A Simple and Efficient Large-Displacement Formulation for Beam Elements

Abstract A simple and effective finite element formulation of beam-column stiffness matrix with the consideration of second-order displacement is presented. The derived second-order stiffness matrix is the simple addition of the small-displacement stiffness matrix and a few other component matrices. The matrix is derived closed form and no integration is necessary during the formation of the element stiffness matrix. The simple additive relation makes it easy to understand the composition of the second-order stiffness matrix and the meaning of each component matrix. The closed-form formulation eliminates the potential numerical error and considerably reduces the amount of computation thereby, increasing the computing speed. The standard finite element approach presented in this paper makes the beam-column compatible with other finite elements and can be incorporated into existing finite element programs with little modification. The analysis of a simply supported beam with axial restraints using the beam-column element shows a good correlation with the test results.