Research And Application Of Constant Curvature Members With Out-of-Plane Deformation

Curved beam is widely used in civil engineering,machinery and aerospace because of its smooth and graceful line shape and its ability to meet special use functions.With the rapid development of the times,the requirements of city construction for aesthetic appearance have increased,and the architectural forms have diversified.In modern structural engineering,more and more buildings adopt curved beam.Curved beams are common in circular balconies,theater halls and other circular buildings.Because of the curvature of curved beam,the coupling of bending deformation and torsion deformation increases the difficulty of research.At present,there is no universally recognized curved beam theory,so the research on curved beam is of great value.In this paper,the Out-of-Plane deformation of constant curvature member is studied.The internal force balance differential equation group and the displacement differential equation group are established by carrying out internal force balance analysis and bending-torsion coupling deformation analysis on the micro-circular section.Solving the differential equations of internal force balance and displacement,the expressions of rod end force and rod end displacement are given,then the element stiffness matrix is derived.According to the displacement expression of any section with equal curvature,the displacement mode of the bar with equal curvature is given.According to the principle of virtual work and displacement mode,the explicit calculation formula of the fixed end force of the constant curvature beam with external deformation under concentrated load is deduced,and then the internal force calculation formula of any section of the constant curvature beam under external load is obtained.Finally,the element stiffness matrix of the member with equal curvature and the calculation formula of the fixed end force in analytical form are applied to calculate the curved beam of a single member,to solve the fixed end force of the curved beam,the internal force of any section,and to draw the internal force diagram and the influence line of the fixed end force.Based on the analysis of the equal curvature bar with external deformation,the calculation formulas of internal force and displacement at any section of the equal curvature bar and the expressions of rod end force and rod end displacement are given.The explicit form of the element stiffness matrix of the member with equal curvature is obtained.The displacement mode of the analytical form of equal curvature bar is given.The calculation formulas of the fixed end force of the constant curvature bar fixed at both ends under multiple external loads and the fixed end force of the constant curvature bar fixed at one end and hinged at one end under multiple external loads are obtained.The fixed end force of curved beam and the internal force of any section in a single equicurvature bar structure are obtained,and the influence line of the fixed end force of internal force diagram is drawn.In this paper,the element stiffness matrix in analytical form and the fixed-end force in analytical form under various external loads are given for out-of-plane deformed members with equal curvature,which can be applied to the finite element method of structural analysis,providing theoretical basis for the analysis of multi-component structural systems containing members with equal curvature by computer,and laying a foundation for the manual analysis of a small number of members with equal curvature.