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