Stability Analysis of Spatial Cubic Spline Geometric Nonlinear Beam Element Considering the Second-Order Effect

To analyze the stability problem of spatial beam structure more accurately,a spatial cubic spline geometric nonlinear beam element was proposed considering the second-order effect.The deformation field was built with cubic spline function,and its curvature degree of freedom(DOF) was eliminated by static condensation method.Then we got the geometric nonlinear stiffness matrix of the new spatial two-node Euler-Bernoulli beam element.Several examples proved calculation accuracy of the critical load by meshing a bar to one element using the method of this paper was equivalent to mesh a bar to 3 or 4 traditional nonlinear beam elements.