Abstract: The shape optimization of structures has played a very important role in the engineering application. The mesh distortion of the finite element in the process of shape optimization can be avoided completely by integrating the meshless method with the shape optimization. A numerical method for discreteness-based design sensitivity analysis is proposed by using the discrete derivatives method in the basis of the element-free Galerkin method, in which the Lagrange multiplier is employed into imposing the essential boundary condition. The main advantage of the approach presented is that the calculating process of sensitivity analysis is similar to the solving of element-free Galerkin method, and the present formulation can be easily implemented. In addition, the mathematics model of shape optimization and design velocity fields are also discussed. An example, which has the exact solution, is presented to testify the sensitivity analysis method derived. The result obtained shows that there exists excellent agreement between the analytical and numerical solution. Finally, by using the presented algorithm of shape optimization based on EFG method, the shape optimization of two engineering examples is achieved.

Key words: Shape optimization, Element-free Galerkin method, Sensitivity analysis Optimal design