396 lines
10 KiB
C
396 lines
10 KiB
C
/*---------------------------------------------------------------------------*\
|
|
========= |
|
|
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
|
\\ / O peration |
|
|
\\ / A nd | Copyright held by original author
|
|
\\/ M anipulation |
|
|
-------------------------------------------------------------------------------
|
|
License
|
|
This file is part of OpenFOAM.
|
|
|
|
OpenFOAM 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 2 of the License, or (at your
|
|
option) any later version.
|
|
|
|
OpenFOAM 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 OpenFOAM; if not, write to the Free Software Foundation,
|
|
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
// ************************************************************************* //
|