功能梯度半空间体的热弹性问题研究  

Study of Thermoelasticity Problem of Half-Space Functionally Graded Material

作　　者：孙飞 刘五祥[1] 张伦伟[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2017年第3期537-544,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学青年基金(11102136);中央高校基本科研业务费专项资金(20153671);广西防灾减灾与结构安全重点实验室开放课题(2014ZDK08)

摘　　要：本文研究半空间非均匀各向同性功能梯度弹性体的热弹性问题.根据功能梯度材料热弹性体的运动方程,热传导方程以及本构方程,利用状态空间法推导出功能梯度材料的热力耦合微分方程,进一步利用特征值分析法和拉普拉斯逆变换进行求解,得到功能梯度热弹性体在分别只受温度和应力荷载作用时,时域内位移,温度,应力三个物理量的解析解.通过图表,数值分析了半空间功能梯度材料弹性体在热-力荷载作用下各物理场的响应,数值曲线的变化趋势反映了热-力荷载之间的耦合效应.这可以很好的利用在材料设计领域,通过控制材料的梯度参数来控制物理场的极值,从而为未来该材料的工厂加工设计提供理论支持.This article is concerned with the study of coupled thermoelasticity in half-space inhomogeneous isotropic functionally graded materials（FGMs）. Using state space method, the differential equations of coupled thermoelasticity of functionally graded materials are established based on the equations of motion, equations of heat conduction and constitutive equations. The analytical solutions of temperature, displacement and stress are calculated by using eigenvalue approach and inversion of the Laplace transformation. Taking a half space FGM medium into consideration, the response of each physical field under thermal-mechanics loads is analyzed. This can be applied to the structural design of the FGMs, to control the extreme values of the physical quantities by choosing different gradient parameters, which can theoretically support the manufacture of the FGMs.

关 键 词：功能梯度材料 热力耦合 状态空间法 解析解 

分 类 号：O345[理学—固体力学]