单广义位移的深梁理论和中厚板理论

龚克

单广义位移的深梁理论和中厚板理论

龚克

无锡工程设备研究所, 江苏无锡214035

详细信息

作者简介:
龚克(1962- ),男,江苏江阴人,助理研究员,硕士.

中图分类号: O341;TB301
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- 被引次数: 0
出版历程
- 收稿日期: 1998-10-01
- 修回日期: 2000-06-03
- 刊出日期: 2000-09-15

Bending Theories for Beams and Plates With Single Generalized Displacement

GONG Ke

Wuxi Institute of Engineering Equipemnt, Wuxi, Jiangsu 214035, P R China

摘要

摘要: 经典的梁板弯曲理论由于未考虑横向剪切变形的影响而只能适用于细长梁和薄板,传统的多广义位移的深梁理论和中厚板理论由于忽视了转角与挠度之间的内在关系而只能适用于短粗梁和中厚板。这两种理论存在着转角的独立性与不独立性之间的矛盾,因而不相兼容。鉴于此从基本假设出发,既考虑了横向剪切影响,又确定了转角与挠度的关系,导出了单广义位移的深梁理论和中厚板理论,给出了几种简单梁的解析解,并用数值算例验证了这一理论的适用性。
- 梁 /
- 板 /
- 弯曲理论 /
- 横向剪切影响 /
- 通用有限单元
Abstract: Classical bending theories for beams and plates can not be used for short,stubby beams and thick plates since transverse shearing effect is excluded,and ordinary theories with multiple generalized displacements can not be used for long,slender beams and thin plates since the innate relation between rotation angle and deflection is ignored.These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle.Based on several basic assumptions,a new type of theories which not only include the transverse shearing effect is presented, but also the relation between rotation angle and deflection is obtained.Analytical solutions of several simple beams are given.It has been testified by numerical examples that the new theories can be used for either long,slender beams and thin plates or short,stubby beams and thick plates.
- beam /
- plate /
- bending theory /
- transverse shearing effect /
- universal finite element

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参考文献(6)

[1]	Timoshenko S P. On the correction for shear of the differential equation for transverse vibration of prismatic bars[J]. Philosophical Magazine,1921,41:744.
[2]	Reissner E. On the theory of bending of elastic plates[J]. Journal of Mathematics and Physics,1944,23:184.
[3]	龚克. 曲率位移非线性影响的数值分析及有限元通用单元[D]. 硕士论文. 长沙: 国防科技大学,1986,36-43.
[4]	龚克. 十二自由度矩形板通用单元[A]. 见:无锡市力学学会编:无锡市力学学会学术交流会论文[C],无锡,1987.
[5]	曹志远,杨升田. 厚板动力学理论及其应用[M].北京:科学出版社,1983,297-383.
[6]	ZHOU Ke-jian, GONG Ke. A triangular finite element with 9-DOF in common use for thin and thick plate vibration problems[A]. In: DU Qing-hua Ed:Proceedings of the ICVPE-Xian[C]. Xi'an: Xi'an Jiaotong University Press,1986,214-219.