Beam - Column Structure Of The Nonlinear Mathematical Models And Applications

The structure of beam-column is the common element of the structural engineering,both in the mechanical engineering and civil engineering,water conservancy projects and space engineering,or in some of high technology can find the application background of beam-column.Due to the development of high-tech,and the structure become lighten,diminution and lengthen,so the issue of non-linear is needed detailed analysis due to the need of the large deformation of beam-column structure and material non-linear,in order to provide more appropriate to design the theoretical foundation.Based on the assumption of finite deformations and the conservation forces,considering of the effection of the beam's shaft force,neutronsphere inertia,moment of inertia,reaction of a foundation,geometrical non-linear,material non-linear and heterogeneity,the Hamilton variational principle is extended to Euler-type beam-column structures and the corresponding mathematical model for analyzing the non-linear mechanical behaviors of structures is established.The model is partial differential equation of coupling and non-linear variable coefficient,it can be applied to different technology fields.As application, the non-linear stability and the post-buckling for a fixed beam with equal cross-section is analyzed.we convert the problem to finite-dimensional bifurcate equation,than accord to the method and the viewpoint of bifurcate theory, analyse the buckling,fork and post-buckling behavior of structure by shooting method. A new method is proposed to calculate the trivial solutions, branch points and branch solutions, we implement successfully the numerical calculation,get the branch solutions and investigate the effection of branch points and branch solutions due to the moment of inertia, reaction of a foundation and boundary condition.As another application,we solute the problem of non-linear dynamics of fixed beam with equal cross-section.First,in the space field,get the non-linear differential equations that in the time field by differential quadrature method dispersing the control equation and get the space-time distributing of coupling system by difference method and investigate the effection of structure dynamics characteristic due to the moment of inertia,geometrical and material non-linear.