The Geometrical Nonlinear Study Of Tensile Structure Based On Conjugate Gradient Method

Tensile Structures are more and more favorite among designers for its high structuralefficiency and the beautiful shape. Broadly speaking, the tension structure contains a varietyof suspension structure, integrated tension system and membrane structure. A common featureof them is flexible structure and prestress must be applied to get stiffness. Therefore, the formfinding analysis of tensile structures is key to the structure design. At the same time, dueto the low stiffness of the tensile structures, the action of prestress and external loads willproduce large displacement and rotation, while the material is still at elastic stage. So it’s needto geometric nonlinear analysis.The force density method is usually used for form-finding analysis of tension structures,but the amount of calculation is very large because the traditional force density methodrequires computing units-node topology matrix. In this paper, the unit force density matrix isintegrated directly into the whole force density matrix by using finite elements integrationideas. For the character of sparse、symmetric and positive definite, this paper using CSRstorage technology and the conjugate gradient method to solve the force density matrix andgot further improve to computational efficiency.The balance equation is a set of nonlinear algebraic equations in the Geometric nonlinearanalysis to the structure. Common analysis methods need to storage tangent stiffness matrixand solving linear equations to calculate the incremental direction for each iteration step, thatmakes large scale structural analysis become difficult. Appling minimum potential energy toanalysis the Non-linear stress of structures is a common application of the energy iterationmethod. This paper deduced the potential energy of cable and bar element based on theprinciple of energy. Application nonlinear conjugate gradient method to optimization thestructure potential and Solving the displacement solution to meet the potentialenergy minimum (at the same time satisfies the equilibrium equation), that avoid to solvethe nonlinear equations.With form-finding analysis of cable and rod support tensioned membrane structure as awhole, the whole force density matrix became nonlinear equations because itcontains the flexibility control unit. This paper has established the unit potential energyfunction represented with unit density value for the first time, and applied nonlinear conjugategradient method to the collaborative form-finding analysis, that make a combination ofminimum potential energy principle with form-finding analysis of membrane structure. According to the potential energy of the space bar elements、prestressed cable element、membrane line element and T element, we can establish the total potential energyof the structure and use the conjugate gradient method to optimization the potential energy.This paper application fortran95language to program composition for geometric nonlinearanalysis of cable-strut tensile structures、Form-finding analysis of membrane structure andcollaborative form-finding analysis of cable and rod supported membrane structure, and gotsome meaningful conclusions through a lot of example analysis.