CLC number: O343.1
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2015-09-15
Cited: 0
Clicked: 4696
Citations: Bibtex RefMan EndNote GB/T7714
Chun-xiao Zhan, Yi-hua Liu. Plane elasticity solutions for beams with fixed ends[J]. Journal of Zhejiang University Science A, 2015, 16(10): 805-819.
@article{title="Plane elasticity solutions for beams with fixed ends",
author="Chun-xiao Zhan, Yi-hua Liu",
journal="Journal of Zhejiang University Science A",
volume="16",
number="10",
pages="805-819",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1500043"
}
%0 Journal Article
%T Plane elasticity solutions for beams with fixed ends
%A Chun-xiao Zhan
%A Yi-hua Liu
%J Journal of Zhejiang University SCIENCE A
%V 16
%N 10
%P 805-819
%@ 1673-565X
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1500043
TY - JOUR
T1 - Plane elasticity solutions for beams with fixed ends
A1 - Chun-xiao Zhan
A1 - Yi-hua Liu
J0 - Journal of Zhejiang University Science A
VL - 16
IS - 10
SP - 805
EP - 819
%@ 1673-565X
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1500043
Abstract: The plane stress problem of beams is a typical one in elasticity theory. In this paper a new set of boundary conditions for the fixed end is proposed to improve the accuracy of the plane elasticity solution for beams with fixed end(s). Plane elasticity solutions are then derived for the cantilever beam, propped cantilever beam, and fixed-fixed beam. The new set of boundary conditions is constructed by combining two conventional ones with a parameter. The parameters for different kinds of beams are determined by minimizing the square sum of the longitudinal displacements through the thickness of the fixed end. Comparison with the results obtained by the finite element method (FEM) shows the efficiency of the new type of boundary conditions. When the beam is a deep one, it is found that different boundary conditions yield different errors, and the elasticity solution obtained by the new boundary conditions best approaches the FEM results.
This is a quite interesting and complete work on the seemingly old but important problem in elasticity. The paper suggests a new mathematical form to express the fixed boundary of a beam, which combines the two existing ones in Timoshenko and Goodier by introducing a parameter which is determined on a reasonable ground. Numerical comparison with FEM shows that the new form enables more accurate results.
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