NUMERICAL ANALYSIS OF BIFURCATION BUCKLING FOR ROTATIONALLY PERIODIC STRUCTURES UNDER ROTATIONALLY PERIODIC LOADS

By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.

TORSIONAL BUCKLING OF SPHERICAL SHELLS UNDER CIRCUMFERENTIAL SHEAR LOADS

By the aid of differential geometry analysis on the initial buckling of shell element, a set of new and exact buckling bifurcation equations of the spherical shells is derived. Making use of Galerkin variational method, the general stability of the hinged spherical shells with the circumferential shear loads is studied. Constructing the buckling mode close to the bifurcation point deformations, the critical eigenvalues, critical load intensities and critical stresses of torsional buckling ranging from the shallow shells to the hemispherical shell are obtained for the first time.

均布外压下球形封头屈曲特性研究

This study aims to experimentally and numerically examine the buckling performances of stainless steel spherical caps under uniform external pressure.Three laboratory-scale caps were fabricated,measured,and tested.The buckling behaviors of these caps were investigated through experiments and three numerical methods,namely,nonlinear Riks algorithm,nonlinear bifurcation,and linear elastic analysis.The buckling of equal-radius caps was numerically analyzed with different methods to identify their applicability under different wall thicknesses.The results obtained from the nonlinear Riks algorithm are in good agreement with the experimental results,which means the nonlinear Riks algorithm can accurately predict the buckling performances of spherical caps,including the magnitude of critical buckling loads and the deformation of post-buckling modes.The nonlinear bifurcation algorithm is only suitable for predicting the buckling loads of ultra-thin or large-span caps,and the linear buckling method is inappropriate for predicting the buckling of metal spherical caps.

An analysis of dynamic stability of an elastic column

By the Lyapunov direct method, dynamic stability of two conservative systems of finite degrees of freedom with one parameter is analyzed. Two Lyapunov functions are proposed for the two systems, respectively. When the number of degree of freedom the two systems tends to infinite, the two systems can simulate dynamic stability of a compressed elastic column with one end fixed and the other clamped in rotation. In the sense of the Lyapunov stability, the column is proved to be dynamically stable when the load equals to the Euler critical load.

In-Plane Elastic Buckling of Arch

The in-plane elastic buckling behavior of arches is investigated using a new finite-element approach for the nonlinear analysis. The linear buckling, nonlinear primary buckling, and secondary bifurcation buckling behavior of arches are compared taking into account the large deformation and the effects of initial geometric imperfections or perturbations. The theoretical investigation emphasizes the nonlinear secondary bifurcation buckling behavior for a full span uniformly distributed load. The efficiency of compact method for tracing secondary buckling path is shown through several examples. Finally, a new structural design, which prevents the secondary bifurcation buckling by adding some crossed cables across the arch, is proposed to improve the limit load carrying capacity.