Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes

摘要

This paper presents an efficient scheme to remove the membrane locking of 4-node quadrilateral flat shell elements using various non-conforming (NC) modes. A series of flat shell elements are established by a linear combination of NC membrane and plate-bending elements which show no signs of membrane locking even though the coarse meshes are used. In the element formulation, NC displacement modes are extensively used for improvement of element behaviors. Hierarchical NC modes used in the membrane component of flat shell element are the most important modes as they supply the polynomial terms which are absent in the derivatives of bilinear shape function to achieve the complete consistence of variable fields. Some detailed discussions for removing membrane locking are also given based on the results of the numerical tests.