Derivation and implementation of one-point quadrature quadrilateral shell element with MITC4+ method (MITC4+R)

Abstract

In this work, a novel degenerated shell element called MITC4+R is developed, which is based on the MITC4+ (an improved MITC quadrilateral shell element) and reduced integration with one point quadrature. The assumed natural strain method is employed to construct the membrane and shear strains. A physical stabilization term is derivated after the assumed natural strains are decomposed into the linear and a constant term with respect to the natural coordinates. The hourglass modes owing to one point quadrature is controlled in the computation of deformation by introducing this physical stabilization term. The developed degenerated shell element is successfully implemented into the implicit static and explicit dynamic analyses. In order to verify its computational accuracy and efficiency, several standard benchmarks and practical problems are performed. These results show that the MITC4+R element eliminates various locking problems common to shell elements, and it significantly improves the computational efficiency of the original MITC4+ element. Meanwhile, the MITC4+R owns the same accuracy and highly consistent convergence as the original MITC4+ element, making it more promising for practical applications.