Three-Dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method
Three-Dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method
复制标题
DOI：
10.1007/s00466-004-0617-6
复制
发表时间：
2005-02
影响因子：
4.1
通讯作者：
L. Qian;R. Batra
中科院分区：
文献类型：
--
作者：
L. Qian;R. Batra
用高阶板理论和无网格局部Petrov-Galerkin(MLPG)方法分析了功能梯度厚板中的瞬时热传导。采用勒让德多项式作为基函数，将温度场沿厚度方向展开。对于板的一个或两个主表面上规定的温度，使用修正的拉格朗日多项式作为基，并在这些展开式中添加附加项以精确匹配给定的温度。利用MLPG方法将勒让德多项式系数演化的偏微分方程组在时间上化为一组耦合的常微分方程组。常微分方程组的积分采用中心差分法。用五阶板理论计算得到的板心温度和温度沿厚度分布的时间历程与解析解符合得很好。
We analyze transient heat conduction in a thick functionally graded plate by using a higher-order plate theory and a meshless local Petrov-Galerkin (MLPG) method. The temperature field is expanded in the thickness direction by using Legendre polynomials as basis functions. For temperature prescribed on one or both major surfaces of the plate, modified Lagrange polynomials are used as basis and additional terms are added to these expansions to exactly match the given temperatures. Partial differential equations for the evolution of the coefficients of the Legendre polynomials are reduced to a set of coupled ordinary differential equations (ODEs) in time by a MLPG method. The ODEs are integrated by the central-difference method. The time history of evolution of the temperature at the plate centroid and through-the-thickness distribution of the temperature computed with the fifth-order plate theory are found to agree very well with those obtained analytically.