Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions

Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions

Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the...

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Main Authors: Sen-Yung Lee, Qian-Zhi Yan
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/646391
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spelling doaj-e217e8ef21d1437ba68bf72c7bbd11b82020-11-24T22:28:52ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/646391646391Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary ConditionsSen-Yung Lee0Qian-Zhi Yan1Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, TaiwanDepartment of Mechanical Engineering, National Cheng Kung University, Tainan 701, TaiwanAnalytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.http://dx.doi.org/10.1155/2015/646391
collection DOAJ
language English
format Article
sources DOAJ
author Sen-Yung Lee
Qian-Zhi Yan
spellingShingle Sen-Yung Lee
Qian-Zhi Yan
Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
Mathematical Problems in Engineering
author_facet Sen-Yung Lee
Qian-Zhi Yan
author_sort Sen-Yung Lee
title Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
title_short Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
title_full Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
title_fullStr Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
title_full_unstemmed Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions
title_sort exact static analysis of in-plane curved timoshenko beams with strong nonlinear boundary conditions
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton’s principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.
url http://dx.doi.org/10.1155/2015/646391
work_keys_str_mv AT senyunglee exactstaticanalysisofinplanecurvedtimoshenkobeamswithstrongnonlinearboundaryconditions
AT qianzhiyan exactstaticanalysisofinplanecurvedtimoshenkobeamswithstrongnonlinearboundaryconditions
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