Deformation Analysis Of Planar Variable Curvature Members Considering Temperature Change

In this paper,the variable curvature beam and arch structure are selected as the main members of the study.The internal forces and deformations of the plane-curvature beam under static force are analyzed.The related research is carried out with the curved beam and parabolic arch as the engineering background.Curved beams have been widely used in municipal engineering,aerospace and mechanical engineering.Due to the influence of curvature,the curved beam will produce a combination of bending and torsion,and its mechanical behavior is more complicated than that of a linear beam.In the actual curved beam bridge accident,there are many phenomena that the bridge deck is damaged due to the excessive displacement of the bridge under the load and temperature.At present,the corresponding design theory,calculation method and technical specification have achieved certain research results,but the formation The theoretical system of mechanical analysis is not perfect enough.The research and results of deformation of the common form of variable curvature curve beam under the influence of plane load are relatively few.In this paper,for different types of variable curvature curve beams,under the action of surface inner diameter and external load and temperature,the effect of shear force with less influence on internal force and deformation is not neglected,and the internal force and deformation of curved beam under different boundary conditions are derived.The expression is solved,and the obtained expression is numerically integrated by MATLAB,and further compared with the corresponding ANSYS finite element calculation results,and the actual case comparison and application research are carried out.The main contents of this paper are as follows:(1)Based on the energy principle,using the method of structural mechanics,the calculation model is placed in the Cartesian coordinate system to determine the relationship between the variables,and the internal force and deformation at the arbitrary position of the elliptical curve beam under the action of the radial load and the temperature are derived.And calculate the numerical solution of its displacement.By changing the constraint method,the statically determined structure,the first statically indeterminate,the second hyperstatic and the three statically indeterminate curved beams are respectively studied.(2)Solving the parabola becomes different boundary conditions of the radial displacement of any point of the beam and the beam hyperbolic curvature of the curve becomes flat at the inner radial load and the curvature of the effect of temperature,the tangential displacement,angular displacement.(3)The ANSYS finite element simulation software is used to establish the corresponding model,and combined with the theory expression of the pre-circular curvature curve beam,the numerical solution is compared with the proposed method to verify the correctness of the derivation method and the result.(4)Combined with the finite element case and the actual engineering case,the displacement is compared with the actual measurement data to verify the correctness and applicability of the theory solution.