基于物理中面FGM经典梁的非线性力学行为

Nonlinear mechanical behavior of FGM classic beams based on physical neutral surface

利用物理中面概念,基于经典非线性梁理论,导出FGM梁的基本方程,分析研究热载荷作用下FGM梁的过屈曲、弯曲以及在这些构形上的振动等问题.假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化.利用打靶法数值地求解所得方程.数值结果表明:热载荷作用下,FGM夹紧梁发生过屈曲变形,而简支梁则发生较为复杂的热弯曲变形;热载荷作用下,FGM夹紧梁和简支梁的动态行为也有明显区别.

Based on the classical non-linear beam theory（CBT）,the basic equations of the FGM beam were derived by using the concept of physical neutral surface.Thermal post-buckling,thermal bending and vibration responses were investigated with respect to these postbuckled or bended configurations of a FGM beam subjected to thermal loads.It was assumed that the properties of the functionally graded material would vary continuously only with the thickness of the beam and their variation would follow a simple power law distribution with respect to the volume fraction of the material constituents.A shooting method was employed to solve numerically the equations resulted.Numerical results obtained herein showed that the post-buckling deformations would be caused by a clamped FGM beam subjected to thermal loads while more complex thermal bending deformations would be caused by a simple supported beam.Moreover,the dynamic behavior of a clamped FGM beam was remarkably different from that of the simple supported beam in the case of idenctical thermal loads.