Towards automatic adaptive geometrically non‐linear shell analysis. Part I: Implementation of an h‐adaptive mesh refinement procedure

Effective methods leading to automated adaptive numerical solutions to geometrically non‐linear shell‐type problems are studied in this work. In particular, procedures for improving the accuracy, the reliability and the computational efficiency of the finite element solutions are of primary interest here. This is addressed using h ‐adaptive mesh refinement based on a posteriori error estimation, self‐adaptive methods in global incremental/iterative processes, as well as smart algorithms and heuristic approaches based on methods of knowledge engineering. Seemless integration of h ‐adaptive finite element methods with adaptive step‐length control makes it possible to maintain a prescribed accuracy while maintaining the solution efficiency without user intervention throughout the process of a non‐linear analysis. Several examples illustrate the merit and potential of the approach studied herein and confirm the feasibility of developing an automatic adaptive environment for geometrically non‐linear analysis of shell structures.