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Size effects on centrosymmetric anisotropic shear deformable beam structures
Aalto University, Finland.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics. Aalto University, Finland.ORCID iD: 0000-0001-8515-9907
Aalto University, Finland.
2017 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 97, no 5, p. 586-601Article in journal (Refereed) Published
Abstract [en]

In this paper, the size effect on beam structures with centrosymmetric anisotropy is studied within strain gradient elasticity theory. Applying dimension reduction to the three dimensional anisotropic gradient elasticity, the third-order shear deformable (TSD) beam is analysed. A variational approach is used to determine the equilibrium equations of TSD beam together with consistent (classical and non-classical) boundary conditions. The TSD beam theory which is suitable for deep beam structures can be replaced by (less complicated) Euler-Bernoulli beam model for thin beam structures. The anisotropic Euler-Bernoulli beam model is also formulated within the framework of strain gradient theory. This anisotropic beam theory can be used to study size effects for any types of centrosymmetric anisotropy. To address the more practical cases of composite structures, the formulation is simplified for orthotropic and transversely isotropic materials. Finally, the analytical solutions are provided for bending of simply supported (TSD and Euler-Bernoulli) beams as well as clamped Euler-Bernoulli beams. The effect of the crystal orientation with respect to the beam geometry is investigated in these examples.

Place, publisher, year, edition, pages
John Wiley & Sons, 2017. Vol. 97, no 5, p. 586-601
Keywords [en]
Anisotropy, strain gradient, shear deformable beam, orthotropy, centrosymmetric
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kau:diva-65049DOI: 10.1002/zamm.201600153ISI: 000403057800006OAI: oai:DiVA.org:kau-65049DiVA, id: diva2:1154086
Available from: 2017-11-01 Created: 2017-11-01 Last updated: 2017-11-01Bibliographically approved

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CiteExportLink to record
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  • apa
  • harvard1
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  • de-DE
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