Development of corotational formulated FEM for application to 30m class large deployable reflector

Abstract

JAXA, Japan Aerospace Exploration Agency, is now developing a corotational formulated finite element analysis method and its software "Origami/ETS" for the development of 30m class large deployable reflectors. For the reason that the deployable reflector is composed of beams, cables and mesh, this analysis method is generalized for finite elements with multiple nodes, which are commonly used in linear finite element analyses. The large displacement and rotation are taken into account by the corotational formulation. The tangent stiffness matrix for finite elements with multiple nodes is obtained as follows; the geometric stiffness matrix of two node elements is derived by taking variation of the element's corotational matrix from the virtual work of finite elements with large displacement; similarly the geometric stiffness matrix for three node elements is derived; as the extension of two and three node element theories, the geometric stiffness matrix for multiple node elements is derived; with the geometric stiffness matrix for multiple node elements, the tangent stiffness matrix is obtained. The analysis method is applied for the deployment analysis and static structural analysis of the 30m class large deployable reflector. In the deployment analysis, it is confirmed that this method stably analyzes the deployment motion from the deployment configuration to the stowed configuration of the reflector. In the static analysis, it is confirmed that the mesh structure is analyzed successfully. The 30m class large deployable reflector is now still being developed and is about to undergo several tests with its prototypes. This analysis method will be used in the tests and verifications of the reflector.