Pasternak地基对FGM圆板非线性弯曲的影响

The Influence of Pasternak Foundation on the Nonlinear Bending of FGM Circular Plate

摘要: 功能梯度材料结构由于容重轻，机械强度高，常常应用于飞机、滑翔机等的航空板中。本文研究了Pasternak地基对FGM圆板在横向载荷下非线性弯曲行为的影响。假设功能梯度材料性质只沿梁厚度方向并且按成分含量的幂指数形式变化；为消除材料非均匀性导致的拉弯耦合效应，引入了物理中面，给出了地基弹性模量kw和地基剪切模量kp对FGM圆板变形的关系，分析了材料梯度指数对不同地基板的影响。结果表明：地基弹性模量是影响FGM板变形的主要因素，kw越大，板的变形越小；材料中金属成分越多，板的变形越大；kw越大，梯度指数对FGM圆板变形的非线性影响越小。

Abstract: Functionally gradient materials (FGM) are often used in aircraft, gliders and other aircraft plates due to their light bulk density and high mechanical strength. The influence of Pasternak foundation on the nonlinear bending behavior of FGM circular plate under transverse load was studied in this paper. It is assumed that the properties of FGM only change along the thickness of plate and change according to the power law distribution with the volume fraction of the constituents. In order to eliminate the tension-bending coupling effect caused by material inhomogeneity, the Physical middle plane was introduced. The relationships between elastic modulus of foundation and shear modulus of foundation on deformation of FGM circular plate were given, and the influences of material gradient index on different ground plates were analyzed. The results show that the elastic modulus of foundation is the main factor affecting the deformation of FGM plate, and the larger the elastic modulus kw is, the smaller the deformation of FGM plate is; The more metal components in the materials, the greater the deformation of the plate will be; The larger kw is, the smaller the nonlinear effect of gradient index on the deformation of FGM circular plate is.