Polygonal shell elements with assumed transverse shear and membrane strains

In this study, a new polygonal shell element is developed to provide greater flexibility in mesh design of complex shell structures. Wachspress coordinates are used to construct shape functions for polygonal shell elements. An assumed covariant shear strain field with respect to the element natural coordinate system is defined by employing the mixed interpolation of tensorial components approach to avoid transverse shear locking in polygonal shell elements. Moreover, an assumed covariant membrane strain field is constructed by using characteristic geometry and displacement vectors defined on quadrilateral subdomains of polygonal shell elements to alleviate membrane locking due to the element curvature. Some benchmark shell problems are solved to evaluate the performance of the proposed polygonal shell elements. Numerical experiments show that they converge much better than triangular shell elements and comparable to quadrilateral shell elements.