惩罚函数法在三维等参杂交元的应用

Application of Penalty Function Method in Isoparametric Hybrid Finite Element Analysis

1.
College of Civil and Architectural Engineering, Hefei University of Technology, Hefei 230009, P. R. China;

摘要: 提出在等参杂交元中用惩罚函数法引入平衡约束条件，具体讨论了惩罚函数法在三维等参杂交元中的运用，并提出采用分项罚数的方法，建立最佳的罚平衡杂交元模型．罚平衡法可以在不增加自由度的前提下，有效地扼制寄生应力．数值实验表明,新建立的单元,可以有效地抑制单元畸变对计算精度的影响，从而大幅度提高畸变网格下的计算精度，方法带有普遍性．
- 杂交元 /
- 平衡条件 /
- 惩罚函数法
Abstract: By aid of the penalty function method, the equilibrium restriction conditions were intr oduced to the isopar ametric hy brid finite element analysis, and the concrete application course of the penalty function method in three-dimension isoparametric hybrid finite element was discussed. The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the par asitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the prese ntedelement not only is effective in improving greatly the numeric calculation precision of distorted grids but also has universality.
- hybrid element /
- equilibrium restriction condition /
- penalty function method

[1]	Pain T H H.Derivation of element stiffness matrices by assumed stress distribution[J].AIAA J,1964，2（2）：1333—1336. doi: 10.2514/3.2546
[2]	Pain T H H，Chen D P.Alternative ways for formulation of hybrid stress elements[J].Internat J Numer Meth Engrg，1982，18（11）：1679—1684. doi: 10.1002/nme.1620181107
[3]	Pain T H H.Sumihara K.Rational approach for assumed stress finite elements[J].Internat J Numer Meth Engrg，1984，20（9）：1685—1695. doi: 10.1002/nme.1620200911
[4]	吴长春,狄生林,黄茂光.杂交元的优化设计[J].科学通报,1986,15(31)：1142—1144.
[5]	焦兆平.罚函数法在等参杂交元中的应用[J].合肥工业大学学报,1991,14(1)：86—95.
[6]	焦兆平,吴长春.三维等参杂交元的优化设计[J].工程力学,1988,5(2)：10—20.
[7]	吴长春，卞学璜.非协调数值分析与杂交元方法[M].北京：科技出版社，1997.
[8]	WU Chang-chun,Bufler H.Multivariable finite elements: consistency and optimization[J].Science in China,Ser A,1991,34(2)：284—299.