Article

# A linear quadrilateral shell element with fast stiffness computation

Institut für Werkstoffe und Mechanik im Bauwesen, Technische Universität Darmstadt, Petersenstraße 12, Darmstadt D-64287, Germany; Institut für Baustatik, Universität Karlsruhe (TH), Kaiserstraße 12, Karlsruhe D-76131, Germany

Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.62). 01/2005; DOI: 10.1016/j.cma.2004.11.005 - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we address the extension of a recently proposed reduced integration eight-node solid-shell finite element to large deformations. The element requires only one integration point within the shell plane and at least two integration points over the thickness. The possibility to choose arbitrarily many Gauss points over the shell thickness enables a realistic and efficient modeling of the non-linear material behavior. Only one enhanced degree-of-freedom is needed to avoid volumetric and Poisson thickness locking. One key point of the formulation is the Taylor expansion of the inverse Jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes. The transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept. Further crucial points are the Taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the Taylor expansion of the second Piola–Kirchhoff stress tensor with respect to the normal through the center of the element. Copyright © 2010 John Wiley & Sons, Ltd.International Journal for Numerical Methods in Engineering 08/2010; 85(3):289 - 329. · 2.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.International Journal of Non-Linear Mechanics 01/2007; 42(6):864-881. · 1.35 Impact Factor -
##### Article: A mixed shell formulation accounting for thickness strains and finite strain 3d material models

[Show abstract] [Hide abstract]

**ABSTRACT:**A non-linear quadrilateral shell element for the analysis of thin structures is presented. The Reissner–Mindlin theory with inextensible director vector is used to develop a three-field variational formulation with independent displacements, stress resultants and shell strains. The interpolation of the independent shell strains consists of two parts. The first part corresponds to the interpolation of the stress resultants. Within the second part independent thickness strains are considered. This allows incorporation of arbitrary non-linear 3d constitutive equations without further modifications. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch test. The essential feature of the new element is the robustness in the equilibrium iterations. It allows very large load steps in comparison with other element formulations. We present results for finite strain elasticity, inelasticity, bifurcation and post-buckling problems. Copyright © 2007 John Wiley & Sons, Ltd.International Journal for Numerical Methods in Engineering 10/2007; 74(6):945 - 970. · 2.06 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.