摘要
在某些边界条件下,功能梯度材料(FGM)梁会由于拉弯耦合产生前屈曲耦合变形,而该变形对FGM梁的稳定性有影响.论文假设FGM梁的材料性质只沿厚度方向进行变化,基于经典非线性梁理论和物理中面概念,推导出FGM梁的平衡方程以及包含前屈曲耦合变形影响的屈曲控制方程,并用打靶法进行数值求解.讨论了前屈曲耦合变形、梯度指数以及材料性质的温度依赖等因素对FGM梁非线性变形和稳定性的影响.
Functionally graded material(FGM)is a kind of composite material with microscopic inhomogeneity.The continuous change of its composition along a certain direction leads to its gradient property.Its excellent engineering performance(such as high temperature resistance)has attracted the attention of many researchers.The pre-buckling coupling deformation of functionally graded material beams may occur due to coupling of stretching and bending in some cases,and this deformation has an effect on the stability of FGM beams.Nonlinear deformation and stability considering the pre-buckling coupling deformation are studied for FGM beams subjected to non-uniform temperature field in this paper.First,it is assumed that the material properties of FGM beams,taking the ceramic(Si3 N4)and metals(SUS304)as an example,only change along the thickness direction.Then based on the classical nonlinear beam theory and the concept of physical neutral surface,the equilibrium equation is derived by using energy principle,and the buckling governing equation including the effect of the pre-buckling coupling deformation of FGM beams is reformulated after the pre-buckling coupling deformation is solved.The equilibrium equations and buckling governing equations are solved numerically by the shooting method.Next,the correctness of the method is verified by comparing with the existing results.The non-single-valued load-deflection curves are obtained,and the effects of gradient index and temperature dependence of material properties on the nonlinear deformation and the effects of pre-buckling coupling deformation and temperature ratio on the stability of FGM beams are discussed.Finally,it is found that there exist multiple configurations for FGM beams,and the configuration of FGM beams may reverse with the change of temperature difference between the upper and lower surfaces.The critical load is larger when the pre-buckling coupling deformation is considered,but smaller when temperature dependence of material properties is considered;and the criti
作者
马连生
戚鹏程
Liansheng Ma;Pengcheng Qi(School of Architectural Engineering,Wei fang University of Science and Technology,Weifang,262700;School of Science,Lanzhou University of Technology,Lanzhou,730050)
出处
《固体力学学报》
CAS
CSCD
北大核心
2022年第2期234-242,共9页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(11862012,12062010)
山东省自然科学基金重点项目(ZR2020KA006)资助。
关键词
功能梯度简支梁
前屈曲耦合变形
打靶法
临界载荷
非均匀温度场
functionally graded material
simply-supported beam
pre-buckling coupling deformation
shooting method
critical load
non-uniform temperature field
