机械载荷作用下功能梯度梁的过屈曲分析

Analysis of mechanical postbuckling behavior of functionally graded beams

基于一阶剪切变形梁理论,对轴向载荷作用下的功能梯度梁的过屈曲行为进行了研究.推导出功能梯度梁非线性静态问题的基本方程、并求得梁过屈曲的精确解.该精确解显式地给出了梁的过屈曲变形与外载荷的非线性关系.根据所得结果,考察了外载荷、材料性质、长细比以及不同的边界条件等因素对功能梯度材料梁过屈曲行为的影响.结果表明,梯度材料性质、横向剪切变形以及不同边界条件对功能梯度材料梁的过屈曲特性均有显著影响.

Based on the first-order shear deformation theory,the post-buckling behavior of functionally gradient beams under axial loading is investigated in this paper.The basic equation for nonlinear static problem of functionally gradient beam is derived and an accurate solution to post-buckling is obtained.By using the accurate solutions herein obtained,effects of various factors such as material gradients,applied loading,transverse shear deformation and boundary conditions on post-buckling behaviors of functionally graded material beams have been investigated.The results obtained show that properties of gradient material,transverse shear deformation and different boundary conditions have significant effects on the post-buckling characteristics of functionally gradient material beams.