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foam-extend4.1-coherent-io/tutorials/solidMechanics/elasticThermalSolidFoam/hotCylinder/analyticalHotCylinder/analyticalHotCylinder.C

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C

/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration |
\\ / A nd | Copyright held by original author
\\/ M anipulation |
-------------------------------------------------------------------------------
License
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under the terms of the GNU General Public License as published by the
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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;
//- create T field
volScalarField T
(
IOobject
(
"analyticalT",
runTime.timeName(),
mesh,
IOobject::NO_READ,
IOobject::AUTO_WRITE
),
mesh,
dimensionedScalar("zero", dimTemperature, 0.0)
);
const volVectorField& C = mesh.C();
//- radial coordinate
volScalarField radii =
C.component(vector::X)*C.component(vector::X) + C.component(vector::Y)*C.component(vector::Y);
forAll(radii.internalField(), celli)
{
radii.internalField()[celli] = ::sqrt(radii.internalField()[celli]);
}
forAll(radii.boundaryField(), patchi)
{
forAll(radii.boundaryField()[patchi], facei)
{
radii.boundaryField()[patchi][facei] = ::sqrt(radii.boundaryField()[patchi][facei]);
}
}
forAll(T.internalField(), celli)
{
const scalar& r = radii[celli];
T.internalField()[celli] =
( (Ti-To)/Foam::log(b/a) ) * Foam::log(b/r);
}
forAll(T.boundaryField(), patchi)
{
forAll(T.boundaryField()[patchi], facei)
{
const scalar& r = radii.boundaryField()[patchi][facei];
T.boundaryField()[patchi][facei] =
( (Ti-To)/Foam::log(b/a) ) * Foam::log(b/r);
}
}
//- write temperature file
Info << "Writing analytical termpature field" << endl;
T.write();
//- create sigma field
volScalarField sigmaR
(
IOobject
(
"sigmaR",
runTime.timeName(),
mesh,
IOobject::NO_READ,
IOobject::AUTO_WRITE
),
mesh,
dimensionedScalar("zero", dimForce/dimArea, 0.0)
);
forAll(sigmaR.internalField(), celli)
{
const scalar& r = radii.internalField()[celli];
sigmaR.internalField()[celli] =
( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
(-Foam::log(b/r) -( a*a/(b*b - a*a))*(1 - (b*b)/(r*r))*Foam::log(b/a));
}
forAll(sigmaR.boundaryField(), patchi)
{
forAll(sigmaR.boundaryField()[patchi], facei)
{
const scalar& r = radii.boundaryField()[patchi][facei];
sigmaR.boundaryField()[patchi][facei] =
( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
( -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 - (b*b)/(r*r))*Foam::log(b/a) );
}
}
//- write temperature file
Info << "\nWriting analytical sigmaR field" << endl;
sigmaR.write();
volScalarField sigmaTheta
(
IOobject
(
"sigmaTheta",
runTime.timeName(),
mesh,
IOobject::NO_READ,
IOobject::AUTO_WRITE
),
mesh,
dimensionedScalar("zero", dimForce/dimArea, 0.0)
);
forAll(sigmaTheta.internalField(), celli)
{
const scalar& r = radii.internalField()[celli];
sigmaTheta.internalField()[celli] =
( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
(1 -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 + (b*b)/(r*r))*Foam::log(b/a) );
}
forAll(sigmaTheta.boundaryField(), patchi)
{
forAll(sigmaTheta.boundaryField()[patchi], facei)
{
const scalar& r = radii.boundaryField()[patchi][facei];
sigmaTheta.boundaryField()[patchi][facei] =
( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
(1 -Foam::log(b/r) - ( a*a/(b*b - a*a))*(1 + (b*b)/(r*r))*Foam::log(b/a) );
}
}
//- write temperature file
Info << "\nWriting analytical sigmaTheta field" << endl;
sigmaTheta.write();
volScalarField sigmaZ
(
IOobject
(
"sigmaZ",
runTime.timeName(),
