Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure  

作　　者：朱媛媛 胡育佳 程昌钧 

机构地区：[1]Department of Computer Science and Technology,Shanghai Normal University [2]College of Mechanical Engineering,University of Shanghai for Science and Technology [3]Department of Mechanics,College of Sciences,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第6期719-728,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Science Foundation for Distinguished Young Scholars of China(No. 11002084);the Shanghai Pujiang Program (No. 07pj14073);the Scientific Research Projectof Shanghai Normal University (No. SK201032)

摘　　要：Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional （3D） mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional （3D） mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.

关 键 词：beam-column structure Hamilton variational principle nonlinear stability shooting method Newton-Raphson iterative method POST-BUCKLING 

分 类 号：O342[理学—固体力学]