功能梯度梁与均匀梁静动态解间的相似转换

ANALOGOUS TRANSFORMATION OF STATIC AND DYNAMIC SOLUTIONS BETWEEN FUNCTIONALLY GRADED MATERIAL BEAMS AND UNIFORM BEAMS

基于Euler-Bernoulli梁理论,研究了功能梯度材料梁的弯曲、屈曲和自由振动.通过分析和比较功能梯度材料梁和均匀梁的控制方程,得到了功能梯度材料梁与均匀梁的解之间的相似转换关系.在给定功能梯度材料梁的材料性质在横向按幂函数分布的情况下,导出了解之间的相似转换系数的解析表达式.该系数集中反映了功能梯度梁的材料非均匀性.因此,可将功能梯度材料梁的静动态问题的求解转换为同样载荷和边界条件下均匀梁的静动态问题求解以及相似转换系数的计算.

Based on the theory of Euler-Bernoulli beams,the bending,buckling and free vibration of functionally graded material（FGM） beams were analyzed.By comparing the governing equations of functionally graded material beams and uniform beams,an analogous transform relation between the solution of FGM beam and that of uniform beam were obtained.If the material properties of FGM beam can be expressed in power functions in the lateral direction,the transformation factors between the solutions of the two kinds of beams were derived in analytical forms,which reflect the non-uniform properties of the functionally graded material beams.Therefore,the solution of static and dynamic problems of FGM beams can be transformed to that of a uniform beam and the calculation of the transformation factors under the same loadings and boundary conditions.This method can provide a simple and convenient approach in analysis of non-uniform beams and find applications in engineering.