基于虚拟元方法的二维带源夹紧方板问题求解

A Virtual Element Method for Solving Two-Dimensional Clamped Square Plate Problem with Source

应用虚拟元方法研究二维带源夹紧方板问题,推导该方板的平面瞬态温度场的数值解并讨论网格剖分的细化程度对二维带源夹紧方板的平面瞬态温度场的影响.通过二维带源夹紧功能梯度材料板的平面瞬态热方程的数值计算,证明了理论分析结果的正确性,并且步长越精细,计算结果越精确,所得的等温线图符合实际温度场分布规律,因此该方法可以为检验其它近似方法提供参考.

This paper studies the solution of the virtual element method for two-dimensional clamped square plate equation with a source,derives the numerical solution of the plane transient temperature field of the plate,and studies the effect of mesh refinement on two-dimensional clamped square plate equation with a source.The correctness of the theoretical analysis results is verified by numerical calculation of two-dimensional transient thermal equa-tion of functionally graded material clamped plate,and the smaller the step,the more accurate the result,obtained isotherm graph is more consistent with the distribution law of the actual temperature field.Therefore,this method can be used as a reference to test other approximate methods.