功能梯度圆板的三维瞬态热弹性分析

THREE-DIMENSIONAL ANALYSIS FOR TRANSIENT THERMAL RESPONSES OF A FUNCTIONALLY GRADED CIRCULAR PLATE

基于线性热弹性理论的基本方程,采用两个位移分量,两个应力分量,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轴对称圆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,根据微分求积法,将状态方程沿径向进行离散。采用Lap lace变换和打靶法,数值求解了材料常数按幂率变化的周边固支圆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圆板的热响应行为,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 a functionally graded axisymmetric circular plate subjected to time-dependent thermal loads is established based on the three-dimensional linear thermoelastic theory using state space approach,in which two displacement components,two stress components,temperature and a heat flux component are chosen as state variables.By discretizing the state space formulation along the radial direction using the technique of differential quadrature,new state equations at discrete points are established.The motional inertial item and the coupled effect during heat conduction are taken into account in the state equations.Giving clamped boundary conditions and assuming that the mechanical properties of the materials have an exponential distribution law along the thickness-coordinate,they are solved using Laplace transformation and the shooting method for the transient thermal responses of the plate subjected to a thermal shork on its top surface.Effects of volume fraction distribution of constituent materials on the thermal responses including temperature change,deflection and stress distributions are investigated.