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Article: Elasticity solution of clamped-simply supported beams with variable thickness
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TitleElasticity solution of clamped-simply supported beams with variable thickness
 
AuthorsXu, YP3
Zhou, D1
Cheung, YK2
 
KeywordsBeam
Clamped Edge
Elasticity Solution
Fourier Expansion
Variable Thickness
 
Issue Date2008
 
PublisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0253-4827
 
CitationApplied Mathematics And Mechanics (English Edition), 2008, v. 29 n. 3, p. 279-290 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s10483-008-0301-1
 
AbstractThis paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differential equations and the boundary conditions at two ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated. © 2008 Comitee of Applied Mathematics.
 
ISSN0253-4827
2012 Impact Factor: 0.647
2012 SCImago Journal Rankings: 0.360
 
DOIhttp://dx.doi.org/10.1007/s10483-008-0301-1
 
ISI Accession Number IDWOS:000254243300001
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorXu, YP
 
dc.contributor.authorZhou, D
 
dc.contributor.authorCheung, YK
 
dc.date.accessioned2012-06-26T06:04:50Z
 
dc.date.available2012-06-26T06:04:50Z
 
dc.date.issued2008
 
dc.description.abstractThis paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differential equations and the boundary conditions at two ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated. © 2008 Comitee of Applied Mathematics.
 
dc.description.natureLink_to_subscribed_fulltext
 
dc.identifier.citationApplied Mathematics And Mechanics (English Edition), 2008, v. 29 n. 3, p. 279-290 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s10483-008-0301-1
 
dc.identifier.doihttp://dx.doi.org/10.1007/s10483-008-0301-1
 
dc.identifier.epage290
 
dc.identifier.isiWOS:000254243300001
 
dc.identifier.issn0253-4827
2012 Impact Factor: 0.647
2012 SCImago Journal Rankings: 0.360
 
dc.identifier.issue3
 
dc.identifier.scopuseid_2-s2.0-41149119556
 
dc.identifier.spage279
 
dc.identifier.urihttp://hdl.handle.net/10722/150444
 
dc.identifier.volume29
 
dc.languageeng
 
dc.publisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0253-4827
 
dc.publisher.placeNetherlands
 
dc.relation.ispartofApplied Mathematics and Mechanics (English Edition)
 
dc.relation.referencesReferences in Scopus
 
dc.subjectBeam
 
dc.subjectClamped Edge
 
dc.subjectElasticity Solution
 
dc.subjectFourier Expansion
 
dc.subjectVariable Thickness
 
dc.titleElasticity solution of clamped-simply supported beams with variable thickness
 
dc.typeArticle
 
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<contributor.author>Cheung, YK</contributor.author>
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<description.abstract>This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differential equations and the boundary conditions at two ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated. &#169; 2008 Comitee of Applied Mathematics.</description.abstract>
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Author Affiliations
  1. Nanjing University of Technology
  2. The University of Hong Kong
  3. Nanjing University of Science and Technology