A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation

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In the last decade, one-point quadrature shell elements attracted many academic and industrial researchers because of their computational performance, especially if applied for explicit finite element simulations. Nowadays, one-point quadrature finite element technology is not only applied for explicit codes, but also for implicit finite element simulations, essentially because of their efficiency in speed and memory usage as well as accuracy. In this work, one-point quadrature shell elements are combined with the enhanced assumed strain (EAS) method to develop a finite element formulation for shell analysis that is, simultaneously, computationally efficient and more accurate. The EAS method is formulated to alleviate locking pathologies existing in the stabilization matrices of one-point quadrature shell elements. An enhanced membrane field is first constructed based on the quadrilateral area coordinate method, to improve element's accuracy under in-plane loads. The finite element matrices were projected following the work of Wilson et al. (Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press: New York, 1973; 43-57) for the incompatible modes approach, but the present implementation led to more accurate results for distorted meshes because of the area coordinate method for quadrilateral interpolation. The EAS method is also used to include two more displacement vectors in the subspace basis of the mixed interpolation of tensorial components (MITC) formulation, thus increasing the dimension of the null space for the transverse shear strains. These two enhancing vectors are shown to be fundamental for the Morley skew plate example in particular, and in improving the element's transverse shear locking behaviour in general. Copyright (c) 2005 John Wiley Sons, Ltd.
Publisher
WILEY-BLACKWELL
Issue Date
2006-04
Language
English
Article Type
Article
Keywords

ASSUMED STRAIN; QUADRILATERAL ELEMENTS; DEFORMATION PROBLEMS; INCOMPATIBLE MODES; FINITE-ELEMENT; DISPLACEMENTS; STABILIZATION; ROTATIONS

Citation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, v.66, no.2, pp.214 - 249

ISSN
0029-5981
DOI
10.1002/nme.1548
URI
http://hdl.handle.net/10203/203807
Appears in Collection
ME-Journal Papers(저널논문)
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