Study On Key Technologies Of Spoke Single-layer Cable Net Structure

The single-layer cable net structure is composed of a series of single cables arranged according to certain rules,which is mainly used in the roof structure of large stadiums and gymnasiums.It is usually designed as a saddle-shaped surface,and the height difference of the surface can effectively provide the roof stiffness.The single-layer cable net structure is lightweight and all cables are in tension,so the material is fully utilized and the structure is efficient.According to the arrangement of the cables,it can be divided into orthogonal single-layer cable net structure and spoke single-layer cable net structure.Taking orthogonal single-layer cable net structure and spoke single-layer cable net structure as the research object,form-finding analysis,load analysis,shape optimization and static performance of the structure are studied systematically.The specific work contents and conclusions are as follows:Firstly,the equilibrium equation and deformation coordination equation of a single cable are deduced,and the analytical calculation method of the single cable problem is obtained.The errors caused by some assumptions in the derivation process are analyzed,and it is shown that the errors caused by various assumptions are small in the small sag problem.On this basis,using the analytical calculation method of continuous theory,the orthogonal single-layer cable net structure is transformed into a membrane that is only subjected to tension in two orthogonal directions,and the equilibrium equation and deformation coordination equation of the cable net are also derived.Subsequently,a new displacement function is proposed to improve the calculation accuracy and reduce the amount of calculation.The unknown parameter in the displacement function is approximately solved by the Galerkin method,and the cubic equation is simplified to a linear equation.Then,the displacement and the force of cable net under the load can be obtained.The form finding and load analysis program of this kind of structure are programmed in ANSYS APDL,and the accuracy of the calculation formulas of displacement and cable force is verified by nonlinear finite element method(NFEM).On the premise that the height difference of the orthogonal cable net is fixed,the sag of orthogonal single-layer cable net structure is taken as the optimization variable.Through parameter analysis,the influence of sag change on structural stiffness and mechanical performance is compared and the minimum in plane bending moment of the outer ring is selected as the optimization objective.On the basis of obtaining the cable force under the load by the continuous method,the cable pretension and force increment are transformed into uniform load and curve distribution load respectively,and the formulas of outer ring bending moment,axial force and horizontal displacement are deduced.And their accuracy of the formulas are verified by finite element method.Taking the minimum in plane bending moment of the outer ring as the optimization objective,the sag as the optimization variable,the cable force,vertical displacement and rise span ratio as the constraints,an analytical method for solving the optimal form of structure is proposed and the optimization process is given.The process of finding the optimal shape by using the analytical method avoids the tedious process of programming and repeated iterative calculation by using finite element and optimization algorithms.The finite element method is used to find the optimal shape of the structure with the same optimization variables and objectives.The accuracy of the analytical optimization method is verified by comparison.Under the optimal configuration of the structure obtained by the analytical method,the bending moment and deformation of the outer ring are greatly reduced,and the axial force is slightly increased,which effectively reduces the stress of the outer ring.The outer ring can be regarded as an axial compression member,which improves the material utilization rate.Finally,for the spoke-type single-layer cable-net structure,according to the classical force density method,an improved force density method is proposed to quickly determine the initial shape of the structure.In this method,the force density of each element is solved according to the equilibrium conditions in the x and y directions of the inner ring node,then,according to the equilibrium condition of z direction,the z coordinate of the inner ring node is solved.This method can directly specify the force of the element rather than the force density,and realize the process of shape to force and then back to shape.The form-finding program is programmed in MATLAB,and the initial shape obtained by the form-finding is imported into ANSYS,which verifies the correctness of the form-finding program.A semi-continuous and semi-discrete displacement calculation method is proposed.By assuming the displacement function,using the solution method of single cable and the equilibrium equation of nodes,the displacement of the structure under load can be quickly estimated.The displacement calculation program is compiled in MATLAB,and the accuracy of this method is verified by NFEM.The finite element software is used to analyze the parameters of the spoke-type single-layer cable network structure.The influences of the projection shape of the inner and outer ring,the height difference of the saddle surface,the initial pretension value of the cable and the cross-sectional area of the cable on the vertical displacement,cable force,support reaction and the internal force of the outer ring are studied respectively.The conclusions can be used to guide the structural design.