Adaptive technique in nonlinear problems

Abstract eng:
In this paper we discuss the use of adaptive methodology in non-linear analysis based on Finite Element Method. It is focused on static problems of elastoplasticity. Because of the path dependence of the solution in analysis with material non-linearity, the loading is applied in an incremental manner. It is convenient to compute in every increment a suitable norm of variables to monitor the accuracy of the solution in order to recognize the necessity of re-meshing. We use energy norm of error based on recovered strains and stresses. The obtained norm is compared with required values which are not, however, constant all over the domain. The highest accuracy is required on boundary of plastic zones and on elements with stress closed to yield surface. The problem of updating the state variables after re-meshing is discussed in some details too. Finally, we conclude our paper by some numerical examples.

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