GONG Ke. Bending Theories for Beams and Plates With Single Generalized Displacement[J]. Applied Mathematics and Mechanics, 2000, 21(9): 984-990.
 Citation: GONG Ke. Bending Theories for Beams and Plates With Single Generalized Displacement[J]. Applied Mathematics and Mechanics, 2000, 21(9): 984-990.

# Bending Theories for Beams and Plates With Single Generalized Displacement

• Rev Recd Date: 2000-06-03
• Publish Date: 2000-09-15
• 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.
•  [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.

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