317 lines
8.5 KiB
C
317 lines
8.5 KiB
C
/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | foam-extend: Open Source CFD
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\\ / O peration | Version: 4.0
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\\ / A nd | Web: http://www.foam-extend.org
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\\/ M anipulation | For copyright notice see file Copyright
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-------------------------------------------------------------------------------
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License
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This file is part of foam-extend.
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foam-extend is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation, either version 3 of the License, or (at your
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option) any later version.
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foam-extend is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with foam-extend. If not, see <http://www.gnu.org/licenses/>.
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Description
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Generate analytical solution for a thick-walled cylinder with a
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temperature gradient.
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Temperature field T and stress field sigma and generated.
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Based on solution outlined in Timoshenko, Theory of Elasticity.
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Author
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philip.cardiff@ucd.ie
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\*---------------------------------------------------------------------------*/
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#include "fvCFD.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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int main(int argc, char *argv[])
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{
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# include "setRootCase.H"
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# include "createTime.H"
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# include "createMesh.H"
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runTime++;
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Info<< "Writing analytical solution for a plain strain cylinder "
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<< "with concentric hole,\nwhere"
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<< "\n\tinner radius = 0.5"
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<< "\n\touter radius = 0.7"
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<< "\n\tinner temperature = 100"
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<< "\n\touter temperature = 0"
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<< "\n\tinner pressure = 0"
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<< "\n\touter pressure = 0"
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<< "\n\tE = 200e9"
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<< "\n\tu = 0.3"
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<< "\n\talpha = 1e-5"
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<< nl << endl;
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//- inner and outer radii and temperatures
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scalar a = 0.5;
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scalar b = 0.7;
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scalar Ti = 100;
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scalar To = 0;
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//- mechanical and thermal properties
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scalar E = 200e9;
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scalar nu = 0.3;
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scalar alpha = 1e-5;
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const volVectorField& C = mesh.C();
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//- radial coordinate
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volScalarField radii
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(
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sqrt
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(
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sqr(C.component(vector::X))
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+ sqr(C.component(vector::Y))
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)/dimensionedScalar("one", dimLength, 1)
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);
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const scalarField& rIn = radii.internalField();
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Info << "Writing analytical termpature field" << endl;
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//- create T field
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volScalarField T
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(
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IOobject
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(
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"analyticalT",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::AUTO_WRITE
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),
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((Ti - To)/Foam::log(b/a))*Foam::log(b/radii)
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);
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T.write();
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//- create sigma field
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Info << "\nWriting analytical sigmaR field" << endl;
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volScalarField sigmaR
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(
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IOobject
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(
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"sigmaR",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::AUTO_WRITE
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),
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((alpha*E*(Ti - To))/(2*(1 - nu)*Foam::log(b/a)))*
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(
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-Foam::log(b/radii)
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- (sqr(a)/(sqr(b) - sqr(a)))*(1 - sqr(b)/sqr(radii))*Foam::log(b/a)
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)
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);
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sigmaR.write();
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Info << "\nWriting analytical sigmaTheta field" << endl;
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volScalarField sigmaTheta
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(
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IOobject
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(
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"sigmaTheta",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::AUTO_WRITE
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),
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((alpha*E*(Ti - To))/(2*(1 - nu)*Foam::log(b/a)))*
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(
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1 - Foam::log(b/radii)
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- (sqr(a)/(sqr(b) - sqr(a)))*(1 + sqr(b)/sqr(radii))*Foam::log(b/a)
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)
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);
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sigmaTheta.write();
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Info << "\nWriting analytical sigmaZ field" << endl;
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volScalarField sigmaZ
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(
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IOobject
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(
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"sigmaZ",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::AUTO_WRITE
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),
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// Timoshenko says this but I am not sure I am not sure the BCs in
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// the z direction
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// ((alpha*E*(Ti - To))/(2*(1 - nu)*Foam::log(b/a)))*
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// (1 - 2*Foam::log(b/radii) - ( 2*sqr(a)/(sqr(b) - sqr(a)))*Foam::log(b/a));
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0.3*(sigmaR + sigmaTheta) - E*alpha*(T)
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);
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sigmaZ.write();
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//- create theta field
