Geometrically nonlinear analysis of 2D and 3D structures by a robust Richardson extrapolation based quadrature

This study presents a novel numerical quadrature based on weighted Richardson extrapolation scheme (WRE) with suitable smoothing function for geometrically nonlinear problems. The recently developed element midpoint method (EM-method) and element edge method (EE-method) have been proposed as improved numerical methods for the traditional finite element method. These methods have significant inherent advantages, including a higher rate of convergence and accuracy, robustness in computation, and continuity in nodal gradients without modifying the basic formulation. A novel quadrature scheme is proposed on quadrilateral elements with less integration points using reduced integration to handle geometrically nonlinear problem. The capability of the developed methods is studied through two- and three-dimensional numerical examples.