A new cylindrical shell finite element based on simple independent strain functions

Ashwell, D.G.; Sabir, A.B.

doi:10.1016/0020-7403(72)90074-4

Cited by 120 publications

(46 citation statements)

References 13 publications

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“…The advantages of the finite elements based on strain approach in comparison with the classical elements based on the displacement model have been illustrated on several two-and three-dimensional elements [4][5][6][7][8]. Belarbi and Charif [8] have developed a hexahedral solid finite element (SBH8) based on the strain approach.…”

Section: Introductionmentioning

confidence: 99%

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A new rectangular finite element based on the strain approach for plate bending

Belounar

Guenfoud

2005

Thin-Walled Structures

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Section: Introductionmentioning

confidence: 99%

“…The first elements developed concerned only with curved elements [4,5]. This approach was later extended to plane elasticity elements [6,7], and three-dimensional elasticity [8].…”

Section: Introductionmentioning

confidence: 99%

A new rectangular finite element based on the strain approach for plate bending

Belounar

Guenfoud

2005

Thin-Walled Structures

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“…The displacement functions (including rigid body displacements) for cylindrical shell element shall be expressed as [13] MT3 triangular element: θ x , θ y and w are linear interpolation functions; MT3-R triangular element: reduced integration with one point quadrature for shear terms; MIT3 triangular element: modified shear strain terms by Bathe et al [10] ; RDTM triangular element: based on Timoshenko beam function [7] ; MQ4 quadrilateral element: θ x , θ y and w are bilinear interpolation functions; MQ4-R quadrilateral element: reduced integration with one point quadrature for shear terms; MTI4 quadrilateral element: modified shear strain terms by Bathe et al [10] ; RDQM quadrilateral element: based on Timoshenko …”

Section: The Patch Test Function Of Constant Shear For the Cylindricamentioning

confidence: 99%

Functions for patch test in finite element analysis of the Mindlin plate and the thin cylindrical shell

Wanji

Wang

Zhao

2009

Sci. China Ser. G-Phys. Mech. Astron.

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Current patch test for Mindlin plate element only satisfies the zero shear deformation condition. The patch test of non-zero constant shear for Mindlin plate problem cannot be performed. For shell element, the patch test does not even exist. Based on the theory of enhanced patch test proposed by Chen W J (2006), the authors proposed the enhanced patch test function for Mindlin plate and thin cylindrical shell elements. This enhanced patch test function can be used to assess the convergence of the Mindlin plate and cylindrical thin shell elements. Mindlin plate, thin cylindrical shell, finite element, enhanced patch test, test functionFinite element method has been widely used in the engineering industries. Various elements were developed for solving suitable problems. However, the convergence theory of the finite element is still not complete. Patch test has long been used as criteria for assessing the convergence of the finite element. Improvement was made in the research of convergence theory [1] . However, the applications of the existing patch test are limited in 2D/3D elasticity and thin plate problem with homogeneous differential equations. It is difficult to accurately assess the convergence of the problem with non-homogeneous different equations, for example, none of the current existing Mindlin plate elements can pass the constant shear patch test.The potential energy function of Mindlin plate element contains only the first order derivatives of the displacement. Therefore, it is C 0 type element. It is fairly easy to establish interpolation functions of deflection and rotation, which satisfy the C 0 continuity condition. However, the C 0 type of element is ineffective in solving the problem with shear-locking phenomenon when the plate becomes thin enough. It even cannot guarantee the convergence of the moderately-thick plate. In the past, the patch test for Mindlin plate element was performed by means of numerical computation of pure bending and pure torsion [2,3] of a small-scale plate. However, this patch test only satisfied the C 0 continuity condition.The evaluation of the shear locking phenomenon has relied on numerical computations on thin plate problem. The elements developed by Batoz [4,5] can eliminate locking phenomenon for very thin plate. However, theoretically, no element is free of shear locking.

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“…This approach is based on determining the exact terms representing all the rigid body modes together with the displacement functions representing the straining of the element by assuming independent strain functions insofar as it is allowed by the compatibility equations. This approach has successfully employed in the development of curved shell elements by Ashwell et al [9][10]; Sabir et al [11-12-13-14]; El-Erris [15][16] and Mousa [17-18-19-20-21-22]. These elements were found to yield faster convergence with other available finite elements.…”

Section: Introductionmentioning

confidence: 99%

Strain-Based Finite Element Analysis of Stiffened Cylindrical Shell Roof

Mousa¹

2017

AJCE

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Abstract:A new triangular cylindrical shell finite element is used to obtain an elastic linear analysis of a cylindrical shell roof. The element's displacement fields are in terms of curvilinear coordinates, satisfy the exact requirement of rigid body modes of deformation and have five degrees of freedom at each of the three corner nodes. The efficiency of the developed element is first tested and then applied to analyze stiffened cylindrical shell roof. The results of the displacement and stress resultant along the stiffener are presented and a parametric study is carried out to find the effect of the varying geometry of the stiffener and the effect of axis rotation of the beam on the level of the internal forces.

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A new cylindrical shell finite element based on simple independent strain functions

Cited by 120 publications

References 13 publications

A new rectangular finite element based on the strain approach for plate bending

A new rectangular finite element based on the strain approach for plate bending

Functions for patch test in finite element analysis of the Mindlin plate and the thin cylindrical shell

Strain-Based Finite Element Analysis of Stiffened Cylindrical Shell Roof

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