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IssuesArchive of Issues2016-4pp.472-483

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Yu.I. Butenko, "Specific Characteristics of Numerical Determination of the Boundary Effect Stress-Strain State for an Orthotropic Strip," Mech. Solids. 51 (4), 472-483 (2016)
Year 2016 Volume 51 Number 4 Pages 472-483
DOI 10.3103/S0025654416040099
Title Specific Characteristics of Numerical Determination of the Boundary Effect Stress-Strain State for an Orthotropic Strip
Author(s) Yu.I. Butenko (Kazan State University of Architecture and Civil Engineering, ul. Zelenaya 1, Kazan, 420043 Russia, info@kgasu.ru)
Abstract The paper deals with the problem of determining the stress-strain state near the boundary of a one-layer strip made of an orthotropic material subjected to a self-balanced load applied at the end of the strip (Saint-Venant effect, boundary effect, and boundary layer). A comparative analysis of two methods for determining the boundary effect is carried out. The first method, i.e., the solution in stresses (with respect to σy), was developed by L. A. Agalovyan and gives good results of one-layer strips. The second approach, i.e., the solution in displacements, was developed by the author, and its results for the one-layer strip practically coincides with the solution in stresses. The obtained results were also verified by FEM. But the solution of the problem of elasticity in displacements is much more promising when analyzing multilayer strips.
Keywords boundary effect, orthotropy, homogeneous solution, characteristic equation, complex roots, numerical realization, collocation method
References
1.  L. A. Agalovyan, Asymptotic Theory of Anisotropic Plates and Shells (Nauka, Moscow, 1997) [in Russian].
2.  Yu. I. Butenko, "Study of the Boundary Layer in a Laminated Plate," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 123-141 (2007) [Mech. Solids (Engl. Transl.) 42 (4), 603-618 (2007)].
3.  Yu. I. Butenko, "Determining the Boundary Layers in the Plane Problem for Three-Layer Strips. Part 1," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 58-76 (2008) [Mech. Solids (Engl. Transl.) 43 (4), 571-585 (2008)].
4.  Yu. I. Butenko, "Determining the Boundary Layers in the Plane Problem for Three-Layer Strips. Part 2," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 136-146 (2009) [Mech. Solids (Engl. Transl.) 44 (1), 105-113 (2009)].
5.  Yu. I. Butenko, Boundary Effects in Two- and Three-Layer Strips and Plates (Izdat. Kazan Univ., Kazan, 2008) [in Russian].
6.  Yu. I. Butenko, "Boundary Effects in Multilayer Strips," in Problems of Nonlinear Mechanics of Deformable Solids. Second International Conference (KGU, Kazan, 2009), pp. 73-76 [in Russian].
7.  Yu. I. Butenko, "Boundary Effects in Multilayer Strips," Izv. Kazan. Gos. Arkhit.-Stroit. Univ., No. 2(12), 103-112 (2009).
8.  Yu. M. Artyukhin, N. G. Gur'yanov, and L. M. Kotlyar, System "Mathematica-4.0" and Its Applications in Mechanics (Izdat. KamPI, Kazan-Naberezhnye Chelny, 2002) [in Russian].
9.  V. V. Vasiliev and S. A. Lur'e, "Plane Problem of Elasticity for an Orthotropic Cantilever Strip," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 125-135 (1984) [Mech. Solids (Engl. Transl.)].
Received 24 February 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416040099
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