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Shell Finite Elements (shell + finite_element)

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Engineering100%

Selected Abstracts

A low-order, hexahedral finite element for modelling shells,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004
Samuel W. Key
Abstract A thin, eight-node, tri-linear displacement, hexahedral finite element is the starting point for the derivation of a constant membrane stress resultant, constant bending stress resultant shell finite element. The derivation begins by introducing a Taylor series expansion for the stress distribution in the isoparametric co-ordinates of the element. The effect of the Taylor series expansion for the stress distribution is to explicitly identify those strain modes of the element that are conjugate to the mean or average stress and the linear variation in stress. The constant membrane stress resultants are identified with the mean stress components, and the constant bending stress resultants are identified with the linear variation in stress through the thickness along with in-plane linear variations of selected components of the transverse shear stress. Further, a plane-stress constitutive assumption is introduced, and an explicit treatment of the finite element's thickness is introduced. A number of elastic simulations show the useful results that can be obtained (tip-loaded twisted beam, point-loaded hemisphere, point-loaded sphere, tip-loaded Raasch hook, and a beam bent into a ring). All of the gradient/divergence operators are evaluated in closed form providing unequivocal evaluations of membrane and bending strain rates along with the appropriate divergence calculations involving the membrane stress and bending stress resultants. The fact that a hexahedral shell finite element has two distinct surfaces aids sliding interface algorithms when a shell folds back on itself when subjected to large deformations. Published in 2004 by John Wiley & Sons, Ltd. [source]

On reduced integration and locking of flat shell finite elements with drilling rotations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2003
Sannelie Geyer
Abstract In recent times, a number of assumed stress membrane finite elements with drilling degrees of freedom have been presented. These highly accurate elements are natural candidates for the membrane component of geometrically simple, yet accurate, flat shell finite elements. Depending on a mixed formulation, these assumed stress membranes are normally integrated using full integration. However, this is not necessarily optimal. Reduced integration using modified quadratures decreases the effects of membrane-bending locking, while the accuracy and rank of the formulation is not impaired. Copyright ©2003 John Wiley & Sons, Ltd. [source]

On the classical shell model underlying bilinear degenerated shell finite elements: general shell geometry

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2002
Mika Malinen
Abstract We study the shell models arising in the numerical modelling of shells by geometrically incompatible finite elements. We build a connection from the so-called bilinear degenerated 3D FEM to the classical 2D shell theory of Reissner,Naghdi type showing how nearly equivalent finite element formulations can be constructed within the classical framework. The connection found here facilitates the mathematical error analysis of the bilinear elements based on the degenerated 3D approach. In particular, the connection reveals the ,secrets' that relate to the treatment of locking effects within this formulation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the classical shell model underlying bilinear degenerated shell finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2001
Mika MalinenArticle first published online: 2 AUG 200
Abstract We study the shell models arising in the numerical modelling of shells by bilinear degenerated shell finite elements. The numerical model of a cylindrical shell obtained by using flat shell elements is given an equivalent formulation based on a classical two-dimensional shell model. We use the connection between the models to explain how a parametric error amplification difficulty or locking is avoided by some elements. Copyright © 2001 John Wiley & Sons, Ltd. [source]