A rotation-free thin shell quadrilateral

FLORES FERNANDO G.; ESTRADA CARLOS F.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ELSEVIER SCIENCE SA

Lugar: Amsterdam; Año: 2007 vol. 196 p. 2631 - 2646

0045-7825

In this paper a four-node quadrilateral finite element for the analysis of smooth thin shells is presented. The main feature of the element,an extension of previous developments in triangles, is that the translational displacements of the middle surface are the onlydegrees of freedom. The membrane behavior results from a standard bilinear interpolation of the geometry within the element. Withthe aim of an efficient element in codes with explicit time integration, one point quadrature is used in the element area. To avoid spuriousdeformation modes (hourglass modes) membrane forces resulting from a perturbation stabilization technique are included. For the computationof the curvature tensor a patch of five elements (the element and the four adjacent elements) is defined. The curvature field,assumed constant within the element, is expressed in terms of the deformation gradient at the element boundary and is dependent onthe position of the twelve nodes included in the patch. In some problems a bending deformed configuration may occur without associatedenergy. A cost-effective perturbation stabilization scheme is used to control it. General boundary conditions are shown to be easily implemented.The element denoted BSQ (for Basic Shell Quadrilateral) is based on a Total Lagrangian Formulation and has been implementedin codes with implicit and explicit integration. To assess the element performance and convergence properties a set ofnumerical examples are presented, including geometrically linear and non-linear problems with large strain plasticity. The resultsobtained show good convergence properties. For several examples different values of the stabilization coefficients have been consideredto study the sensitivity of the results to such coefficients. In general this sensitivity appears to be low as the mesh is refined and the resultsare obtained with a fixed set of coefficients.