基于物理中面与高阶剪切变形理论双参数弹性地基上FGM梁的非线性弯曲分析

NONLINEAR BENDING ANALYSIS OF FGM BEAMS RESTING ON TWO-PARAMETER ELASTIC FOUNDATIONS BASED ON PHYSICAL NEUTRAL SURFACE AND HIGH ORDER SHEAR DEFORMATION THEORY

在论文中,基于物理中面概念与高阶剪切变形理论,用Ritz法给出双参数弹性地基上FGM梁非线性弯曲的近似解答,并且讨论不同温度场、地基参数、不同边界条件、以及体积分数变化对FGM梁力学行为的影响.值得进一步指出的是:在基准温度场中,Winkler地基FGM梁的挠度介于Pasternak型与无地基梁之间;在热传导场中固支FGM梁的挠度介于均匀热场与基准温度场之间,而简支FGM梁由于有初始热挠度的影响,并非总是如此.

In this paper, approximate solutions for nonlinear bending of FGM beams were given by Ritz method based on the physical neutral surface assumption and high-order shear deformation theory,and the influences of different supported boundaries, elastic foundations, thermal environmental conditions and volume fraction index were discussed in detail. It is worth pointing out the following conclusions that the deflections of the beams resting on Winkler elastic foundation are between those of foundationless beams and the beams resting on Pasternak elastic foundation in the reference temperature field,and the deflections of the beams with immovable clamped ends in the heat conduction temperature field are between those of beams in the uniform reference temperature field, while this is not always true for the beams with immovable simply supported ends due to initial thermal deflections.