Study on weight functions in shape optimization based on meshless method

The choice of the weight functions can affect the performance of meshless method in structural shape optimization. Ones can randomly choose the weight function and its index or parameters on the basis of user's experiences. In fact, it is very difficult to make an explicit decision, since there is implicit relation between the weight function and the shape function in the meshless method. In this paper, the moving least-square approximation, the shape design sensitivity equation and various weight functions, such as cubic spline, quartic spline, parabola function, conical function, triangle function and exponential function, are described briefly. In the process of sensitivity analysis, the aforementioned weight functions are tested by means of an example with analytical solution, and the relative errors of the displacement sensitivity are compared and studied. Finally, we gain some advice for choosing of the weight function and its index or parameter in shape optimization based on meshless method.