A thin cylindrical shell finite element based on a mixed formulation

Altman, Wolf; Iguti, Fernando

doi:10.1016/0045-7949(76)90065-1

Cited by 14 publications

(2 citation statements)

References 10 publications

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“…The displacements and forces have been assumed separately, i.e., independent of each other in the studies on the mixed method [Herrman (1967); Visser (1969); Poceski (1975); Reddy and Oden (1975); Altman and Iguti (1976); Talaslidis and Wunderlich (1979); Aköz and Kadıo g glu (1996)]. They assumed that w ¼ f ðw j Þ and…”

Section: Introductionmentioning

confidence: 99%

A mixed finite element formulation for timoshenko beam on winkler foundation

Ergüven

Gedikli

2003

Computational Mechanics

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A mixed formulation for Timoshenko beam element on Winkler foundation has been derived by defining the total curvature in terms of the bending moment and its second order derivation. Displacement and moment have been chosen as primary variables, while slope and first derivation of moment have been chosen as secondary variables. The behaviour matrix for Timoshenko beam element has been obtained in mixed form by using weak formulation with equilibrium and compatibility equations. The presented formulation makes the analysis of beams free of shear locking.

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Section: Introductionmentioning

confidence: 99%

A mixed finite element formulation for timoshenko beam on winkler foundation

Ergüven

Gedikli

2003

Computational Mechanics

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“…The straight edges are free while the curved edges are supported on rigid diagrams along their plan considering the symmetry of the problem only one quarter of the roof is analyzed. The results obtained by the new present element for the vertical displacement at the midpoint B of the free edge of the roof are compared to other kinds of shells elements Omurtag et al [23]; Altman et al [24] as shown in Table 1. Table 1 shows the new present element shows very good agreement.…”

Section: Patch Testmentioning

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 functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells

Aköz

Özütok

2000

Int. J. Numer. Meth. Engng.

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In this study a higher-order shell theory is proposed for arbitrary shell geometries which allows the cross-section to rotate with respect to the middle surface and to warp into a non-planar surface. This new kinematic assumption satis"es the shear-free surface boundary condition (BC) automatically. A new internal force expression is obtained based on this kinematic assumption. A new functional for arbitrary shell geometries is obtained employing Ga( teaux di!erential method. During this variational process the BC is constructed and introduced to the functional in a systematic way. Two di!erent mixed elements PRSH52 and CRSH52 are derived for parabolic and circular cylindrical shells, respectively, using the new functional. The element does not su!er from shear locking. The excellent performance of the new elements is veri"ed by applying the method to some test problems.(i) The theory of shells used in the formulation of thin or thick shells theories (Kirchho!, Reissner and higher-order shell theories) (ii) The chosen element, independent parameters, element interpolation function and special techniques such as reduced/selective integration, discrete Kirchho! theory, etc. (iii) The method used to derive FEM such as potential energy theorem, Hu}washizu and Hellinger}Reissner theory, variational formulation, weak formulation, Ga( teaux derivatives.Kirchho! hypothesis states that the normal remains straight and normal to the middle surface. The conventional treatment of shell structures based on Kirchho! hypothesis de"nes fully the displacement pattern by the middle surface. A great di$culty arises in satisfying the necessary continuity of slopes at interface. Also, Kirchho! hypothesis cannot take into account the transverse shear [6].Despite these di$culties, an extensive literature exists on applications of the FEM to Kirchho! shells. Detailed references to these approaches can be found in Zienkiewicz and Cheung [10], Przemieniecki et al. [11], De Veubeke [12], Zienkiewicz and Holister [13], Argyris [14], Clough and Tocher [15], and Jones and Strome [16]. In Reissner plate theory only C shape function continuity is required; hence, an interpolation "eld is more easily constructed [17,18].Most of the C shell elements that have appeared in the literature, have been derived by means of the potential energy theorem assuming the displacement and two rotations as independent parameters [19]. These elements, often exhibit the well-known shear-locking phenomenon [5,6]. Shear-locking mechanism has been studied and explained by numerous authors [19,20].To alleviate shear locking, Zienkiewicz et al. [20] have introduced the reduced integration, followed by Pawsey and Clough who have introduced the selective integration [22}26]. In dynamic analysis the last method leads to zero energy modes to avoid the di$culty. Belytschko [27] has developed the stabilization matrix.Also discrete Kirchho!}Mindlin element has been developed by numerous authors [27}29]. Discrete Kirchho! elements impose the Kirchho! conditions are at a discret...

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A thin cylindrical shell finite element based on a mixed formulation

Cited by 14 publications

References 10 publications

A mixed finite element formulation for timoshenko beam on winkler foundation

A mixed finite element formulation for timoshenko beam on winkler foundation

Strain-Based Finite Element Analysis of Stiffened Cylindrical Shell Roof

A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells

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