Automatic adaptive refinement finite element procedure for 3D stress analysis

Abstract

An automatic adaptive refinement procedure for 3D finite element analysis is presented. Based on a carefully designed procedure to eliminate the instability of the superconvergent patch recovery technique, accurate smoothed stress field for 3D elasticity problem can be established. Well graded adaptive tetrahedral meshes with node spacing compatible with the specifications as required by the refinement strategy are generated by newly developed mesh refinement scheme. Iterative solution solver employing the preconditioned conjugate gradient technique is used for the solution of large system of simultaneous equations. Practical examples solved by using the quadratic T10 tetrahedral element indicate that the procedure is reliable and effective. Even in the presence of singularities, the optimal convergence rate is achieved and the asymptotic convergence of the error estimator is also observed. Numerical results in this study demonstrate that by combining theoretical derivations with appropriate computation algorithms, it is completely feasible to carry out automatic adaptive analyses even for full 3D problems. Many advantages of the adaptive refinement over the traditional one-pass finite element analysis or uniform refinement are revealed, especially when the exact solution of the problem is difficult and singular points are present inside the problem domain.