Asymptotic closed-form solutions including boundary-layers for orthotropic beams

In this paper, asymptotic closed-form solutions with boundary-layers are explicitly obtained. The virtual work principle is applied to the problem by employing the method of multiple-scales, which allows one to systematically separate two-dimensional elasticity problems into the interior and boundar...

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Bibliographic Details
Published in:	European journal of mechanics, A, Solids A, Solids, 2022-07, Vol.94, p.104541, Article 104541
Main Author:	Kim, Jun-Sik
Format:	Article
Language:	eng
Subjects:	Asymptotic method Asymptotic properties Boundary conditions Boundary-layers Closed form solutions Decay rate Displacement Exact solutions Finite element method Multiple-scales Multiscale analysis Orthotropic beams Saint Venant principle Timoshenko’s elasticity solution Two dimensional analysis
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Summary:	In this paper, asymptotic closed-form solutions with boundary-layers are explicitly obtained. The virtual work principle is applied to the problem by employing the method of multiple-scales, which allows one to systematically separate two-dimensional elasticity problems into the interior and boundary-layer problems. From the interior problem, we calculate the warping displacements first and then construct boundary-layer displacements by employing them as a basis. Saint-Venant’s principle is applied to the boundary-layers so that they satisfy the surface boundary conditions in a weak sense. For stress prescribed boundaries, the minimization process is enforced to satisfy the conditions, which allow one to predict the free-edge boundary-layers. Cantilevers with three types of materials are taken as numerical examples. Asymptotic closed-form decay rates, displacements, and stresses are derived and compared to a two-dimensional finite element analysis. The results obtained herein clearly show that the present approach yields a reliable prediction of boundary-layers for orthotropic beams. [Display omitted] •The explicit form of asymptotic boundary-layer solutions is derived for the cantilever.•The method of multiple-scale is employed to formulate the problem.•The boundary layers are constructed based on interior warping functions.•The displacement boundary conditions are significant in the interior state.
ISSN:	0997-7538 1873-7285