THE RIGID BODY RULE FOR THE NONLINEAR ANALYSIS OF MEMBRANE STRUCTURES

A new geometric non-linear analysis method for elastic space membrane structures is proposed. According to the rigid body rule, when an initial stressed element undergoes rigid body displacement, the directions of the nodal forces at the element will change with the rigid rotation of the element while the magnitude of the nodal forces will remain unchanged in order to keep the element in balance. A new triangular space membrane element is presented. This membrane element is composed of three bars to form a pin-joint triangle with a triangle film stretched inside. The material of the bars is assumed the same as that of the film. The geometric stiffness matrix of the proposed membrane element is derived by the geometric stiffness matrix of a spatial bar element of rigid body rule qualified. According to the rigid body rule, it is considered that the rigid body motion has the major contribution to the total deformation of the membrane element than that of the element elastic deformation. By rooting the rigid body rule into the UL incremental-iteration method, the effect of rigid body rotation is fully considered in each stage of analysis and the residual effects of natural deformation is treated by the linearization. The derivation of the geometric stiffness matrix of the proposed membrane element is quite clear without introducing any assumption on the large deformation of the membrane element and can be easily degenerated into a plane membrane element. The accuracy and efficiency of the present membrane element as well as the rigid-body-rule-rooted nonlinear analysis method are proved by the analysis of several typical space membrane structures and by the comparison with the results of other methods.