纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中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。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。

Nonlinear bending and post-buckling of functionally graded beams under transverse and axial loads

Based on the non-linear first-order shear deformation beam theory(FBT)and the physical neutral surface concept,the governing equations for nonlinear bending and post-buckling of the functionally graded material(FGM)beams subjected to transversally and axially loading are derived and exact solutions for the nonlinear static responses are obtained.By using the exact solutions,the effects of various factors such as the material gradients,applied loading,transverse shear deformation and boundary conditions on nonlinear mechanical behavior of functionally graded material beams have been investigated.It is 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 results show that under the transversally and axially loading,there exist infinitely many bending configurations for a functionally graded material beam.And moreover,with the increase of gradient index,the deformation of the beam decreases and the critical load increases.Also with the increase of slender ratio,the influence of transversely shear deformation decreases.