private static void TestConsistentMass0()
{
IQuadrature2D quadratureForMass = TriangleQuadratureSymmetricGaussian.Order4Points6;
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var tri6 = new ContinuumElement2D(thickness, nodeSet0, InterpolationTri6.UniqueInstance,
TriangleQuadratureSymmetricGaussian.Order2Points3, quadratureForMass,
ExtrapolationGaussTriangular3Points.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = tri6.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 11.83599396, 0, -1.829621484, 0, -1.968668415, 0, 0.702983761, 0, -6.922261694, 0, 0.623796095, 0, },
{ 0, 11.83599396, 0, -1.829621484, 0, -1.968668415, 0, 0.702983761, 0, -6.922261694, 0, 0.623796095, },
{ -1.829621484, 0, 9.926994738, 0, -1.638252825, 0, -0.618678599, 0, -0.46271906, 0, -7.392556104, 0, },
{ 0, -1.829621484, 0, 9.926994738, 0, -1.638252825, 0, -0.618678599, 0, -0.46271906, 0, -7.392556104, },
{ -1.968668415, 0, -1.638252825, 0, 10.74103411, 0, -7.234180772, 0, 9.35E-02, 0, -0.141678539, 0, },
{ 0, -1.968668415, 0, -1.638252825, 0, 10.74103411, 0, -7.234180772, 0, 9.35E-02, 0, -0.141678539, },
{ 0.702983761, 0, -0.618678599, 0, -7.234180772, 0, 57.86118359, 0, 28.31288493, 0, 29.25347375, 0, },
{ 0, 0.702983761, 0, -0.618678599, 0, -7.234180772, 0, 57.86118359, 0, 28.31288493, 0, 29.25347375, },
{ -6.922261694, 0, -0.46271906, 0, 9.35E-02, 0, 28.31288493, 0, 56.00999156, 0, 28.6296356, 0, },
{ 0, -6.922261694, 0, -0.46271906, 0, 9.35E-02, 0, 28.31288493, 0, 56.00999156, 0, 28.6296356, },
{ 0.623796095, 0, -7.392556104, 0, -0.141678539, 0, 29.25347375, 0, 28.6296356, 0, 58.49121809, 0, },
{ 0, 0.623796095, 0, -7.392556104, 0, -0.141678539, 0, 29.25347375, 0, 28.6296356, 0, 58.49121809, }
}); // from Abaqus
Assert.True(M.Equals(expectedM, 1e-3));
}
private static void TestStiffness0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, dynamicMaterial);
ContinuumElement2D quad8 = factory.CreateElement(CellType.Quad8, nodeSet0);
IMatrix K = quad8.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 375957.1179055000, -130889.8953535400, 150398.7276607000, -30577.4536395990, 256263.9470137800, -74238.0130438120, 120262.5252654800, -29264.7336935000, -201002.5528104600, 86903.8674540020, -257013.8069723100, 62503.0900498910, -46878.8680758500, 18155.7769717120, -397987.0899868400, 97407.3612548510 },
{ -130889.8953535400, 264620.9765739100, -32500.5305626760, 108395.9237548000, -74238.0130438120, 148536.2310068900, -27341.6567704230, 66761.0027359010, 94596.1751463100, -240343.8078467800, 62503.0900498910, -121948.9418401700, 18155.7769717120, -45778.2662465080, 89715.0535625430, -180243.1181380300 },
{ 150398.7276607000, -32500.5305626760, 227070.8522891000, 24999.1791433860, 228075.7272750800, -35916.2249916640, 84715.8706078410, 5691.9746958972, -125567.3958918900, -7749.8459233937, -292871.0398821500, 29891.4228662980, -48734.4768523870, -12619.4433884890, -223088.2652062900, 28203.4681606430 },
{ -30577.4536395990, 108395.9237548000, 24999.1791433860, 135717.9797677600, -37839.3019147410, 115695.2678105500, 5691.9746958972, 47395.7262976820, -15442.1536157010, -174789.3743509800, 37583.7305586050, -85742.6925983560, -12619.4433884890, -59359.2032811550, 28203.4681606430, -87313.6274002970 },
