Two refined non-conforming quadrilateral flat shell elements

Two re ned quadrilateral at shell elements named RSQ20 and RSQ24 are constructed in this paper based on the re ned non-conforming element method, and the elements can satisfy the displacement compatibility requirement at the interelement of the non-planar elements by introducing the common displacements suggested by Chen and Cheung. A re ned quadrilateral plate element RPQ4 and a plane quadrilateral isopara- metric element are combined to obtain the re ned quadrilateral at shell element RSQ20, and a re ned quadrilateral at shell element RSQ24 is constructed on the basis of a RPQ4 element and a quadrilateral isoparametric element with drilling degrees of freedom. The numerical examples show that the present method can improve the accuracy of shell analysis and that the two new re ned quadrilateral at shell elements are e cient and accurate in the linear analysis of some shell structures