Form Finding Analysis Of Tensile Membrane Structuresby Curved Quadrilateral Element

Tensile membrane structures resist external forces by prestress force and flexing. The selection of the initial forms of such structures allows little freeness, which must take into account the equilibrium and architect need. Based on the geometrical nonlinear finite element (GNFE) theory, a curved quadrilateral isoperimetric element with 8 nodes for initial form analysis of tensile membrane structures is presented. The main works of this thesis are as follows: according to the GNFE theory, stress and strain tensors are selected; equations of the membrane structures-related problem, say the large displacements and small strains one, are derived; the mode of curved membrane element in curvilinear coordinates are studied, and the components caused by curvatures are thereupon added to the equilibrium equations; The element displacement mode and interpolate functions are presented; the expressions of element stiffness matrix and nodal force array are derived; the methods of solving nonlinear equations set were also briefly discussed; the methods of modifying the constitutive relationship matrix of membrane elements were explored, with the property of orthotropy under consideration; several special problems, such as minimal surface and wrinkling, are studied; the equations of curved cable element with 3 nodes are figured out, and the complete procedures of solving the initial form problems are analyzed. A second job of this thesis is the use of constant strain triangle element as comparison to test the accuracy and efficiency of the previous method. The equations of constant strain triangle and cable element are also derived. FORTRAN 90 language is employed to make programs of computer aided initial form analysis for membrane structures. And several numerical examples are given.Numerical examples indicate that the method of this thesis is efficient, reliable, and stable. More accurate results is available with relatively fewer iterations to satisfy the need of engineering, and which is not sensitive to the division of grids with even errors and stable results.