Research On Out-of-plane Stability Of Arches With Elastic End Restraints Under Coupled Linear Temperature Gradient-Loads

Arch structures are widely used in many engineering fields owing to their excellent mechanical properties and outstanding appearances.The out-of-plane stability of arch structures has attracted wide attention for a long time.However,it is not clear yet those influences on the out-of-plane stability of the arch such as temperature field,complex boundary conditions and shear deformation,which become an obstacle for the development of arches.In order to investigate the influence of temperature field on the out-of-plane stability of arches,improve the theoretical system of the out-of-plane stability of arch structure,and fill the gap of the design specifications.In this paper,based on the energy method,a systematic theoretical study on the out-of-plane stability of arches with elastic end restraints under coupled thermomechanical situation is carried out as follows:(1)Study on the mechanical behavior of circular arches with elastic end restraints in prebuckling under coupled thermo-mechanical situation.The pre-buckling energy equation of arches with elastic end restraints under uniform distributed radial load,linear temperature gradient field,linear temperature gradient field as well as uniform distributed radial load,are established,respectively.The analytical solutions of the displacement,stress,strain,bending moment,axial force and shear force of circular arches with elastic end restraints in pre-buckling are derived,respectively.Moreover,the influence of the linear temperature gradient on the variation of the internal force of arches are discussed,before a study on the out-of-plane instability of circular arches with elastic end restraints under coupled thermo-mechanical situation.The correctness of the analytical solution of the internal force are further verified by the finite element numerical simulation.(2)Study on the out-of-plane stability of circular arches with elastic end restraints under coupled thermo-mechanical situation.The displacement function and total energy equations of the out-of-plane buckling of circular arches with elastic end restraints under uniform distributed radial load,linear temperature gradient field and uniform distributed radial load are established,respectively.After that,the analytical solutions of the effective bending stiffness,the effective warping stiffness,and the effective torsional stiffness of I-section under linear temperature gradient field are derived.Meanwhile,the out-of-plane critical buckling loads of circular arches with elastic end restraints are determinated accordingly,and the analytical solution of the outof-plane critical buckling load are verified by finite element numerical simulation.(3)Parameters analysis for the out-of-plane instability of circular arches with elastic end restraints under coupled thermo-mechanical situation.The influence analysis of linear gradient temperature field,flexibility of elastic end restraints,slenderness ratio,shear deformation and other design parameters on the internal forces of arches in pre-buckling and the out-of-plane critical buckling load are performed.Subsequently,the out-of-plane buckling mode of arches under coupled thermo-mechanical situation is described,and the instability mechanism for arches are revealed.Finally,it is pointed that the necessity of the research for the out-of-plane instability of arches under coupled thermo-mechanical situation.