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Explicit integration for three‐dimensional degenerated shell finite elements
Author(s) -
Vlachoutsis Stefanos
Publication year - 1990
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.1620290413
Subject(s) - jacobian matrix and determinant , mathematics , finite element method , shell (structure) , matrix (chemical analysis) , stiffness , stiffness matrix , mathematical analysis , displacement (psychology) , transformation matrix , power series , numerical integration , transformation (genetics) , surface (topology) , geometry , homogeneous , kinematics , structural engineering , classical mechanics , materials science , physics , engineering , psychology , biochemistry , chemistry , composite material , psychotherapist , gene , combinatorics
Explicit integration across the thickness for three‐dimensional degenerated shell finite elements is analysed. For this purpose a modifed formulation is proposed. The Jacobian matrix of the physical–parameter spaces transformation is decomposed into a product of ‘in‐middle‐surface’ and ‘out‐of‐middle‐surface’ terms. This enables an expansion to be carried out of the strain–displacement matrix into power series of the thickness variable. Explicit integration is then performed and the corresponding formulae of the stiffness and mass matrices are given. The possibility of ‘locking’ for thin structures is explained. The analysis is applied to homogeneous and multilayered structures. Numerical applications for linear problems are given in the last part of the paper.