Theory Research On Form Finding Of Cable Nets And Membrane Structures

Cable nets and membranes are kinds of new and original spatial tension structures. Due to their special mechanical properties, they have much difference with traditional structures in analysis, design and construction. Form finding is a crucial problem in the design of cable nets and membrane structures and is the basis for load analysis and membrane cutting. In the dissertation, this problem is systematically studied and some practical method and theory for calculation are proposed, which have great value and importance in engineering practice and analytical theory.Started from establishment of the equilibrium equation for structural assembly, the four basic vector subspaces' meaning and calculation method are discussed. The two aspects of structure system's instability are analyzed and the method to segregate internal mechanisms and rigid-body mechanisms is presented. The distinguish condition and algorithm procedure for first-order infinitesimal mechanisms are introduced.Based on the geometrical nonlinear theory, the equations for form finding of cable nets and membrane structures are established. At the same time a new form finding method is presented which is built on the nonlinear analysis of cable nets and membrane structures but with no requirement to assemble global stiffness matrices. It is more simple and efficient than nonlinear displacement method.According to the nodal equilibrium condition, the basic formulations are constructed for form finding of cable nets by force density method and of tension membranes and air-supported membranes by surface stress density method. Simultaneously the following conclusions are proved: the square sum has the minimal value in the equilibrium surface of cable nets with equal force density; the equilibrium surface of cable nets with equal internal forces is just the minimum surface; the equilibrium surface of tension membranes with equal stresses is just the minimum surface. The inherent relationship between the two different form finding methods is founded and it is demonstrated that the surface stress density method is in fact a special case of nonlinear displacement method.The basic theory and solution strategy of dynamic relaxation method for form finding are systematically discussed. The re-initialisation at kinetic energy peaks during calculation and the numerical stability are analyzed. And the calculation method of element internal forces and nodal stiffness for cable nets, tension membranes and air-supported membranes are given. In which a new way to calculate element internal forces and nodal stiffness directly without transformation from membrane element to equal bar element is submitted. It makes communication between dynamic relaxation method and nonlinear displacement method.The solution strategies of nonlinear displacement method and force density method for initial form finding of cable nets are given and the algorithm programs are designed. They are proved to be correct by numerical examples. And some important conclusions are obtained: In the nonlinear displacement method, material modulus of elasticity is a major factor which has influence on the final shape and internal forces; in the force density method, the force densities of cable elements are crucial parameters, the shape and rigidity of cable nets are governed by the force density ratio between boundary cables and internal cables but not their absolute value; the cable nets deform seriously near control points during form finding by the nonlinear displacement method; by assuming different force density ratio and control points' coordinates different surfaces can be obtained from arbitrary initial plane meshes, and the force density method is simple and efficient for form finding of cable nets.The solution strategies for form finding of tension membranes and air-supported membranes with equal stress densities or equal stresses are proposed and the algorithm programs are designed. They are proved to be correct by numerical examples. And some important conclusions are obtained: In the stress densit...