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A new boundary‐type finite element for 2‐D‐ and 3‐D‐elastic structures
Author(s) -
Peters K.,
Stein E.,
Wagner W.
Publication year - 1994
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.1620370608
Subject(s) - finite element method , compatibility (geochemistry) , polygon mesh , mathematics , linear elasticity , mathematical analysis , boundary value problem , numerical analysis , type (biology) , boundary element method , variational principle , geometry , structural engineering , engineering , ecology , chemical engineering , biology
In this paper we discuss the theoretical and numerical formulation of 3‐D Trefitz elements. Starting from the variational principle with the so‐called hybrid stress method, the trial functions for the stresses have to fulfil the Beltrami equations, which means also the compatibility equations for the strains. The divergence theorem can be applied, and one arrives at a pure boundary formulation in the sense of the Trefftz method. Besides the resulting variational formulation, different regularizations of the interelement conditions are investigated by numerical tests. Two examples show the numerical efficiency of the derived elements. First, a geometric linear 3‐D example is presented to show the effects on distorted element meshes. The third example shows the geometrically non‐linear analysis of a shallow cylindrical shell segment under a singe load.