The Research Based On Force Density Method For Form-finding And Loadanalysis Of Pneumatic Membrane Structure

With the development of high-performance control technologies and the emergence of new membrane material, coupled with low cost, convenience factors such as the construction, the pneumatic membrane structures get people's attention once more, its applications in practical engineerings have a wide range up gradually, it is set structure, control and strict management in one embodiment for high-level structure.Currently the explorations in the field of the tensioned membrane structure and the rigid boundary membrane structure have made great progress and developed a preliminary technical standards, but for pneumatic membrane structure,China still is lack of the necessary knowledge and understanding, and no technical specifications. The broad prospect for development in pneumatic membrane structure,makes the pneumatic membrane structure in-depth study particularly essential under the present conditions that it is extremely lack of design theory and practical experience.In this paper,form-finding and load analysis for air-supported membrane structure which belong to pneumatic membrane strcuture were studied based on force density method.This paper firstly analyses the core factor which is the internal air pressure in the form-finding analysis of pneumatic membrane.The internal air pressure is always the direction which is normal to membrane surface element so that the need to constantly modify directions when you do calculations is necessary.Next this paper has derived element force density matrix including membrane line element and T element under internal air pressure on the basis of force density method and the finite element method. According to the law which is how the element density matrix is integrated into overall density matrix,this paper put forward the concept of matrix coordinate method; A linear balance equations be established on the force density method and the CSR sparse matrix storage technology be used to store the coefficient matrix, The Gauss-Seidel iteration method be used to solve the equations and improves the computational efficiency;Some conclutions of law be drew from the examples.According to the post-form-finding of membrane surface morphology and the stress-strain relationship,equivalent to the original membrane surface unit length and the equivalent stiffness are derived. The common loads in the pneumatic membrane are analysed and the formula for calculating the membrane surface equivalent nodal loads is derived. According to one-dimension character,geometric relationship and stress-strain relationship of cable element and T element,The non-linear balance equations and geometric stiffness matrix are established. Matrix coordinate method is used to integrate the overall geometric stiffness matrix,the full Newton-Raphson method is used to solve the nonlinear equations,and the tangent stiffness matrix of T element is mainly derived.And some fo suggestions are proposed through the example.