Geometrical Nonlinear Analysis of Plane Problems by Corotational Formulation

Abstract

This study deals with the geometric nonlinear analysis of the plane problem based on the corotational formulation. Both analytical solutions and hybrid stress functional will be utilized in the proposed technique. A quadrilateral four-node element with drilling degrees of freedom is proposed for the finite-element analysis. The corotational method is applied for the nonlinear behavior. In this way, small strains and rigid body motions can be separated. Based on analytical solution, the hybrid stress scheme is used in the local coordinates for small strains. By using Allman’s quadratic displacement, the boundary condition for this element is introduced. In this approach, added drilling degrees of freedom increase the accuracy and robustness of the element. Furthermore, the corotational formulas are written in the local and global coordinates system to derive the nonlinear relations. These equations were solved by using the arc-length algorithm. To investigate the accuracy and capability of the suggested element, several numerical tests are performed. Findings prove the advantage of the proposed element in the geometric nonlinear analysis of plane problems.