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

Abstract

The present paper proposes a procedure for the resolution of non‐linear structural problems. It includes a study of the reliability of the results and the adaptive meshing. The iterative phase of the solution of the equilibrium 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 that the FE analysis fails to yield precise results, but also, owing to problems deriving from the numerical ill‐conditioning, that continuation may be impractical. To facilitate the study of these results, we developed an error estimator of the flux projection type, which is based on the mechanical deformation 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 regularization based on the aspect ratio of their elements. The mesh contour may be affected by the refinement and regularization processes, for which reason we developed a procedure for its updating. This procedure is of more importance in the case of contact problems, its primary object being to avoid interpenetration. The work was done in the ZATILAN code, developed by the Department of Mechanical Engineering of the University of the Basque Country.

Citation

Hernández, A., Albizuri, J., Avilés, R. and Amezua, E. (1999), "An adaptive procedure for the finite element computation of non‐linear structural problems", Engineering Computations, Vol. 16 No. 4, pp. 443-467. https://doi.org/10.1108/02644409910271885