{ 256263.9470137800, -74238.0130438120, 228075.7272750800, -37839.3019147410, 758698.8330168600, -151201.1982884900, 164115.4999410500, -25847.0928360870, -256843.4834062300, 67264.1450855650, -543079.2639940800, 68308.1044726010, -237729.8010194900, 72706.8336500980, -369501.4588269600, 80846.5228748690 },
{ -74238.0130438120, 148536.2310068900, -35916.2249916640, 115695.2678105500, -151201.1982884900, 368478.4546134000, -27770.1697591640, 85552.6038287820, 67264.1450855650, -166187.6357417500, 60615.7967802930, -223855.9737213700, 80399.1413424050, -193251.7815799700, 80846.5228748690, -134967.1662165300 },
{ 120262.5252654800, -27341.6567704230, 84715.8706078410, 5691.9746958972, 164115.4999410500, -27770.1697591640, 120174.7405891600, 2419.9582040241, -64973.3681564819, 9886.9381472210, -156296.6219667900, 10235.6574488430, -29392.1129538440, -12237.5732893820, -238606.5333264100, 39114.8713229830 },
{ -29264.7336935000, 66761.0027359010, 5691.9746958972, 47395.7262976820, -25847.0928360870, 85552.6038287820, 2419.9582040241, 63320.7521890160, 9886.9381472210, -67395.8289291320, 10235.6574488430, -47867.5471489640, -19929.8809816900, -81314.4790110740, 46807.1790152900, -66452.2299622090 },
{ -201002.5528104600, 94596.1751463100, -125567.3958918900, -15442.1536157010, -256843.4834062300, 67264.1450855650, -64973.3681564819, 9886.9381472210, 429358.6456627000, -85681.3574299900, 91327.9338391870, 31186.8509038820, -120846.2914647200, 7660.6709468983, 248546.5122279100, -109471.2691841800 },
{ 86903.8674540020, -240343.8078467800, -7749.8459233937, -174789.3743509800, 67264.1450855650, -166187.6357417500, 9886.9381472210, -67395.8289291320, -85681.3574299900, 501789.8020087000, 31186.8509038820, -24500.7443298540, 7660.6709468983, 60837.6092548520, -109471.2691841800, 110589.9799349400 },
{ -257013.8069723100, 62503.0900498910, -292871.0398821500, 37583.7305586050, -543079.2639940800, 60615.7967802930, -156296.6219667900, 10235.6574488430, 91327.9338391870, 31186.8509038820, 618909.3895160900, -107045.7505943100, 156953.5398894400, -38863.3219066200, 382069.8695706200, -56216.0532405820 },
{ 62503.0900498910, -121948.9418401700, 29891.4228662980, -85742.6925983560, 68308.1044726010, -223855.9737213700, 10235.6574488430, -47867.5471489640, 31186.8509038820, -24500.7443298540, -107045.7505943100, 363810.1766979700, -38863.3219066200, 60473.5634510330, -56216.0532405820, 79632.1594897160 },
{ -46878.8680758500, 18155.7769717120, -48734.4768523870, -12619.4433884890, -237729.8010194900, 80399.1413424050, -29392.1129538440, -19929.8809816900, -120846.2914647200, 7660.6709468983, 156953.5398894400, -38863.3219066200, 585811.6805262000, -190782.6753367700, -259183.6700493400, 155979.7323525500 },
{ 18155.7769717120, -45778.2662465080, -12619.4433884890, -59359.2032811550, 72706.8336500980, -193251.7815799700, -12237.5732893820, -81314.4790110740, 7660.6709468983, 60837.6092548520, -38863.3219066200, 60473.5634510330, -190782.6753367700, 616593.8061240300, 155979.7323525500, -358201.2487112100 },
{ -397987.0899868400, 89715.0535625430, -223088.2652062900, 28203.4681606430, -369501.4588269600, 80846.5228748690, -238606.5333264100, 46807.1790152900, 248546.5122279100, -109471.2691841800, 382069.8695706200, -56216.0532405820, -259183.6700493400, 155979.7323525500, 857750.6355973100, -235864.6335411300 },
