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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.
In this paper, we study the thermoelasticity of half-space non-uniform isotropic functional graded elastomers.According to the motion equations, heat conduction equations and constitutive equations of the functional graded thermoelastic materials, the state-space method is used to derive the thermodynamic coupling differential equations , And further using the eigenvalue analysis and Laplace inverse transform to solve, get the analytic solution of the three physical quantities of displacement, temperature and stress in the time domain of the functional gradient thermal elastomers under temperature and stress loading respectively. , Numerical analysis of the response of the half-space functionally graded material elastomers to each physical field under thermo-mechanical loading shows that the trend of numerical curves reflects the coupling effect between thermo-mechanical loads, which can be well used in material design Field, by controlling the gradient parameters of the material to control the extreme value of the physical field, which will provide theoretical support for the factory’s processing design of the material in the future.