In this paper, a spatial–temporal generalized finite difference method (GFDM) with an additional condition is proposed for two-dimensional (2D) transient heat conduction analysis of functionally graded materials (FGMs). The 2D time dependent problem is explored as the three-dimensional (3D) stationary problem by treating the temporal direction as the third dimension. Based on the time-marching procedure with the GFDM, an additional condition is introduced to ensure well-posedness of the 3D stationary problem. Numerical experiment is presented to illustrate the performance of the developed method, and a comparison of numerical precision is made between the present approach and the conventional GFDM.

本文针对功能梯度材料（FGM）的二维（2D）瞬态热传导分析，提出了带有附加条件的时空广义有限差分法（GFDM）。通过将时间方向视为第三维，将2D时间相关问题视为三维（3D）平稳问题。基于GFDM的时间前进过程，引入了附加条件以确保3D平稳问题的适定性。数值实验表明了该方法的性能，并对本方法与传统的GFDM方法进行了数值精度的比较。