A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM)

In this paper, a three-dimensional (3-D) adaptive analysis procedure is proposed using the meshfree node-based smoothed point interpolation method (NS-PIM). Previous study has shown that the NS-PIM works well with the simplest four-node tetrahedral mesh, which is easy to be implemented for complicated geometry. In contrast to the displacement-based FEM providing lower bound solutions, the NS-PIM possesses the attractive property of providing upper bound solutions in strain energy norm. In the present adaptive procedure, a novel error indicator is devised for NS-PIM settings, which evaluates the maximum difference of strain energy values among four nodes in each of the tetrahedral cells. A simple h-type local refinement scheme is adopted and coupled with 3-D mesh automatic generator based on Delaunay technology. Numerical results indicate that the adaptive refinement procedure can effectively capture the stress concentration and solution singularities, and carry out local refinement automatically. The present adaptive procedure achieves much higher convergence in strain energy solution compared to the uniform refinement, and obtains upper bound solution in strain energy efficiently for force driven problems.

► A three-dimensional adaptive analysis algorithm has been developed for the NS-PIM.
► A novel error indicator was proposed by evaluating the nodal strain energy.
► NS-PIM works well with tetrahedron elements facilitating the h-type refinement.
► The adaptive algorithm can effectively capture the stress concentration.
► The adaptive NS-PIM can provide highly convergent upper bound solutions.