在几何非线性和热局部平衡条件下, 研究不可压流体饱和多孔热弹性半平面在受到表面温度载荷作用下的动力学特性. 首先, 基于多孔介质混合物理论, 考虑几何非线性的影响, 给出了问题的数学模型; 然后, 提出了一种综合数值计算方法, 该方法通过微分求积法和二阶后向差分格式分别在空间域和时间域离散数学模型, 利用 Newton-Raphson 法求解非线性代数方程组, 从而可得到问题的数值结果. 研究表明, 本方法是有效可靠的, 且具有计算量小、精度高等优点. 最后, 考虑了材料参数和几何非线性的影响研究了流体饱和多孔热弹性半平面在表面温度载荷作用下的热力学特性.

To address problems related to geometric nonlinearity and the local thermal equilibrium, the thermodynamic characteristics of an incompressible fluid-saturated porous thermo-elastic half-plane subjected to surface temperature loadings are studied. First, a mathematical model of the problem of geometric nonlinearity is established based on the porous media theory. Then, a synthetic numerical computation method is presented to simulate the numerical results of the problem. Here, the differential quadrature method and second-order backward difference scheme are applied to discretize the mathematical model in the spatial and time domains, respectively. In addition, the Newton-Raphson iterative method is used to solve nonlinear algebraic equations and to present the numerical results of the problem. The method presented in this study is proven to be effective and reliable, where its advantages include a small calculated amount and high accuracy. Finally, the thermodynamic characteristics of the fluid-saturated porous thermo-elastic half-plane subjected to surface temperature loadings are studied, and the effects of material parameters and geometric nonlinearity on the dynamic characteristics are considered in detail.