离散Kirchhoff三角形薄板单元的改进

本文构造了一类改进的离散Ｋｉｒｃｈｈｏｆｆ三角形薄板单元。通过对离散Ｋｉｒｃｈｈｏｆｆ单元能量表达式的分解，发现存在一项不影响单元的收敛，但能控制单元精度的积分－－有关绕Ｚ轴的转动偶的积分。该项在经典薄板理论下是不存在的，但在粗网络下它会对单元的精度产生重要影响。通过合理调整该项在能量泛函中的比例，会使单元的精度得到明显改善。

Improvement of Discrete Kirchhoff TriangularThin Plate Bending Element

An improved discrete Kirchhoff triangular element for thin plate bending is derived in this paper.From disassembling the energy expreesion of discrete Kirchhoff element, it is discovered that there ex-ists an integration of a rotation couple round z-axis which does not affect the element convergency butcan control the elernent nccuracy.This term is not appear under the classical thin plate theory. It canhowever impose an important influence on the element accuracy in the case of coarse meshes. So longas the proportion of the term in energy functional is appropriately readjusted,the element accuracy canremarkably improved.