A SPATIAL BEAM ELEMENT AND ITS APPLICATION TO BUCKLING ANALYSIS FOR FRAMED STRUCTURES

A spatial two-node nonlinear Euler-Bernoulli beam element is derived. The displacement fields of the spatial three-node beam element are constructed using the interpolation theory of the conventional finite element method. The quadratic Lagrange interpolation polynomial is used for the torsional and axial displacement fields and the quintic Hermite interpolation polynomial for the transverse displacement fields. Then the linear and geometric stiffness matrices of the three-node beam element are derived from the displacement fields. A three-dimensional two-node beam element is developed by eliminating the degrees of freedom of the interior node of the three-node element using the static condensation method. The results of several structural buckling examples show that only one of the new beam element has the same accuracy with that of 3―4 conventional two-node beam elements and the critical force with high accuracy can be obtained even each beam is discretized into one element.