Interior formulation of axisymmetric Levinson plate theory

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Interior formulation of axisymmetric Levinson plate theory. / Karttunen, Anssi T.; Von Hertzen, Raimo.

In: MECHANICS RESEARCH COMMUNICATIONS, Vol. 74, 01.06.2016, p. 34-38.

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@article{8a2aa9e4decc44f9acc0d16908e8a5d3,
title = "Interior formulation of axisymmetric Levinson plate theory",
abstract = "In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.",
keywords = "Clapeyron's theorem, Finite element, Interior plate, Levinson theory, Saint Venant's principle",
author = "Karttunen, {Anssi T.} and {Von Hertzen}, Raimo",
year = "2016",
month = "6",
day = "1",
doi = "10.1016/j.mechrescom.2016.03.008",
language = "English",
volume = "74",
pages = "34--38",
journal = "MECHANICS RESEARCH COMMUNICATIONS",
issn = "0093-6413",

}

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TY - JOUR

T1 - Interior formulation of axisymmetric Levinson plate theory

AU - Karttunen, Anssi T.

AU - Von Hertzen, Raimo

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.

AB - In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.

KW - Clapeyron's theorem

KW - Finite element

KW - Interior plate

KW - Levinson theory

KW - Saint Venant's principle

UR - http://www.scopus.com/inward/record.url?scp=84963900772&partnerID=8YFLogxK

U2 - 10.1016/j.mechrescom.2016.03.008

DO - 10.1016/j.mechrescom.2016.03.008

M3 - Article

VL - 74

SP - 34

EP - 38

JO - MECHANICS RESEARCH COMMUNICATIONS

JF - MECHANICS RESEARCH COMMUNICATIONS

SN - 0093-6413

ER -

ID: 3301196