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One-dimensional models of a beam made of an anisotropic material with oblique anisotropy. / Tovstik, P. E.; Tovstik, Tatiana Petrovna.

In: Mechanics of Solids, Vol. 46, No. 6, 12.2011, p. 888-897.

Research output: Contribution to journal › Article › peer-review

Harvard

Tovstik, PE & Tovstik, TP 2011, 'One-dimensional models of a beam made of an anisotropic material with oblique anisotropy', Mechanics of Solids, vol. 46, no. 6, pp. 888-897. https://doi.org/10.3103/S0025654411060082

APA

Tovstik, P. E., & Tovstik, T. P. (2011). One-dimensional models of a beam made of an anisotropic material with oblique anisotropy. Mechanics of Solids, 46(6), 888-897. https://doi.org/10.3103/S0025654411060082

Vancouver

Tovstik PE, Tovstik TP. One-dimensional models of a beam made of an anisotropic material with oblique anisotropy. Mechanics of Solids. 2011 Dec;46(6):888-897. https://doi.org/10.3103/S0025654411060082

Author

Tovstik, P. E. ; Tovstik, Tatiana Petrovna. / One-dimensional models of a beam made of an anisotropic material with oblique anisotropy. In: Mechanics of Solids. 2011 ; Vol. 46, No. 6. pp. 888-897.

BibTeX

@article{e9c79a013cd048f49266bd25aeff42f4,
title = "One-dimensional models of a beam made of an anisotropic material with oblique anisotropy",
abstract = "One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed.",
keywords = "approximate models, beams, dispersion equation, oblique anisotropy, vibration",
author = "Tovstik, {P. E.} and Tovstik, {Tatiana Petrovna}",
year = "2011",
month = dec,
doi = "10.3103/S0025654411060082",
language = "English",
volume = "46",
pages = "888--897",
journal = "Mechanics of Solids",
issn = "0025-6544",
publisher = "Allerton Press, Inc.",
number = "6",

}

RIS

TY - JOUR

T1 - One-dimensional models of a beam made of an anisotropic material with oblique anisotropy

AU - Tovstik, P. E.

AU - Tovstik, Tatiana Petrovna

PY - 2011/12

Y1 - 2011/12

N2 - One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed.

AB - One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed.

KW - approximate models

KW - beams

KW - dispersion equation

KW - oblique anisotropy

KW - vibration

UR - http://www.scopus.com/inward/record.url?scp=84855527390&partnerID=8YFLogxK

U2 - 10.3103/S0025654411060082

DO - 10.3103/S0025654411060082

M3 - Article

AN - SCOPUS:84855527390

VL - 46

SP - 888

EP - 897

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 6

ER -

ID: 9283319