Splitting Modulus Finite Element Method for Orthogonal Anisotropic Plate Bending
-
摘要: 讨论了建立分裂模量有限元法的必要性,推导了正交各向异性薄板弯曲问题分裂模量变分原理的泛函,以此为基础建立了该问题的分裂模量有限元法。该模型的特点是其中含有一个被称为分裂因子的参数,通过算例说明:适当调整分裂因子的值,可以达到调整有限元模型的刚度、降低有限元刚度矩阵的谱条件数、克服常规有限元病态问题的目的,最后分析了克服病态问题的机理。Abstract: Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
-
[1] Clough R W. The finite element method in plane stress analysis[J]. Pro Amer Soc Civil Eng,1960,87:345-378. [2] Argyris J H. Energy Theorems and Structural Analysis[M]. Butterworth,1960. [3] Turner M J, Clough R W, Martin H G, et al. Stiffness and deflection analysis of complex structures[J]. J Aero Sci,1956,23:805-823. [4] Fraeijs de Veubeke B. Displacement and equilibrium models in the finite element method[A]. In: Zienkiewicz O C, Holister G S Eds.Stress Analysis[C]. London: John Wiley and Sons Ltd. 1965,145-197. [5] Pian T H H. Derivation of element stiffness matrices[J]. AIAA J,1964,2:576-577. [6] Pian T H H. Derivation of element stiffness matrices by assumed stress distributions[J]. AIAA J,1964,2:1333-1336. [7] Herrmann L R. A bending analysis for plates[A]. In: 1st Conf Matrix Methods in Structural Mechanics[C]. Ohio: Wright-Patterson Air Force Base,1965,577-604. [8] Pan Y S, Chen D P. Formulation of hybrid/mixed plate bending element with splitting and partialy compatible displacements[A]. In: Proc of International Conf on Computational Engineering Mechanics[C],Beijing:1987,37-42. [9] Fraeijs de Veubeke B. Upper and lower bounds in matrix structural analysis[A]. In: Fraeijs de Veubeke B Ed. Matrix Methods of Structural Analysis[C]. New York: MacMillian,1964,1:165-201. [10] Sander P G. Bormes superieures et inferieures dans 1'analyse matricielle des plaques en flexion-torsion[J]. Bull Soc Royale Seiences Liege,1964,33(7):456-494. [11] 荣廷玉. 弹性力学广义混合变分原理及有限元广义混合法[A]. 见:四川省力学学会及重庆市力学学会第一届计算力学学术论文报告会论文集[C]. 第一集,1983,1-13. [12] RONG Ting-yu. Generalized mixed variational principles and new FEM models in solid mechanics[J]. Int J Solid Structures,1988,24(1):1131-1140. [13] Zienkiwicz O C. The Finite Element Method in Engineering Science[M]. McGraw-Hill Book Company,1971. [14] Leknitskii S G. Anisotropic Plates[M]. London: Gordon & Breach,1968. [15] Timoshenko S, Woinowsky-Kreger S. Theory of Plates & Shells[M]. New York: McGraw-Hill Book Company,1959. [16] 徐次达,华伯浩. 固体力学有限元理论、方法及程序[M]. 北京:水利电力学院,1983. [17] 党发宁. 有限元广义混合法及其在克服有限元病态问题研究中的应用[D]. 成都:西南交通大学博士学位论文,1998,1:54-74.
点击查看大图
计量
- 文章访问数: 1819
- HTML全文浏览量: 94
- PDF下载量: 654
- 被引次数: 0