Developing a New Co-rotational Method for Nonlinear Geometrical Analysis of Twodimensional Truss Structures Based on Small Strains

Most structures experience large deformations under applied loads. Due to the deforming of geometry of structures, geometrical nonlinear analysis is needed. The co-rotational method is a simple and practical technique for nonlinear geometrical analysis. In this technique, unlike other nonlinear methods, is supposed the strain of the element to be small. The aim of this research is to develop a new co-rotational method for geometrical nonlinear analysis of two-dimensional truss structures based on small strains. A co-rotational method makes the separation of rigid body motion and small strains possible for a truss element. Therefore, global and local coordinate systems are utilized. Linear stiffness matrix of two-node element is used for small strains in local coordinate systems. Then, by writing co-rotational equations, transformation matrix is introduced for this element. The transformation matrix is used to calculate tangential stiffness matrix and element node force vector in global coordinate systems. At the end, the accuracy of the proposed method is evaluated by numerical tests. These tests confirm high accuracy of the proposed element for geometrical nonlinear analysis of twodimensional truss structures.