{ 97407.3612548510, -180243.1181380300, 28203.4681606430, -87313.6274002970, 80846.5228748690, -134967.1662165300, 39114.8713229830, -66452.2299622090, -109471.2691841800, 110589.9799349400, -56216.0532405820, 79632.1594897160, 155979.7323525500, -358201.2487112100, -235864.6335411300, 636955.2510036100 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
public static void TestStrainsStresses0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, null);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet0);
// Abaqus results
double[] displacements =
{
0.0, 0.0, // Node 1
0.0, 0.0, // Node 2
-3.1797E-03, -8.6560E-03, // Node 3
4.4274E-03, -1.8570E-02 // Node 4
};
// The Gauss points in Abaqus have the same order as in GaussLegendre2D.Order2x2: Xi major, Eta minor
double[][] expectedStrainsAtGPs =
{
new double[] { 1.1178E-03, 1.5988E-03, -7.4619E-03 }, // Gauss point 1
new double[] { -1.2757E-03, 8.6753E-04, -4.5415E-03 }, // Gauss point 2
new double[] { 2.8614E-04, -7.3510E-04, -4.0517E-03 }, // Gauss point 3
new double[] { -2.3014E-03, -1.8646E-03, -5.0422E-04 } // Gauss point 4
};
double[][] expectedStressesAtGPs =
{
new double[] { 368.6, 446.3, -602.7 }, // Gauss point 1
new double[] { -234.3, 111.9, -366.8 }, // Gauss point 2
new double[] { 15.14, -149.8, -327.3 }, // Gauss point 3
new double[] { -660.2, -589.6, -40.73 } // Gauss point 4
};
// However the order of nodes is different, since in that Abaqus job the preprocessor numbered them differently from
// the counter-clockwise order of Quad4 nodes.
double[][] expectedStrainsAtNodes =
{
new double[] { 2.2723E-03, 2.6674E-03, -9.6950E-03 }, // Node 1
new double[] { -1.7504E-03, 1.6532E-03, -5.0343E-03 }, // Node 2
new double[] { -3.6499E-03, -3.3314E-03, 2.3560E-03 }, // Node 3
new double[] { 9.5484E-04, -1.1226E-03, -4.1860E-03 } // Node 4
};
double[][] expectedStressesAtNodes =
{
new double[] { 709.0, 772.9, -783.1 }, // Node 1
new double[] { -289.5, 260.3, -406.6 }, // Node 2
new double[] { -1073.0, -1021.0, 190.3 }, // Node 3
new double[] { 142.6, -193.0, -338.1 } // Node 4
};
(IReadOnlyList <double[]> strainsAtGPs, IReadOnlyList <double[]> stressesAtGPs) =
quad4.UpdateStrainsStressesAtGaussPoints(displacements);
IReadOnlyList <double[]> strainsAtNodes =
quad4.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(strainsAtGPs, quad4.Interpolation);
IReadOnlyList <double[]> stressesAtNodes =
quad4.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(stressesAtGPs, quad4.Interpolation);
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtGPs, strainsAtGPs, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtGPs, stressesAtGPs, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtNodes, strainsAtNodes, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtNodes, stressesAtNodes, 1e-3));
}
public static void TestStrainsStresses1()
{
var factory = new ContinuumElement2DFactory(thickness, material0, null);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet2);
// Abaqus results
double[] displacements =
{
0.0, 0.0, // Node 1
0.0, 0.0, // Node 2
1.0, -499.614E-03, // Node 4
