| At present,the application of arch structure in engineering construction is more and more extensive.High performance materials and thin-walled structure are widely used in the structure.The span is more and more large,and the risk of arch structure instability is more prominent.This paper takes a mono-symmetrical arches as the research object,analyzes its out-of-plane stability when subjected to elastic rotation constraints,and uses theoretical deduction and finite element numerical simulation to study the critical load of out-of-plane instability of the arch,as follows:（1）Analyze the fully articulated constrained mono-symmetrical circular arch under the concentrated force of the dome,construct a new curvature and strain function of the arch to improve the accuracy of the calculation,use the energy method and the force method to obtain the arch loss The total energy equation in the plane before stabilization is solved,and the axial force,bending moment and shear force before the arch instability are obtained.By assuming the out-of-plane displacement function,the Rayleigh-Ritz method is used to solve the problem,and the out-of-plane bending and torsion of the arch is derived analytical solution of critical load for instability in the event of instability.（2）The in-plane boundary conditions are given by the definition of elastic constraints,obtain the axial force,bending moment and shear force under the in-plane elastic constraints,and the parameters related to the critical load Qcrconsidering the in-plane elastic rotation constraints are obtained,and the plane is obtained a quadratic equation related to Qcrunder internal elastic constraints.（3）According to the analytical solution of the axial force and bending moment of the in-plane elastic restraint and out-of-plane hinged arch,and the one-dimensional quadratic equation related to the out-of-plane instability critical load Qcr,the parameter analysis was carried out,and the central angle and length of the arch were discussed.The influence of slenderness ratio and in-plane elastic restraint flexibility parameters on the axial force,bending moment and critical load of out-of-plane instability before arch instability.（4）The torsion force of the torsion spring is used to provide elastic restraint,and the different boundary restraint conditions of the arch structure are satisfied through a new concept of the support.Taking aluminum as the analysis object,the out-of-plane instability critical load of the T-shaped aluminum arches with different boundary conditions and different rise-span ratios under a central concentrated load was analyzed by finite element numerical simulation,and eigenvalue buckling analysis method and arc length method was adopted to solve the critical value of instability.（5）The theoretical solution of out-of-plane buckling critical load varying with rise-span ratios of T-shaped circular arch with in-plane elastic restraint is compared with the finite element results.The comparison results are in good agreement,which shows that the theoretical solution is accurate. |
