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Hybrid‐Trefftz plate bending elements with p‐method capabilities
Author(s) -
Jirousek J.
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620240712
Subject(s) - gravitational singularity , convergence (economics) , singularity , grid , bending , displacement (psychology) , connection (principal bundle) , stress (linguistics) , mathematics , basis (linear algebra) , mathematical optimization , process (computing) , series (stratigraphy) , computer science , mathematical analysis , geometry , structural engineering , engineering , paleontology , linguistics , philosophy , economics , psychotherapist , biology , economic growth , operating system , psychology
The p‐method capabilities have thus far been used only in connection with the assumed displacement model elements. When such elements are used, singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity. This paper presents an alternative formulation which circumvents this drawback and enables excellent solution results to be obtained with uniform FE‐grids. The formulation is based on the recently presented hybrid‐Trefftz FE‐model and makes use of optional expansion sets for various singularities or stress concentrations. Stress concentrations due to concentrated loads are also properly accounted for. It is shown that by augmenting the order of approximation over a fixed grid of such elements rapid convergence towards the accurate solution is obtained in the most efficient way. This paper summarizes the results of a preliminary study that had been undertaken to critically evaluate the potential of the new approach as a suitable basis for subsequent developments of a fully automated adaptive process.