Spatial beam analysis with large displacement for deployable truss structures

A formula of multibody finite element analysis based on the corotational formulated finite element method and the direct coordinate partitioning for deployable truss structures is proposed. A beam element used in linear finite element analyses is a basic element in the formula. A corotational frame is defined by node coordinate systems attached to a beam element. A tangent stiffness matrix contains a virtual rotation displacement of the corotational frame. By the appropriate transformation of this virtual displacement, a simple geometric stiffness for the formula is obtained. The formula makes it possible to analyze the deploying motions of large deformed deployable truss structures, to be applicable to general finite elements, and to increase convergence speed of the Newton method in a solution algorithm. This improvement is achieved by neglecting virtual work done by rigid body motion in the process of employing the geometric stiffness to the conventional formula. A validity of this formula is confirmed through results of a numerical deployment analysis of a deployable beam structure.