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A new finite element scheme for instability analysis of thin shells
Author(s) -
Matsui Tetsuya,
Matsuoka Osamu
Publication year - 1976
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.1620100112
Subject(s) - quadrilateral , direct stiffness method , stiffness matrix , finite element method , instability , stiffness , mathematics , rigid body , mathematical analysis , matrix (chemical analysis) , linear elasticity , geometry , structural engineering , classical mechanics , physics , mechanics , materials science , engineering , composite material
Abstract This paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non‐linear stiffness and tangential stiffness matrices for a doubly‐curved quadrilateral element defined by co‐ordinate lines. The essential feature is the explicit addition of the non‐linear terms into the rigid‐body motion of the element. Thus the non‐linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non‐linear terms of these matrices are separated into a number of component terms multiplied by the rigid‐body rotations. These component terms can be stored permanently and used to calculate efficiently the non‐linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.