Four-node Membrane Element of Vector Form Intrinsic Finite Element for Large Deformation Analysis of Membrane Structures

Based on fundamental principles of the vector form intrinsic finite element (VFIFE), the basic formulas of 4-node quadrilateral membrane element were first derived in this paper. The procedure for the determination of pure nodal deformation through reverse movement was elaborated, and the method for the calculation of internal nodal forces through deformation coordinate system was presented. Feasible approaches were also proposed for several issues for 4-node membrane element, including the location statuses and the numerical integration for internal forces. A computer program of 4-node membrane element was developed. By the analysis of the numerical example, the correctness and validity of the membrane element theory and the computer program were verified. Then the approach was applied for more analysis of large deformation and large rotation problems of membrane structures, including cushion inflating and cloth draping.