The Analysis For Non-linnear Large Deformation Of Curved Beams

This thesis studied the large deformation problems of continuous curved beams and double-layer curved beams under the static mechanical loads. The main contents of research were given as follows.Firstly, geometrical nonlinear control equations of Euler-Bernoulli curved beams (element) under the mechanical and thermal load was introduced. In order to get numerical solutions of the control equations, ordinary differential equations for two-point boundary value problems was translated into initial value problems by using shooting method. Bending plane problem of the oblique and arc-shaped beams under various boundary conditions and loads were calculated. With this method, this thesis obtained the numerical solution, gave the equilibrium path and equilibrium configuration of the problem, and discussed the effect of various load parameters on the deformation of curved beams.Secondly, the mathematical model of the above research was extended to the continuous curved beam structure, by using the derived equations, this thesis solved the geometry nonlinear large deformation problems of plane framework with a circular arc and two kinds of simple rectangular frame structure, obtained the static mechanical response of continuous curved beam under different external loads, analyzed the nonlinear elastic deformation of a continuous curved beam under mechanical loads, investigated the effects of different loading parameters on the equilibrium path of the structure, at last, compared the deformation response of the flat rectangular frame under uniform external pressure and uniform internal pressure.Finally, basing on the geometry nonlinear theory of extensible axis curved beams, this thesis established the mathematical model of the double-layer Euler Bernoulli curved beam (element) under mechanical and thermal load, which the control equations contains the pull-curved coupling term due to non-uniform distribution of the materials in horizontal direction. By using the shooting method of ordinary differential equations for two-point boundary value problems, this thesis obtained the large deformation numerical solutions of arc curved beams, which is an end fixed and an end simply supported, under normal dynamic loads, and compared the results of double-layer Euler Bernoulli curved beam with that of single-layered curved beams, and finally discussed the effect of the geometrical and physical parameters on the deformation of curved beams.