A linear quadrilateral shell element with fast stiffness computation

Gruttmann, Friedrich; Wagner, Werner

doi:10.1016/j.cma.2004.11.005

Cited by 53 publications

(29 citation statements)

References 32 publications

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“…1 and 2. The linear version [34] based on a Hellinger-Reissner functional with flat projection and warping transformation exhibits a slightly oscillating convergence behaviour where this is not the case for the present element. The displacements u z and u y are plotted for the respective load case on the deformed configurations in Fig.…”

Section: Linear Test Problem: Twisted Beammentioning

confidence: 98%

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A robust non-linear mixed hybrid quadrilateral shell element

Wagner

Gruttmann

2005

Int. J. Numer. Meth. Engng

107

142

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Section: Linear Test Problem: Twisted Beammentioning

confidence: 98%

“…where M I (h I ) is defined in (34) and the allocation of the midside nodes M, L to the corner nodes in (30).…”

Section: Second Variation Of the Functionalmentioning

confidence: 99%

A robust non-linear mixed hybrid quadrilateral shell element

Wagner

Gruttmann

2005

Int. J. Numer. Meth. Engng

107

142

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“…Gru05-Gruttmann and Wagner [46]: ANS mixed stress resultant element (ri) Gru04-Gruttmann and Wagner [64]: ANS mixed stress resultant element (ri) Cho03-Cho and Roh [65]: EAS element (fi) Car02-Cardoso et al [66]: ANS element (ri) And93b-Andelfinger and Ramm [19]: EAS/ANS element EAS7-ANS (fi) Sim89-Simo and Fox [67]: ANS mixed stress resultant element (fi) Bat85-Bathe and Dvorkin [1]: ANS element (fi)…”

Section: Full Integration (Fi) and Reduced Integration (Ri) Shell Elementioning

confidence: 98%

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems

Schwarze

Reese

2009

Numerical Meth Engineering

144

147

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SUMMARYIn this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu-Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional material models can be implemented without additional assumptions.

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“…For the geometrical and physical linear case an analytical integration of all matrices is possible along with a flat projection, see Ref. [24] on basis of a Hellinger-Reissner functional.…”

Section: Linearized Variational Formulationmentioning

confidence: 99%

Structural analysis of composite laminates using a mixed hybrid shell element

Gruttmann

Wagner

2005

Comput Mech

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The structural analysis of thin composite structures requires robust and effective shell elements. In this paper the variational formulation is based on a Hu-Washizu functional with independent displacements, stress resultants and shell strains. For the independent shell strains an enhanced interpolation part is introduced. This yields an improved convergence behaviour especially for laminated shells with coupled membrane and bending stiffness. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch test. The formulation is tested by several nonlinear examples including bifurcation and post-buckling response. The essential feature of the new element is the robustness in nonlinear computations with large rigid body motions. It allows very large load steps in comparison to standard displacement models.

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A linear quadrilateral shell element with fast stiffness computation

Abstract: A linear quadrilateral shell element with fast stiffness computation

Cited by 53 publications

References 32 publications

A robust non-linear mixed hybrid quadrilateral shell element

A robust non-linear mixed hybrid quadrilateral shell element

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems

Structural analysis of composite laminates using a mixed hybrid shell element

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