Three-dimensional analysis of transient thermal stresses in functionally graded plates
Three-dimensional analysis of transient thermal stresses in functionally graded plates
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DOI：
10.1016/s0020-7683(03)00361-5
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发表时间：
2003-12
影响因子：
3.6
通讯作者：
S. Vel;R. Batra
中科院分区：
文献类型：
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作者：
S. Vel;R. Batra
提出了简支功能梯度 (FG) 矩形板的三维热机械变形的解析解，该矩形板在其顶面和/或底面受到随时间变化的热载荷。材料属性被视为厚度坐标的解析函数。采用非耦合准静态线性热弹性理论，其中忽略由于变形而引起的温度变化（如果有的话）。采用同样满足边缘热边界条件的温度函数和拉普拉斯变换技术，将控制瞬态热传导的方程简化为厚度坐标下的常微分方程（ODE），并通过幂级数法求解。接下来，通过使用同样满足边缘边界条件的位移函数来分析每个瞬时温度分布的简支板的弹性问题。由此产生的具有可变系数的耦合常微分方程也可以通过幂级数法求解。该解析解适用于任意厚度的板。给出了双成分金属陶瓷 FG 矩形板的结果，其成分体积分数在厚度方向上呈幂律变化。某一点的有效弹性模量由 Mori-Tanaka 或自洽格式确定。给出了受顶表面规定的时间相关温度或热通量影响的板在几个关键位置的瞬态温度、位移和热应力。还给出了两种成分的各种体积分数、体积分数分布和两种均化方案的结果。
An analytical solution is presented for three-dimensional thermomechanical deformations of a simply supported functionally graded (FG) rectangular plate subjected to time-dependent thermal loads on its top and/or bottom surfaces. Material properties are taken to be analytical functions of the thickness coordinate. The uncoupled quasi-static linear thermoelasticity theory is adopted in which the change in temperature, if any, due to deformations is neglected. A temperature function that identically satisfies thermal boundary conditions at the edges and the Laplace transformation technique are used to reduce equations governing the transient heat conduction to an ordinary differential equation (ODE) in the thickness coordinate which is solved by the power series method. Next, the elasticity problem for the simply supported plate for each instantaneous temperature distribution is analyzed by using displacement functions that identically satisfy boundary conditions at the edges. The resulting coupled ODEs with variable coefficients are also solved by the power series method. The analytical solution is applicable to a plate of arbitrary thickness. Results are given for two-constituent metal-ceramic FG rectangular plates with a power-law through-the-thickness variation of the volume fraction of the constituents. The effective elastic moduli at a point are determined by either the Mori–Tanaka or the self-consistent scheme. The transient temperature, displacements, and thermal stresses at several critical locations are presented for plates subjected to either time-dependent temperature or heat flux prescribed on the top surface. Results are also given for various volume fractions of the two constituents, volume fraction profiles and the two homogenization schemes.