功能梯度材料瞬态热传导问题的降维精细积分法

DECREMENT-DIMENSIONAL PRECISE TIME INTEGRATION OF 2-D TRANSIENT HEAT CONDUCTION EQUATION FOR FUNCTIONALLY GRADED MATERIALS

针对功能梯度材料(FGMs)的二维瞬态热传导问题,提出了一种有效的降维精细积分法.通过空间坐标的分步离散,将原二维问题的精细积分转化为一系列一维问题的精细积分,解决了直接精细积分算法所面临的传递矩阵规模过大的问题,从而大幅度降低了计算量和存储量.算例表明了本文方法的有效性.

An efficient algorithm（Decrement-dimensional Precise Time Integration method,DPTI） of two-dimensional transient heat conduction equation is presented for Functionally Graded Materials（FGMs） based on the Precise Time Integration method （PTI）. DPTI realizes the matrix storage optimization, and thus,solves the problem of large-scale coefficient matrix H, encountered by PTI, when calculating the transfer matrix T. DPTI also make full use of the similarity of the equation after decreased dimension to reduce the computation time greatly which achieve the optimization of the computational efficiency. The numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method.