Abstract
Modeling of elastic thin-walled beams, plates and shells as 1D- and 2D-boundary value problems due to kinematical hypotheses, for example, the normal hypothesis, is valid in undisturbed subdomains. Disturbances near supports and free edges, in the vicinity of concentrated loads and at thickness jumps cannot be described by 1D- and 2D-BVPs. In these disturbed subdomains dimensional adaptivity has to be verformed with respect to the 3D-theory. Dimensional adaptivity (d-adaptivity) coupled with a mixed h- or p-adaptivity becomes necessary in order to guarantee a reliable overall solution. The error analysis for a mixed h-(mesh refinement), p-(polynomial expansion) and d-(dimensional expansion) adaptive process is treated in detail. Errorestimators including the discretization and dimensional errors and additionally the model error are derived. A main emphasis is the description of the additional hierarchical test-spaces (h- and p-test-space) for effective and robust overall convergence. By these new combinations of error-estimation a quality jump of FEM is intended.
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Stein, E., Ohnimus, S. Dimensional adaptivity in linear elasticity with hierarchical test-spaces for h- and p-refinement processes. Engineering with Computers 12, 107–119 (1996). https://doi.org/10.1007/BF01299396
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DOI: https://doi.org/10.1007/BF01299396