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A family of hybrid plate elements
Author(s) -
Tong Pin
Publication year - 1982
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.1620181003
Subject(s) - mathematics , midpoint , matrix (chemical analysis) , inverse , finite element method , moment (physics) , bending moment , boundary element method , boundary (topology) , mathematical analysis , stiffness matrix , inversion (geology) , geometry , structural engineering , engineering , physics , classical mechanics , geology , paleontology , materials science , structural basin , composite material
Hybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time‐consuming, and the matrix inversion can result in a loss of numerical accuracy. This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an element.