142 lines
3.9 KiB
C
142 lines
3.9 KiB
C
/*---------------------------------------------------------------------------*\
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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 infinite plaste with a circular
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hole.
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Stress field sigma is generated.
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Based on solution outlined in Timoshenko, Theory of Elasticity.
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Author
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plateHoleSolution function by Z. Tukovic
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utility assembled by P. Cardiff
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\*---------------------------------------------------------------------------*/
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#include "fvCFD.H"
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#include "volFields.H"
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#include "fvc.H"
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#include "fixedValueFvPatchFields.H"
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#include "coordinateSystem.H"
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symmTensor plateHoleSolution(const vector& C);
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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 an infinite plate with a circular hole,\nwhere"
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<< "\n\tradius = 0.5"
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<< "\n\tdistant traction = (10,000 0 0 )"
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<< nl << endl;
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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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const volVectorField& C = mesh.C();
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forAll(sigma.internalField(), celli)
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{
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vector curR = vector(C[celli].x(), C[celli].y(), 0);
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sigma.internalField()[celli] = plateHoleSolution(curR);
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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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vector curR = vector(C.boundaryField()[patchi][facei].x(), C.boundaryField()[patchi][facei].y(), 0);
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sigma.boundaryField()[patchi][facei] = plateHoleSolution(curR);
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}
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}
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Info << "Writing analytical sigma tensor" << endl;
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sigma.write();
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Info << nl << "End" << endl;
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return 0;
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}
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// ************************************************************************* //
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symmTensor plateHoleSolution(const vector& C)
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{
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tensor sigma = tensor::zero;
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scalar T = 10000;
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scalar a = 0.5;
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scalar r = ::sqrt(sqr(C.x()) + sqr(C.y()));
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scalar theta = Foam::atan2(C.y(), C.x());
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coordinateSystem cs("polarCS", C, vector(0, 0, 1), C/mag(C));
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sigma.xx() =
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T*(1 - sqr(a)/sqr(r))/2
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+ T*(1 + 3*pow(a,4)/pow(r,4) - 4*sqr(a)/sqr(r))*::cos(2*theta)/2;
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sigma.xy() =
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- T*(1 - 3*pow(a,4)/pow(r,4) + 2*sqr(a)/sqr(r))*::sin(2*theta)/2;
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sigma.yx() = sigma.xy();
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sigma.yy() =
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T*(1 + sqr(a)/sqr(r))/2
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- T*(1 + 3*pow(a,4)/pow(r,4))*::cos(2*theta)/2;
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// Transformation to global coordinate system
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sigma = ((cs.R()&sigma)&cs.R().T());
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symmTensor S = symmTensor::zero;
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S.xx() = sigma.xx();
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S.xy() = sigma.xy();
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S.yy() = sigma.yy();
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return S;
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}
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