A COROTATIONAL UPDATED LAGRANGIAN FORMULATION FOR GEOMETRICALLY NONLINEAR ANALYSIS OF 2D FRAMES

A method is presented for geometrically nonlinear analysis of 2D frames. An updated Lagrangian (UL) formulation is used to calculate the incremental nodal displacements, and incremental nodal forces are recovered by a corotational formulation whose configuration (Cr) is derived from a rigid-body motion of the last calculated configuration (C1) in equilibrium. Firstly, the equation of virtual work is expressed in terms of incremental nodal natural deformations in Cr; then, the relations are deduced between the incremental nodal natural deformations in Cr and the incremental nodal displacement vector in C1. Adopting the relations in the equation of virtual work, the tangent stiffness matrix for incremental nodal forces is obtained for Cr, and it can pass a rigid-body test. The analysis has considered the loaded deformations which will result in an additional matrix in the tangent stiffness matrix. The numerical examples show that: with fewer elements, the presented method can achieve similar precision to UL formulation；the matrix with respect to the loaded deformation can effectively improve the efficiency, but it may result in membrane locking if the deformation is large.