An adaptive procedure for the finite element computation of non-linear structural problems

The present paper proposes a procedure for the resolution of non-linear str uctural problems. It includes a study of the reliability of the results and the adaptive meshing The iterative phase of the solution of the equilibriu m equations entails an adaptive strategy for updating the tangent stiffness matrix, with a control of the load step. This results in a higher rate of convergence for the iterative process. The mechanical deformation processes here considered may give rise to considerable geometric distortion in the finite elements of the mesh. If they do, the consequence will be not only t hat the FE analysis fails to yield precise results, but also, owing to prob lems deriving from the numerical ill-conditioning that continuation may be impractical. To facilitate the study of these results, we developed an erro r estimator of the flux projection type, which is based on the mechanical d eformation power It is also used as a refinement criterion for the FE mesh. Distorted meshes can be fully or partially submitted to a process of regul arization based on the aspect ratio of their elements. The mesh contour may be affected by the refinement and regularization processes, for which reas on we developed a procedure for its updating. This procedure is of more imp ortance in the case of contact problems, its Primary object being to avoid interpenetration. The work was done in the ZATILAN code, developed by the D epartment of Mechanical Engineering of the University of the Basque County.