梯形载荷作用下功能梯度简支梁弯曲的解析解

基于应力函数法,对梯形分布载荷作用下、材料属性在厚度上任意变化的功能梯度简支梁弯曲问题的解析解进行了研究。首先引入了一个应力函数,根据平面应力问题的基本方程,得出了功能梯度梁的应力函数应满足的偏微分方程,并根据应力边界条件得出了应力函数及各向应力的表达式;进而根据功能梯度材料的本构方程和位移边界条件,得出了各向应变与位移的显式解析表达式。在算例中,分别采用文中方法和经典理论对均质各向同性梁进行求解,验证了文中方法的正确性;并求解了材料组分呈幂律分布的功能梯度梁的应力和位移分布,分析了上下表层材料的弹性模量比λ与组分材料体积分数指数 n 对应力和位移分布的影响。     

Free vibration analysis of cylindrical and rectangular sandwich panels with a functionally graded core

Based on the Reissner assumptions, the free vibration analysis of simply supported cylindrical and rectangular sandwich panels with isotropic face sheets and a functionally graded core is concerned. Firstly, the expressions of the displacements, stresses and internal forces are presented according to the constitutive relations and stress states of the core and face sheets. Then, the dynamic stability and compatibility equations are given for cylindrical sandwich panels with functionally graded core, elastic modulus and density in which vary continuously in the thickness direction. Finally, the proposed solutions are validated by comparing the results of degenerate example with classical solutions, and a numerical analysis is performed on the example of simply supported cylindrical and rectangular sandwich panels. The elastic modulus and density of the functionally graded core are assumed to be graded by a power law distribution of volume fractions of the constituents, and the Poisson ratio is held constant. The effects of the distribution of functionally graded core's properties, the thickness-side ratios and ratio of radius(R) to length(l) κ = R/l are also examined.