The refined theory of deep rectangular beams based on general solutions of elasticity

作     者：GAO Yang1 & WANG Minzhong2 1. College of Science, China Agricultural University, Beijing 100083, China 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engi- neering Science, Peking University, Beijing 100871, China 

作者机构：College of Science China Agricultural University Beijing 100083 China State Key Laboratory for Turbulence Complex Systems Department of Mechanics Engineering Science Peking University Beijing 100871 China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2006年第49卷第3期

页      面：291-303页

核心收录：

学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China  NSFC  (10372003) 

主　　题：deep rectangular beams,the refined theory,Papkovich-Neuber solution,Lur'e method,governing equation 

摘      要：The problem of deducing one-dimensional theory from two-dimensional the- ory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the re- fined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two ex- amples, it is shown that the new theory provides better results than Levinson’s beam the- ory when compared with those obtained from the linear theory of elasticity.