Rewrite and clean-up
This commit is contained in:
Hrvoje Jasak
parent
298bf9d822
commit
995e56c8a7
1 changed files with 244 additions and 320 deletions
|
|
@ -26,7 +26,7 @@ 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.
|
||||
Based on solution outlined in Timoshenko, Theory of Elasticity.
|
||||
|
||||
Author
|
||||
philip.cardiff@ucd.ie
|
||||
|
|
@ -43,351 +43,275 @@ int main(int argc, char *argv[])
|
|||
# include "createTime.H"
|
||||
# include "createMesh.H"
|
||||
|
||||
runTime++;
|
||||
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;
|
||||
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;
|
||||
|
||||
//- mechanical and thermal properties
|
||||
scalar E = 200e9;
|
||||
scalar nu = 0.3;
|
||||
scalar alpha = 1e-5;
|
||||
//- inner and outer radii and temperatures
|
||||
scalar a = 0.5;
|
||||
scalar b = 0.7;
|
||||
scalar Ti = 100;
|
||||
scalar To = 0;
|
||||
|
||||
//- create T field
|
||||
volScalarField T
|
||||
//- mechanical and thermal properties
|
||||
scalar E = 200e9;
|
||||
scalar nu = 0.3;
|
||||
scalar alpha = 1e-5;
|
||||
|
||||
const volVectorField& C = mesh.C();
|
||||
|
||||
//- radial coordinate
|
||||
volScalarField radii
|
||||
(
|
||||
IOobject
|
||||
(
|
||||
"analyticalT",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::AUTO_WRITE
|
||||
),
|
||||
mesh,
|
||||
dimensionedScalar("zero", dimTemperature, 0.0)
|
||||
);
|
||||
|
||||
const volVectorField& C = mesh.C();
|
||||
sqrt
|
||||
(
|
||||
sqr(C.component(vector::X))
|
||||
+ sqr(C.component(vector::Y))
|
||||
)/dimensionedScalar("one", dimLength, 1)
|
||||
);
|
||||
|
||||
//- 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]);
|
||||
}
|
||||
}
|
||||
const scalarField& rIn = radii.internalField();
|
||||
|
||||
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
|
||||
Info << "Writing analytical termpature field" << endl;
|
||||
//- create T field
|
||||
volScalarField T
|
||||
(
|
||||
IOobject
|
||||
(
|
||||
"sigmaR",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::AUTO_WRITE
|
||||
),
|
||||
mesh,
|
||||
dimensionedScalar("zero", dimForce/dimArea, 0.0)
|
||||
);
|
||||
IOobject
|
||||
(
|
||||
"analyticalT",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::AUTO_WRITE
|
||||
),
|
||||
((Ti - To)/Foam::log(b/a))*Foam::log(b/radii)
|
||||
);
|
||||
T.write();
|
||||
|
||||
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
|
||||
//- create sigma field
|
||||
Info << "\nWriting analytical sigmaR field" << endl;
|
||||
volScalarField sigmaR
|
||||
(
|
||||
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) );
|
||||
}
|
||||
}
|
||||
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();
|
||||
|
||||
|
||||
//- write temperature file
|
||||
Info << "\nWriting analytical sigmaTheta field" << endl;
|
||||
sigmaTheta.write();
|
||||
|
||||
volScalarField sigmaZ
|
||||
Info << "\nWriting analytical sigmaTheta field" << endl;
|
||||
volScalarField sigmaTheta
|
||||
(
|
||||
IOobject
|
||||
(
|
||||
"sigmaZ",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::AUTO_WRITE
|
||||
),
|
||||
mesh,
|
||||
dimensionedScalar("zero", dimForce/dimArea, 0.0)
|
||||
);
|
||||
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();
|
||||
|
||||
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
|
||||
Info << "\nWriting analytical sigmaZ field" << endl;
|
||||
volScalarField sigmaZ
|
||||
(
|
||||
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];
|
||||
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();
|
||||
|
||||
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
|
||||
//- create theta field
|
||||
volScalarField yOverX
|
||||
(
|
||||
IOobject
|
||||
(
|
||||
"rotMat",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::NO_WRITE
|
||||
),
|
||||
mesh,
|
||||
dimensionedTensor("zero", dimless, tensor::zero)
|
||||
);
|
||||
"yOverX",
|
||||
Foam::max
|
||||
(
|
||||
scalar(-1),
|
||||
Foam::min
|
||||
(
|
||||
scalar(1),
|
||||
mesh.C().component(vector::Y)/
|
||||
stabilise
|
||||
(
|
||||
mesh.C().component(vector::X),
|
||||
dimensionedScalar("small", dimLength, SMALL)
|
||||
)
|
||||
)
|
||||
)
|
||||
);
|
||||
|
||||
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
|
||||
volScalarField theta
|
||||
(
|
||||
IOobject
|
||||
(
|
||||
"analyticalSigma",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::AUTO_WRITE
|
||||
),
|
||||
mesh,
|
||||
dimensionedSymmTensor("zero", dimForce/dimArea, symmTensor::zero)
|
||||
);
|
||||
IOobject
|
||||
(
|
||||
"theta",
|
||||
runTime.timeName(),
|
||||
mesh,
|
||||
IOobject::NO_READ,
|
||||
IOobject::NO_WRITE
|
||||
),
|
||||
Foam::atan(yOverX)
|
||||
);
|
||||
|
||||
forAll(sigma.internalField(), celli)
|
||||
//- 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& r = sigmaR.internalField()[celli];
|
||||
const scalar& t = sigmaTheta.internalField()[celli];
|
||||
const scalar& z = sigmaZ.internalField()[celli];
|
||||
const scalar& t = tIn[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);
|
||||
}
|
||||
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];
|
||||
|
||||
Info << "\nWriting analytical sigma tensor" << endl;
|
||||
sigma.write();
|
||||
rotMat.boundaryField()[patchi][facei] =
|
||||
tensor
|
||||
(
|
||||
Foam::cos(t), Foam::sin(t), 0,
|
||||
-Foam::sin(t), Foam::cos(t), 0,
|
||||
0, 0, 1
|
||||
);
|
||||
}
|
||||
}
|
||||
|
||||
Info << nl << "End" << endl;
|
||||
|
||||
return 0;
|
||||
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;
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
Reference in a new issue