An isoparametric quadratic thick curved beam element

Abstract

SUMMARYA three-noded curved beam element with transverse shear deformation, based on independent isoparametric quadratic interpolations, is designed from field-consistency principles. It is shown that a quadratic element that is field-inconsistent in membrane strain suffers from 'membrane locking'-i.e. an error of the second kind propagates indefinitely as the element length to thickness ratio and/or the element length to radius of curvature ratio increase, in nearly inextensional bending. However, field-inconsistency in shear strain does not lead to 'shear locking' but degrades its performance to exactly that of a field-consistent linear element. It is also seen that field-inconsistency leads to severe axial force and shear force oscillations. Error estimates for locking are derived, wherever possible, and confirmed by numerical experiments. The field-consistent element offered here is the most efficient quadratic curved beam element possible.

An accurate two-node finite element for shear deformable curved beams

“…1 Early literature 1,2 felt that the poor performance was due to the improper description of the rigid body modes. More recently, researchers 3 felt that the poor behaviour was due to both shear and membrane locking, where an overly stiff behaviour of a curved beam is due to large axial stiffness relative to the bending stiffness. The membrane locking phenomenon becomes less severe as the element becomes shallower.…”

“…Recently higher-order polynomials has been successfully used for shape functions to alleviate the locking phenomenon but they required more nodes per element or more degrees of freedom per node. [3][4][5][6][7][8][9] Some of these formulations 4 use higher-order polynomials with constraints to limit the number of nodes and/or degrees of freedom used. The most accurate element published to date is the one developed in Reference 4 which is a three-node element.…”

An effective composite laminated curved beam element

“…These early attempts [1][2][3][4][5][6] are unsuccessful and su er from an excessive bending sti ness, called membrane locking, in the limit of inextensional bending or excessive shear sti ness, called shear locking, in the limit of thin beam. To alleviate these numerical di culties, special techniques based on the most popular minimum potential energy principle are proposed, such as the selective=reduced integration technique [5,6,10], ÿeld-consistent element [11,12] and anisoparametric element [13], etc. Besides these displacement elements, hybrid-mixed ÿnite elements [14][15][16] based on the Hellinger-Reissner variational principle have been shown to be quite successful.…”

Improved Thin-Walled Finite Curved Beam Elements

“…They examined the role of the nodeless degrees of freedom and the effect of the field consistency. Prathap and Babu [9] and Babu and Prathap [10] derived a three-noded curved beam element based on the independent isoparametric interpolation and field-consistency approach which identifies the spurious constraints of the inconsistent strain field and drops them in advance. This field consistency approach ensured a variationally correct and orthogonally consistent strain field.…”