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总览 评价 李世荣 1，* ， 万泽青 2， （ 1、 扬州大学建筑科学与工程学院； 2、 School of Civil Science and Enginering, Yangzhou University； ） 摘要： 本文研究了受轴向压的缩功能梯度Timoshenko 梁与均匀Euler-Bernoulli 梁的屈曲解之间的解析关系.
李世荣1，*， 万泽青2，
（
1、扬州大学建筑科学与工程学院； 2、School of Civil Science and Enginering, Yangzhou University； ）
摘要：
本文研究了受轴向压的缩功能梯度Timoshenko 梁与均匀Euler-Bernoulli 梁的屈曲解之间的解析关系.基于一阶剪切理论建立了只用挠度表示的材料性质沿厚度任意连续变化的功能梯度材料梁的屈曲控制方程,它与均匀Euler-Berboulli梁的屈曲控制方程完全相同.通过求解该方程在给定边界条件下的特解,得到了功能梯度Timoshenko梁与均匀Euler-Bernoulli梁的临界载荷之间的解析关系，该关系对于对于两端夹紧 (C-C), 两端简支(S-S) 以及一端夹紧一端自由(C-F) 边界约束都适应.遗憾的是该关系对于一端夹紧一端简支(C-S)约束不适应. 但是,这里给出了求解C-S功能梯度Timoshenko梁临界载荷的特征方程，该方程与均匀Euler-Bernoulli 梁的特征方程相似.于是,如果知道了均匀Euler-Bernoulli梁的临界载荷，则具有C-C、S-S 和 C-F 约束的功能梯度Timoshenko梁的临界载荷的计算可以简化为两个由梁的材料性质变化梯度规律以及几何尺寸决定的参数的计算。
关键词：
功能梯度材料；Timoshenko 梁；屈曲；临界载荷；解析解
Shirong Li*， Zeqing Wan
（
School of Civil Science and Enginering, Yangzhou University； ）
Abstract：
Analytical relationships between the solutions of buckling of functionally graded material (FGM) Timoshenko beams and those of the homogenous Euler-Bernoulli beams subjected to axial compressive load were investigated for different boundary conditions. Based on the first order shear deformation theory, governing equation of buckling of FGM beams with the material properties changing continuously arbitrarily in the thickness direction were derived only in terms of the deflection, which has the same form as that of the homogenous Euler-Bernoulli beams. By solving the governing equation with specific boundary conditions, an analytical relationship between the critical buckling loads of the FGM Timoshenko beams and those of the corresponding Euler-Bernoulli beams were obtained which is valid for the clamped-clamped(C-C), simply supported-simply supported (S-S) and clamped-free(C-F) end constraints. Unfortunately, the above mentioned relationship is not valid for the beams with clamped-simply supported (C-S) ends. However, a simple eigenvalue equation is presented to find the critical buckling load for a C-S FGM Timoshenko beam. Consequently, buckling loads of FGM Timoshenko beams with C-C, S-S and C-F ends can be simplified as calculations of two coefficients determined by the material gradients and the geometry of the FGM beams when the critical buckling load parameters are known.)
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