mesh,
IOobject::NO_READ,
IOobject::AUTO_WRITE
),
mesh,
dimensionedScalar("zero", dimForce/dimArea, 0.0)
);
forAll(sigmaZ.internalField(), celli)
{
//- Timoshenko says this but I am not sure I am not sure the BCs in
//- the z direction
// sigmaZ.internalField()[celli] =
// ( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
// (1 - 2*Foam::log(b/r) - ( 2*a*a/(b*b - a*a))*Foam::log(b/a));
sigmaZ.internalField()[celli] =
0.3*(sigmaR.internalField()[celli] + sigmaTheta.internalField()[celli])
- E*alpha*(T.internalField()[celli]);
}
forAll(sigmaZ.boundaryField(), patchi)
{
forAll(sigmaZ.boundaryField()[patchi], facei)
{
//- Timoshenko says this but I am not sure I am not sure the BCs in
//- the z direction
//sigmaZ.boundaryField()[patchi][facei] =
//( (alpha*E*(Ti-To))/(2*(1-nu)*Foam::log(b/a)) ) *
//(1 - 2*Foam::log(b/r) - ( 2*a*a/(b*b - a*a))*Foam::log(b/a));
//-for general 2-D plain strain problems, the axial stress is given by this:
sigmaZ.boundaryField()[patchi][facei] =
nu*(sigmaR.boundaryField()[patchi][facei] + sigmaTheta.boundaryField()[patchi][facei])
- E*alpha*(T.boundaryField()[patchi][facei]);
}
}
//- write temperature file
Info << "\nWriting analytical sigmaZ field" << endl;
sigmaZ.write();
//- create analytical sigma tensor
//- create theta field
volScalarField theta
(
IOobject
(
"theta",
runTime.timeName(),
mesh,
IOobject::NO_READ,
IOobject::NO_WRITE
),
mesh,
dimensionedScalar("zero", dimless, 0.0)
);
forAll(theta.internalField(), celli)
{
const scalar& x = mesh.C().internalField()[celli][vector::X];
const scalar& y = mesh.C().internalField()[celli][vector::Y];
theta.internalField()[celli] = Foam::atan(y/x);
}
forAll(theta.boundaryField(), patchi)
{
forAll(theta.boundaryField()[patchi], facei)
{
const scalar& x = mesh.C().boundaryField()[patchi][facei][vector::X];
const scalar& y = mesh.C().boundaryField()[patchi][facei][vector::Y];
theta.boundaryField()[patchi][facei] = Foam::atan(y/x);
}
}
//- 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)
);
forAll(rotMat.internalField(), celli)
{
const scalar& t = theta.internalField()[celli];
rotMat.internalField()[celli] = tensor(::cos(t), ::sin(t), 0,
-::sin(t), ::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(::cos(t), ::sin(t), 0,
-::sin(t), ::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)
);
forAll(sigma.internalField(), celli)
{
const scalar& r = sigmaR.internalField()[celli];
const scalar& t = sigmaTheta.internalField()[celli];
const scalar& z = sigmaZ.internalField()[celli];
const tensor& rot = rotMat.internalField()[celli];
symmTensor sigmaCart(r, 0, 0,
t, 0,
z);
sigma.internalField()[celli] =
symm(rot.T() & sigmaCart & rot);
//-for general 2-D plain strain problems, the axial stress is given by this:
//- (which is not equal to the solution by Timoshenko... hmmmnn)
// sigma.internalField()[celli][symmTensor::ZZ] =
// 0.3*(sigma.internalField()[celli][symmTensor::XX] + sigma.internalField()[celli][symmTensor::YY])
// - E*alpha*(T.internalField()[celli]);
}
forAll(sigma.boundaryField(), patchi)
{
forAll(sigma.boundaryField()[patchi], facei)
{
const scalar& r = sigmaR.boundaryField()[patchi][facei];
const scalar& t = sigmaTheta.boundaryField()[patchi][facei];
const scalar& z = sigmaZ.boundaryField()[patchi][facei];
const tensor& rot = rotMat.boundaryField()[patchi][facei];
symmTensor sigmaCart(r, 0, 0,
t, 0,
z);
sigma.boundaryField()[patchi][facei] =
symm(rot.T() & sigmaCart & rot);
}
}
Info << "\nWriting analytical sigma tensor" << endl;
sigma.write();
Info << nl << "End" << endl;
return 0;
}
// ************************************************************************* //