A new strategy for finite-element analysis of shell structures using trimmed quadrilateral shell meshes: A paving and cutting algorithm and a pentagonal shell element

In this paper, we present a novel scheme to generate trimmed quadrilateral shell meshes using a paving and cutting algorithm. Paving with well-shaped quadrilateral shell elements is initiated from a seed element placed in the interior of a geometric surface and proceeds around the boundary of the paved mesh in all directions. The paved all-quadrilateral mesh covering the entire domain is cut by the boundaries of a geometric surface. Pentagonal shell elements are created by cutting the corners of quadrilateral shell elements at the domain boundaries. Pentagonal shape functions are constructed using Wachspress coordinates, and assumed natural strains in the form of the mixed interpolation of tensorial components approach are employed to avoid the transverse shear locking of pentagonal shell elements. Several numerical examples are investigated to show the effectiveness of the present method.