A class of simple and efficient degenerated shell elements—Analysis of global spurious-mode filtering

Abstract

Results obtained for a class of degenerated shell elements formulated in convected (curvilinear) coordinates are presented. Each node has five degrees of freedom, with displacements expressed directly in global coordinates. Rotations of directors are treated in an efficient manner that preserves continuity across interelement boundaries, and allows treatment of general boundary conditions. A contibuous field of local triads can be generated by a method proposed herein. A plane stress linear constitutive relation is developed with respect to a general system of curvilinear coordinates whose transverse coordinate is not necessarily normal to the shell lamina. Element stiffness matrices are obtained in a form directly ready for global assemblage, avoiding completely local-global transformations. Uniform reduced-integration is employed to relieve shear and membrane locking. It is shown analytically that spurious zero-energy modes are invariant under change of element geometry. These spurious modes are filtered in a reliable and efficient manner that preserves consistency of the element, and is insensitive to change of material constants and geometric parameters. Spurious-mode filtering is performed directly at the global level. The element passes patch tests, and is robust under severe element distortions. Extensive numerical results are presented to assess the performance of the element. Practical aspects of implementing the present formulation are also discussed. The same filtering methodology can be applied to other shell formulations as well.