Comparison of solutions from different displacement boundary conditions at fixed end of cantilever beams
YANG Lian-zhi1,2, ZHANG Liang-liang2,3, YU Lian-ying2, SHANG Lan-ge2, GAO Yang2, WANG Min-zhong4
1. Civil and Environmental Engineering School, University of Science and Technology Beijing, Beijing 100083, China; 2. College of Science, China Agricultural University, Beijing 100083, China; 3. College of Engineering, China Agricultural University, Beijing 100083, China; 4. Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China
To obtain the influence of different displacement boundary conditions for the fixed end on analytical solutions of a cantilever beam, three load cases for a cantilever beam were investigated, which were a transverse shear force at the free end, a uniformly distributed load at the top surface, and a linearly distributed load at the top surface, respectively. Analytical solutions were given for Levinson theory, Timoshenko theory, and the elastic theory by using the conventional displacement boundary condition and the boundary condition through least squares method at the fixed end of the beam, and were compared with the solutions by finite element method. It is shown that the solutions from Timoshenko theory by using both the conventional displacement boundary condition and the condition through least squares method are the same; Levinson theory and the elastic theory by using the boundary condition through least squares method provide better results than those by using the conventional boundary condition. With an increase in the order of the load, the superiority becomes more and more obvious．
YANG Lian-zhi, ZHANG Liang-liang, YU Lian-ying, SHANG Lan-ge, GAO Yang, WANG Min-zhong. Comparison of solutions from different displacement boundary conditions at fixed end of cantilever beams. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2014, 48(11): 1955-1961.
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