interface element satisfies the linear consistency exactly. By taking...