In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress ÿeld. The qualitative properties of the recovered stress ÿeld necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A speciÿc procedure for recovery of an improved stress ÿeld is then developed. The procedure can be classiÿed as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisÿed a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. ? 1998 John Wiley & Sons, Ltd.
In this paper, we study an approach for recovery of an improved stress resultant ÿeld for plate bending problems, which then is used for a posteriori error estimation of the ÿnite element solution. The new recovery procedure can be classiÿed as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of interior equilibrium and natural boundary conditions. The interior equilibrium is satisÿed a priori over each nodal patch by selecting polynomial basis functions that fulÿl the point-wise equilibrium equations. The natural boundary conditions are accounted for in a discrete least-squares manner. The performance of the developed recovery procedure is illustrated by analysing two plate bending problems with known analytical solutions. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative error estimate.
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 CI 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.
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