Euler型梁-柱结构的非线性稳定性和后屈曲分析

Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure

在有限变形的假设下,建立了位于非线性弹性基础上非线性弹性Euler型梁-柱结构的广义Hamilton变分原理,并由此导出了任意变截面Euler型梁-柱结构的3维非线性数学模型,其中考虑了转动惯性、几何非线性、材料非线性等因素的影响.作为模型的应用,分析了弹性基础上一端完全固支另一端部分固支,并受轴力作用的均质等截面线性弹性Euler型梁的非线性稳定性和后屈曲;结合打靶法和Newton法,给出了一种计算平凡解(前屈曲状态)、分叉点(临界载荷)和分叉解(后屈曲状态)的数值方法,对前两个分支点和相应分支解,成功地实现了数值计算,并考虑了基础反力和惯性矩对分支点的影响.

Based on the assumption of fmite deformation, the Hamilton variational principle was extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation, and the corresponding 3-dimension mathematical model for analyzing the non-linear mechanical behaviors of structures was established, in which the effects of rotation inertia, non-linearity of material and geometry were considered. As application, the non-linear stability and the post-buckling for a linear elastic beam with equal cross-section and located on an elastic foundation were analyzed, here, one end of beam was fully fLxed, and the other was partially fLxed and subjected to an axial force. A new numerical technique was proposed to calculate the trivial solution, bifurcation points and bifurcation solutions by the shooting method and Newton-Raphson interactive method. The first and the second bifurcation points and the corresponding bifurcation solutions were calculated successfully. The effects of foundation resistances and inertia moments on the bifurcation points were considered.