N-sided polygonal cell-based smoothed finite element method (nCS-FEM) based on Wachspress shape function for modal analysis

In this article, an n-sided polygonal cell-based smoothed finite element (nCS-FEM) based on the Wachspress shape function is formulated for free and forced vibration of solid structures. Cell-based smoothing domains are constructed in n-sided polygonal element mesh. Using the gradient smoothing technique, the computation of the strain-displacement matrix requires only the value of the Wachspress shape function, not the derivatives of the shape function or the mapping relationship. The Lanczos algorithm is used to solve eigenvalue problems that produces vibration modes of a given structure, and the vibration modes and modal superposition techniques are used to obtain transient dynamic responses of structures subjected to arbitrary dynamics forces. The nCS-FEM is applied to solve a number of solid structures for modal analysis and compared with the Polygonal FEM, nES-FEM and ABAQUS, it is found that nCS-FEM has high precision, high efficiency and super convergence.