Development of a novel meshless Local Kriging (LoKriging) method for structural dynamic analysis Original Research Article

This paper presents a novel meshless approach to study the dynamic responses of structures. It is called Local Kriging (LoKriging) method, where the Kriging interpolation is employed to construct the field approximation function and meshless shape functions, and the local weak form of partial differential governing equations is derived by the weighted residual technique. Since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points, the essential boundary condition can be easily imposed. In implementation of local weak form, the spline function with high continuity is used as the weight function. No mesh is required either for integration of the local weak form, or for construction of the shape functions. Thus the present LoKriging method is a truly meshless method. Several numerical examinations for the free/forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems (MEMS) device are carried out to demonstrate the accuracy and efficiency of the LoKriging method. The numerical results show that the presently developed method is quite easy to implement, very accurate and highly efficient for the problems considered.