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volScalarField yOverX
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(
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"yOverX",
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Foam::max
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(
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scalar(-1),
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Foam::min
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(
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scalar(1),
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mesh.C().component(vector::Y)/
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stabilise
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(
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mesh.C().component(vector::X),
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dimensionedScalar("small", dimLength, SMALL)
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)
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)
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)
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);
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volScalarField theta
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(
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IOobject
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(
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"theta",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::NO_WRITE
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),
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Foam::atan(yOverX)
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);
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//- rotation matrix to convert polar stresses to cartesian
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volTensorField rotMat
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(
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IOobject
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(
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"rotMat",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::NO_WRITE
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),
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mesh,
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dimensionedTensor("zero", dimless, tensor::zero)
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);
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tensorField& rotMatIn = rotMat.internalField();
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const scalarField tIn = theta.internalField();
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forAll (rotMatIn, celli)
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{
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const scalar& t = tIn[celli];
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rotMatIn[celli] =
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tensor
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(
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Foam::cos(t), Foam::sin(t), 0,
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-Foam::sin(t), Foam::cos(t), 0,
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0, 0, 1
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);
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}
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forAll (rotMat.boundaryField(), patchi)
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{
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forAll (rotMat.boundaryField()[patchi], facei)
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{
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const scalar& t = theta.boundaryField()[patchi][facei];
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rotMat.boundaryField()[patchi][facei] =
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tensor
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(
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Foam::cos(t), Foam::sin(t), 0,
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-Foam::sin(t), Foam::cos(t), 0,
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0, 0, 1
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);
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}
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}
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volSymmTensorField sigma
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(
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IOobject
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(
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"analyticalSigma",
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runTime.timeName(),
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mesh,
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IOobject::NO_READ,
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IOobject::AUTO_WRITE
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),
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mesh,
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dimensionedSymmTensor("zero", dimForce/dimArea, symmTensor::zero)
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);
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{
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symmTensorField& sigmaIn = sigma.internalField();
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const scalarField& rIn = sigmaR.internalField();
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const scalarField& tIn = sigmaTheta.internalField();
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const scalarField& zIn = sigmaZ.internalField();
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forAll (sigmaIn, celli)
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{
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symmTensor sigmaCart
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(
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rIn[celli], 0, 0,
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tIn[celli], 0,
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zIn[celli]
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);
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const tensor& rot = rotMatIn[celli];
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sigmaIn[celli] = symm(rot.T() & sigmaCart & rot);
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// for general 2-D plain strain problems, the axial stress is:
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// (which is not equal to the solution by Timoshenko... hmmmnn)
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// sigmaIn[celli][symmTensor::ZZ] =
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// 0.3*(sigmaIn[celli][symmTensor::XX]
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// + sigmaIn[celli][symmTensor::YY])
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// - E*alpha*(T.internalField()[celli]);
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}
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}
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forAll (sigma.boundaryField(), patchi)
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{
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symmTensorField& pSigma = sigma.boundaryField()[patchi];
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const scalarField& pR = sigmaR.boundaryField()[patchi];
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const scalarField& pT = sigmaTheta.boundaryField()[patchi];
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const scalarField& pZ = sigmaZ.boundaryField()[patchi];
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const tensorField pRot = rotMat.boundaryField()[patchi];
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forAll (pSigma, facei)
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{
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const tensor& rot = pRot[facei];
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symmTensor sigmaCart
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(
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pR[facei], 0, 0,
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pT[facei], 0,
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pZ[facei]
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);
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pSigma[facei] = symm(rot.T() & sigmaCart & rot);
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}
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}
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Info << "\nWriting analytical sigma tensor" << endl;
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sigma.write();
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Info << nl << "End" << endl;
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return 0;
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}
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// ************************************************************************* //
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