A higher-order quadrilateral shell finite element for geometrically nonlinear analysis

In this paper, we present a geometrically nonlinear formulation for a nine-node shell finite element and demonstrate its performance. The total Lagrangian formulation is utilized to allow for large displacements and large rotations. The mixed interpolation of tensorial components (MITC) technique is applied to effectively reduce the membrane and shear locking phenomena without refining mesh, introducing additional nodes, and using reduced integrations. Many-core accelerators with GPU-compatible libraries are used to achieve the highest speed-up for the solution process. The performance of the present nine-node shell element is compared with those of the four-node and six-node shell elements in several benchmark problems, including Cook's skew beam, cantilever plate, pinched cylindrical shell, slit annular plate, and hemisphere shell. The present element achieves excellent performance even when the coarse mesh is used.