功能梯度材料矩形板的三维瞬态热弹性分析

THREE-DIMENSIONAL ANALYSIS FOR TRANSIENT HERMAL RESPONSES OF FUNCTIONALLY GRADED RECTANGULAR PLATE

基于三维线性热弹性理论的基本方程,采用三个位移分量、三个应力分量、温度变量和一个热流分量作为状态变量,应用状态空间理论,建立了功能梯度材料板结构在动态热载荷作用下的状态方程,考虑了运动惯性项以及热传导过程中的耦合效应。采用Laplace变换和打靶法,数值求解了材料常数按幂率变化的四边简支矩形板在热冲击下的热响应。为求解功能梯度结构三维热弹性瞬态响应提供了一种方法。分析了组分材料分布对功能梯度板的热响应行为,包括板内温度变化,横向挠度以及板内应力分量的影响规律。

The state equation of functionally graded rectangular plate subjected to time-dependent thermal loads was established based on the three-dimensional linear thermoelastic theory and using state space approach, in which three displacement components, three stress components, temperature components and a heat flux component were chosen as state variables. The state equation took into account the motional inertial item and the coupling effect during heat conduction. A simply supported three dimensional functionally graded rectangular plate was analyzed assuming the mechanical properties of the materials exponentially distributed along the thickness. The transient thermal responses due to a thermal shock on its top surface were obtained using the Laplace transformations and shooting methods. Effects of the volume fraction distributions of constituent materials on the thermal responses, including the temperature change, the displacement and the stress distributions were investigated.