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Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity
Aalto university, Finland.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). Aalto university, Finland.ORCID iD: 0000-0001-8515-9907
Aalto university, Finland.
2017 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 109, p. 84-92Article in journal (Refereed) Published
Abstract [en]

Buckling of centrosymmetric anisotropic beams is studied within strain gradient theory. First, the three dimensional anisotropic gradient elasticity theory is outlined. Then the dimension of the three dimensional theory is reduced, resulting in Timoshenko beam as well as Euler–Bernoulli beam theories. The governing differential equations together with the consistent (classical and non-classical) boundary conditions are derived for centrosymmetric anisotropic beams through a variational approach. By considering von Kármán nonlinear strains, the geometric nonlinearity is taken into account. The obtained nonlinear formulation can be used to study the postbuckling configuration. The analysis of size effect on anisotropic beam structures is missing in the literature so far, while the present model allows one to characterize the size effect on the buckling of the centrosymmetric anisotropic micro- and nano-scale beam structures such as micropillars. As a specific case, the governing buckling equation is obtained for the more practical case of orthotropic beams. Finally, the buckling loads for orthotropic simply supported Timoshenko and Euler–Bernoulli beams as well as a clamped Euler–Bernoulli beam are obtained analytically and the effect of the internal length scale parameters on the buckling load is depicted.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 109, p. 84-92
Keywords [en]
Buckling; Anisotropic beam; Strain gradient; Orthotropy; Timoshenko beam; Euler–Bernoulli beam
National Category
Mechanical Engineering
Research subject
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kau:diva-62796DOI: 10.1016/j.ijsolstr.2017.01.009ISI: 000394071700008OAI: oai:DiVA.org:kau-62796DiVA, id: diva2:1135952
Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2018-06-26Bibliographically approved

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Publisher's full texthttp://www.sciencedirect.com/science/article/pii/S0020768317300094

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Mousavi, Mahmoud

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