A NEW BEAM ELEMENT FOR SECOND-ORDER EFFECT ANALYSIS OF BEAM STRUCTURES

A new two-node beam element considering the second-order effect of beams is developed. Based on the interpolation theory, the displacement fields of the three-node Euler-Bernoulli beam element are constructed at first: the quintic Hermite interpolation polynomial is used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then the linear and geometric stiffness matrices of the three-node beam element are derived according to the nonlinear finite element theory. Finally the degrees of freedom of the middle node of the element are eliminated using the static condensation method, and a new two-node beam element including axial-force effect is obtained. The results of several examples show that the second-order displacements and internal forces with high precision can be obtained with this new beam element.