Alleviation of membrane locking in continuum-mechanics based 4-node quadrilateral shell elements

Abstract

In this paper, several continuum-mechanics based finite elements are developed by remedying their deficiencies. Our focus is to develop reliable and efficient shell and solid-shell elements satisfying the ellipticity, consistency and inf-sup conditions. That is, basic tests including the isotropy, patch and zero energy mode tests should be passed and the elements should show uniformly optimal convergence to reference solutions regardless of asymptotic categories of the shell structures considered. Membrane locking severely deteriorates the performance of the of 4-node quadrilateral shell elements when curved geometries are solved with distorted meshes. Previous studies to remedy membrane locking based on reduced integration and assumed strain method has not been successful in developing reliable 4-node shell elements. In the present study, membrane locking in 4-node quadrilateral shell elements is deeply studied for arbitrary mesh geometry. Three new 4-node shell elements developed are presented. In addition, 6-node triangular solid-shell element is developed as an extension of previous shear locking treatment of 3-node shell element and the remedies of thickness locking in the previous literatures. The newly developed continuum-mechanics based shell elements are examined through basic numerical tests as well as comprehensive convergence studies encompassing the practical range of shell thickness.