397 lines
10 KiB
C
397 lines
10 KiB
C
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright held by original author
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM 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 2 of the License, or (at your
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option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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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 OpenFOAM; if not, write to the Free Software Foundation,
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Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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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 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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//- 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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mesh,
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dimensionedScalar("zero", dimTemperature, 0.0)
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);
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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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C.component(vector::X)*C.component(vector::X) + C.component(vector::Y)*C.component(vector::Y);
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forAll(radii.internalField(), celli)
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{
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radii.internalField()[celli] = ::sqrt(radii.internalField()[celli]);
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}
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forAll(radii.boundaryField(), patchi)
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{
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forAll(radii.boundaryField()[patchi], facei)
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{
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radii.boundaryField()[patchi][facei] = ::sqrt(radii.boundaryField()[patchi][facei]);
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}
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}
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forAll(T.internalField(), celli)
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{
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const scalar& r = radii[celli];
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T.internalField()[celli] =
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( (Ti-To)/Foam::log(b/a) ) * Foam::log(b/r);
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}
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forAll(T.boundaryField(), patchi)
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{
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forAll(T.boundaryField()[patchi], facei)
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{
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const scalar& r = radii.boundaryField()[patchi][facei];
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T.boundaryField()[patchi][facei] =
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( (Ti-To)/Foam::log(b/a) ) * Foam::log(b/r);
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}
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}
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//- write temperature file
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Info << "Writing analytical termpature field" << endl;
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T.write();
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//- create sigma field
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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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mesh,
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dimensionedScalar("zero", dimForce/dimArea, 0.0)
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);
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forAll(sigmaR.internalField(), celli)
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{
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const scalar& r = radii.internalField()[celli];
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sigmaR.internalField()[celli] =
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( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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(-Foam::log(b/r) -( a*a/(b*b - a*a))*(1 - (b*b)/(r*r))*Foam::log(b/a));
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}
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forAll(sigmaR.boundaryField(), patchi)
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{
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forAll(sigmaR.boundaryField()[patchi], facei)
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{
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const scalar& r = radii.boundaryField()[patchi][facei];
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sigmaR.boundaryField()[patchi][facei] =
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( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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( -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 - (b*b)/(r*r))*Foam::log(b/a) );
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}
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}
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//- write temperature file
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Info << "\nWriting analytical sigmaR field" << endl;
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sigmaR.write();
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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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mesh,
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dimensionedScalar("zero", dimForce/dimArea, 0.0)
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);
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forAll(sigmaTheta.internalField(), celli)
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{
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const scalar& r = radii.internalField()[celli];
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sigmaTheta.internalField()[celli] =
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( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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(1 -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 + (b*b)/(r*r))*Foam::log(b/a) );
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}
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forAll(sigmaTheta.boundaryField(), patchi)
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{
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forAll(sigmaTheta.boundaryField()[patchi], facei)
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{
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const scalar& r = radii.boundaryField()[patchi][facei];
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sigmaTheta.boundaryField()[patchi][facei] =
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( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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(1 -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 + (b*b)/(r*r))*Foam::log(b/a) );
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}
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}
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//- write temperature file
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Info << "\nWriting analytical sigmaTheta field" << endl;
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sigmaTheta.write();
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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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mesh,
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dimensionedScalar("zero", dimForce/dimArea, 0.0)
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);
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forAll(sigmaZ.internalField(), celli)
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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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// sigmaZ.internalField()[celli] =
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// ( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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// (1 - 2*Foam::log(b/r) - ( 2*a*a/(b*b - a*a))*Foam::log(b/a));
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sigmaZ.internalField()[celli] =
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0.3*(sigmaR.internalField()[celli] + sigmaTheta.internalField()[celli])
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- E*alpha*(T.internalField()[celli]);
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}
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forAll(sigmaZ.boundaryField(), patchi)
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{
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forAll(sigmaZ.boundaryField()[patchi], facei)
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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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//sigmaZ.boundaryField()[patchi][facei] =
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//( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
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//(1 - 2*Foam::log(b/r) - ( 2*a*a/(b*b - a*a))*Foam::log(b/a));
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//-for general 2-D plain strain problems, the axial stress is given by this:
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sigmaZ.boundaryField()[patchi][facei] =
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nu*(sigmaR.boundaryField()[patchi][facei] + sigmaTheta.boundaryField()[patchi][facei])
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- E*alpha*(T.boundaryField()[patchi][facei]);
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}
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}
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//- write temperature file
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Info << "\nWriting analytical sigmaZ field" << endl;
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sigmaZ.write();
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//- create analytical sigma tensor
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//- create theta field
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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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mesh,
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dimensionedScalar("zero", dimless, 0.0)
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);
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forAll(theta.internalField(), celli)
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{
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const scalar& x = mesh.C().internalField()[celli][vector::X];
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const scalar& y = mesh.C().internalField()[celli][vector::Y];
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theta.internalField()[celli] = Foam::atan(y/x);
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}
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forAll(theta.boundaryField(), patchi)
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{
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forAll(theta.boundaryField()[patchi], facei)
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{
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const scalar& x = mesh.C().boundaryField()[patchi][facei][vector::X];
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const scalar& y = mesh.C().boundaryField()[patchi][facei][vector::Y];
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theta.boundaryField()[patchi][facei] = Foam::atan(y/x);
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}
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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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forAll(rotMat.internalField(), celli)
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{
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const scalar& t = theta.internalField()[celli];
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rotMat.internalField()[celli] = tensor(::cos(t), ::sin(t), 0,
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-::sin(t), ::cos(t), 0,
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0, 0, 1);
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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] = tensor(::cos(t), ::sin(t), 0,
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-::sin(t), ::cos(t), 0,
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0, 0, 1);
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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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forAll(sigma.internalField(), celli)
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{
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const scalar& r = sigmaR.internalField()[celli];
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const scalar& t = sigmaTheta.internalField()[celli];
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const scalar& z = sigmaZ.internalField()[celli];
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const tensor& rot = rotMat.internalField()[celli];
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symmTensor sigmaCart(r, 0, 0,
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t, 0,
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z);
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sigma.internalField()[celli] =
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symm(rot.T() & sigmaCart & rot);
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//-for general 2-D plain strain problems, the axial stress is given by this:
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//- (which is not equal to the solution by Timoshenko... hmmmnn)
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// sigma.internalField()[celli][symmTensor::ZZ] =
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// 0.3*(sigma.internalField()[celli][symmTensor::XX] + sigma.internalField()[celli][symmTensor::YY])
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// - E*alpha*(T.internalField()[celli]);
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}
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forAll(sigma.boundaryField(), patchi)
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{
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forAll(sigma.boundaryField()[patchi], facei)
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{
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const scalar& r = sigmaR.boundaryField()[patchi][facei];
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const scalar& t = sigmaTheta.boundaryField()[patchi][facei];
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const scalar& z = sigmaZ.boundaryField()[patchi][facei];
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const tensor& rot = rotMat.boundaryField()[patchi][facei];
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symmTensor sigmaCart(r, 0, 0,
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t, 0,
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z);
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sigma.boundaryField()[patchi][facei] =
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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();
|
||
|
|
|
||
|
|
Info << nl << "End" << endl;
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// ************************************************************************* //
|