基于物理中面FGM梁的非线性力学行为

NONLINEAR MECHANICAL BEHAVIORS OF FGM BEAMS BASED ON THE PHYSICAL NEUTRAL SURFACE

当坐标面置于功能梯度材料(FGM)梁的物理中面上时,其本构方程中,面内力与弯矩并不耦合,这使得问题的控制方程以及边界条件得以简化。该文利用物理中面概念,基于一阶非线性梁理论,导出了FGM梁的基本方程,分析研究了热载荷作用下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了所得方程。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;另外,剪切变形对FGM梁的力学行为也有显著的影响。

The stretching-bending coupling in constitutive equations of a functionally graded materials（FGM） beam does not exist when the coordinate system is located at the physical neutral surface of the FGM beam,thus the governing equations and boundary conditions for the FGM beam can be simplified.Based on the non-linear first-order shear deformation beam theory（FBT）,the basic equations of the FGM beam are derived using the physical neutral surface concept.The thermal post-buckling,thermal bending and vibration response of postbuckled or bended configurations of an FGM beam subjected to uniformly thermal loads are investigated.It was assumed that the properties of the functionally graded material vary continuously only with the thickness of the beam and their variation has a simple power law distribution with the volume fraction of the constituents.The shooting method is employed to numerically solve the resulting equations.Numerical results obtained herein showed that thermal loads can cause the post-buckling deformations in a clamped FGM beam,while more complex thermal bending deformations in a simple supported beam.And moreover,the dynamic behavior of a clamped FGM beam was also different from that of the simple supported beam.Transversely shear deformation played an important role in the mechanical behavior of the FGM beams.