Flat Spherical Nonlinear Mechanical Behavior Of The Network Shell

In this paper, nonlinear mechanics behavior of the shallow reticulated spherical shell is studied. The state of interior of country and overseas are introduced. Analysis and calculation of the shallow reticulated spherical shell in the aspect of static and dynamical are studied systematically. According to the nonlinear dynamical theory of plate and shell, modern analytic method of nonlinear dynamic is selected, and ideology of continuous quasi-shell method is used, reticulated shell is transformed into continuous shell, nonlinear dynamical governing equations are elected, boundary conditions and initial conditions are given. The nonlinear bending problem of shallow reticulated spherical shell, nonlinear natural frequency problem of the shallow spherical reticulated shell, dynamical stability problem of the shallow spherical reticulated shell, bifurcation problem and chaos problem of the shallow spherical reticulated shell are studied.In preface of chapter 1, the research meaning of reticulated shells, bifurcation, chaos are introduced. In the following the condition of interior of country and overseas.In chapter two, the nonlinear bending problem of shallow reticulated spherical shell is studied. The equations of middle cross section of the three-dimensional reticulated frame and initial deflection are added to the equations of three-dimensional reticulated frame, then the equations of shallow spherical reticulated shell are obtained. Under the boundary conditions of fixed and clamped, the nonlinear bending problems of the shallow spherical reticulated shell objected to even load are solved by the method of modified iteration. The quadratic approximate analytic solution with the much higher accuracy is presented. The diagram of curves of loads and deflections with quadratic eigenvalue is superior to the diagram of first eigenvalue .In chapter three, the nonlinear natural frequency of the shallow spherical reticulated shell is solved. According to nonlinear dynamical theory of shallow shell, nonlinear dynamical equations of the shallow spherical reticulated shell is obtained by the method of quasi-shell. The maximal amplitude in the center of the shallow spherical reticulated shell is selected as the perturbation parameter, and the problem is solved by perturbation variation. In its first approximate equations, linear naturalfrequency is obtained, in its second approximate equations, nonlinear natural frequency of the shallow spherical reticulated shell is obtained.In chapter four, nonlinear dynamical stability of this shallow spherical reticulated shell is analyzed. From nonlinear dynamical variation equations and compatible equations, under the fixed and clamped boundary conditions, a nonlinear differential equation with quadric items is obtained by the method of Galerkin. In order to discuss chaos motion, a kind of nonlinear dynamical free oscillation equation is solved. An accurate solution to the free oscillation of the shallow spherical reticulated shell is obtained. Then Melnikov function is solved, critical condition of chaos motion is given, and the existence of chaos motion is confirmed from digital simulation phase plans.In chapter five, nonlinear dynamical stability of this shallow spherical reticulated shell is analyzed by the method of catastrophe. Firstly, potential function of the globe character is obtained, the static and dynamical stability of this system is analyzed separately. Top and bottom critical values of the amplitude is given when the static load is selected maximal and minimal; then top and bottom critical values of the amplitude is given when the dynamical load is selected maximal and minimal. Thevariation value scope of is discussed when this system is stabile,critical and unstable.