Geometric Stiffness of Membranes Using Symbolic Algebra
Resource
Engineering Structures 26 (6): 759-767
Journal
Engineering Structures
Journal Volume
26
Journal Issue
6
Pages
759-767
Date Issued
2004
Date
2004
Author(s)
Levy, R.
Chen, C.-S.
Lin, C-W.
Yang, Yeong-Bin
Abstract
This paper is concerned with derivation of the geometric stiffness matrix for membrane shells which are represented by constant stress triangular finite elements. Symbolic algebra is used to calculate the gradient of the member nodal force vector of each element when the stresses are kept fixed. This gradient defines the geometric stiffness matrix of the element in global coordinates. The present approach follows the earlier works associated with trusses, plane frames and space frames. It has the advantage of explicitness in derivation, while showing clear physical insight. For the case of small rotations, all the mathematical manipulations can be handled by hand. However, for the case of finite rotations, one must have recourse to symbolic algebra programs. The geometric stiffness matrices derived were implanted into an existing nonlinear membrane analysis program that was used to study two examples from the available literature. © 2004 Elsevier Ltd. All rights reserved.
Type
journal article
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