基于平面弹性-板弯曲模拟关系的薄板有限元列式——从膜单元到薄板单元  

On a new formulation of thin plate element based on the similarity between plane elasticity and plate bending──-from membrane elements to thin plate elements

作　　者：郑长良[1] 黄若煜[1] 姚伟岸[1] 钟万勰[1] 

机构地区：[1]大连理工大学工程力学系,辽宁大连116023

出　　处：《计算力学学报》2001年第3期253-258,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金 (1 973 2 0 2 0 ) ;教委博士点专项基金 (970 1 41 1 9)资助课题

摘　　要：本文全面讨论了基于平面弹性 -板弯曲模拟关系的薄板有限单元的理论和方法。由于直接对弯矩函数进行插值 ,c1连续性的要求得以自然避免。薄板单元可以直接在 c0 连续的层面上加以构造 ,无需借用 Reissner- Mindlin的中厚板理论 ,由之引发的闭锁问题也得以避免。本文系统地阐明了平面弹性膜单元与薄板弯曲单元的对应关系 ,及由平面弹性膜单元向薄板弯曲单元转换的一整套方法 ,为薄板单元的构造提供了一条新的有效的途径。文中给出了对应于平面弹性膜单元CST、LST、Q4、Q8的薄板单元 ,我们称之为 MPS板单元。MPS板元以挠度和转角为自由度 ,便于实际应用 ,和其它板单元相比具有非常高的精度。A new theory and approach of thin plate element on the basis of the similarity theory between plane elasticity and plate bending has been discussed. Because of using approximation of bending moment functions, the requirement of c 1 continuity of displacement in thin plate elements can be avoided naturally. Thin plate elements can be formulated directly at c 0 continuity level for bending moment functions instead of the Reissner Mindlin's thick plate theory for rotations. The locking problems can also be avoided. The relationship between membrane elements and plate bending elements and an approach to transform membrane elements to plate bending ones are presented systematically. A new effective path is supplied to construct high performance thin plate elements. The thin plate elements, called MPS (Membrane Plate Similarity) elements, correspondent to the membrane CST, LST, Q4 and Q8 elements are given. The degrees of freedom of the MPS thin plate elements are deflection and rotations, They can be used easily in practices. Numerical results show that the MPS thin plate elements have a very high precision compared with other plate elements.

关 键 词：板弯曲 膜-板模拟 收敛性 有限元 平面弹性问题 

分 类 号：O343.1[理学—固体力学] O241.82[理学—力学]