Internal Force Analysis Of Tensile Membrane Structures By Curved Quadrilateral Element

Membrane structure is one kind of spatial structure that develops rapidly in thepast several years. Tensile membrane structures will deform largely under theexternal forces and the internal force will distribute again. The deforming and theinternal force under the external forces are studied in the internal force analysis.Based on the geometrical nonlinear finite element (GNFE) theory, thepaper use a curved quadrilateral isoperimetric element with 8 nodes to makeprograms of computer aided the internal force analysis for membranestructures. The main works of this thesis are as follows: according to theGNFE theory, the mode of curved membrane element in curvilinearcoordinates are studied, and the components caused by curvatures arethereupon added to the equilibrium equations;The external load which actson the membrane structures are studied and the equivalent nodal force arrayfor snow load and wind load are derived. the methods of modifying theconstitutive relationship matrix of membrane elements were explored, withthe property of orthotropy under consideration;For the wrinkling element ofthe membrane structures, the average main stress wrinkling judge rule ispresented, and the displacement converge rule and the imbalance forceconverge rule are used at the same time. the methods of solving nonlinearequations set were also briefly discussed;FORTRAN 90 language is employed to make programs of computeraided the internal force analysis for membrane structures with cable elementand membrane element. And the numerical examples, are systematicallyexamined for internal force considering different parameter combinations ofbeginning prestress, load style and height to span. The parameters ofbeginning and height to span produce to the internal force and the distortionaffects greatly, but other parameter influences is not big.Numerical examples indicate that the method of this thesis is efficient,reliable, and stable. The judging rule presented in this paper make doing withwrinkling element easier, but keeps high precision for integration.