A simple quadrilateral shell element

MacNeal, Richard H.

doi:10.1016/0045-7949(78)90020-2

Cited by 318 publications

(92 citation statements)

References 5 publications

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“…An effective method to avoid transverse shear locking is based on assumed shear strain fields first proposed in Ref. [11], and subsequently extended among others in References [12,13,14]. The variational basis for these methods is given with the Hu-Washizu functional.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Structural analysis of composite laminates using a mixed hybrid shell element

Gruttmann

Wagner

2005

Comput Mech

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“…La sous intégration est généralement réservée à la partie élastique afin d'éliminer le problème de vérouillage en cisaillement introduit par l'utilisation de fonctions d'interpolation N i linéaires, qui sont responsables d'une énergie de cisaillement artificiellement élevée [84]. L'utilisation de la sous intégration est ici étendue à la partie cinématique venant de la rotation et uniquement pour θ.…”

Section: (B) Vibrations Non Linéairesunclassified

Optimization of Shunted Piezoelectric Patches for Vibration Reduction of Complex Structures: Application to a Turbojet Fan Blade

Sénéchal¹,

Thomas²,

Deü³

2010

Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise

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“…(8), B is an interpolation matrix obtained by imposing the considered set of shape functions and J is the determinant of the Jacobian matrix. Geometric stiffness (Martin, 1966;Marcal, 1969;MacNeal, 1978) is the first order approximation of geometrically nonlinear behavior and it is particularly useful in the linearizing buckling problem. The terms in the geometric stiffness matrix for an element are linear functions of the components of stress in the element.…”

Section: Stiffness Geometric Stiffness and Mass Matrixmentioning

confidence: 99%