A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems

A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis. In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula. The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems. In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do. And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods. Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified.