STUDY ON THE RADIAL POINT INTERPOLATION MESHLESS METHOD FOR COUPLE STRESS THEORY

Displacement’s second order derivatives and the higher order boundary conditions are introduced in the couple stress theory. In its finite element implementation, displacements’ shape functions are required to be C1 continuous across the adjacent elements’ boundaries for the couple stress theory, which is a rigorous requirement for the traditional finite element method. A meshless method can realize the higher order continuity of displacement shape functions. Based on the virtual wok principle, the meshless implementation process for the couple stress theory is derived. Generally, the shape functions of the meshless method do not possess the merits of interpolation functions, and the essential boundary conditions cannot be exerted directly. In order to overcome this defect, the radial point interpolation method coupled with the polynomials is adopted to develop the shape functions. The resulted shape functions have the merits of interpolation characteristics and the essential boundary condition can be exerted directly. Numerical results show that the developed meshless method can deliver stable and precise results.