986.100E-03, 1.0 // Node 3
};
// The Gauss points in Abaqus have the same order as in GaussLegendre2D.Order2x2: Xi major, Eta minor
double[][] expectedStrainsAtGPs =
{
new double[] { 1.46867E-03, 341.547E-03, 336.066E-03 }, // Gauss point 1
new double[] { 1.46867E-03, -91.3541E-03, 340.078E-03 }, // Gauss point 2
new double[] { 5.48114E-03, 341.547E-03, -96.8352E-03 }, // Gauss point 3
new double[] { 5.48114E-03, -91.3541E-03, -92.8228E-03 } // Gauss point 4
};
double[][] expectedStressesAtGPs =
{
new double[] { 23.9845E+03, 78.9202E+03, 27.1438E+03 }, // Gauss point 1
new double[] { -5.98559E+03, -20.9800E+03, 27.4679E+03 }, // Gauss point 2
new double[] { 24.9104E+03, 79.1980E+03, -7.82131E+03 }, // Gauss point 3
new double[] { -5.05964E+03, -20.7023E+03, -7.49722E+03 } // Gauss point 4
};
// The order of the nodes is also the same (at least in this job)
double[][] expectedStrainsAtNodes =
{
new double[] { 58.2077E-12, 500.000E-03, 493.050E-03 }, // Node 1
new double[] { 0.0, -249.807E-03, 500.0E-03 }, // Node 2
new double[] { 6.94981E-03, -249.807E-03, -249.807E-03 }, // Node 4
new double[] { 6.94981E-03, 500.000E-03, -256.757E-03 } // Node 3
};
double[][] expectedStressesAtNodes =
{
new double[] { 34.6154E+03, 115.385E+03, 39.8233E+03 }, // Node 1
new double[] { -17.2943E+03, -57.6478E+03, 40.3846E+03 }, // Node 2
new double[] { -15.6905E+03, -57.1666E+03, -20.1767E+03 }, // Node 4
new double[] { 36.2192E+03, 115.866E+03, -20.7380E+03 } // Node 3
};
(IReadOnlyList <double[]> strainsAtGPs, IReadOnlyList <double[]> stressesAtGPs) =
quad4.UpdateStrainsStressesAtGaussPoints(displacements);
IReadOnlyList <double[]> strainsAtNodes =
quad4.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(strainsAtGPs, quad4.Interpolation);
IReadOnlyList <double[]> stressesAtNodes =
quad4.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(stressesAtGPs, quad4.Interpolation);
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtGPs, strainsAtGPs, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtGPs, stressesAtGPs, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtNodes, strainsAtNodes, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtNodes, stressesAtNodes, 1e-4));
}
public static void TestStrainsStresses0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, null);
ContinuumElement2D tri3 = factory.CreateElement(CellType.Tri3, nodeSet0);
// Abaqus results
double[] displacements =
{
0.0, 0.0, // Node 1
0.0, 0.0, // Node 2
-1.4632E-03, -1.2747E-02 // Node 3
};
// There is only 1 Gauss point.
double[][] expectedStrainsAtGPs =
{
new double[] { -4.8201E-04, 7.4983E-04, -4.1130E-03 } // Gauss point 1
};
double[][] expectedStressesAtGPs =
{
new double[] { -59.32, 139.7, -332.2 } // Gauss point 1
};
// The order of the nodes is the same (at least in this job)
double[][] expectedStrainsAtNodes =
{
new double[] { -4.8201E-04, 7.4983E-04, -4.1130E-03 }, // Node 1
new double[] { -4.8201E-04, 7.4983E-04, -4.1130E-03 }, // Node 2
new double[] { -4.8201E-04, 7.4983E-04, -4.1130E-03 } // Node 3
};
double[][] expectedStressesAtNodes =
{
new double[] { -59.32, 139.7, -332.2 }, // Node 1
new double[] { -59.32, 139.7, -332.2 }, // Node 2
new double[] { -59.32, 139.7, -332.2 } // Node 3
};
(IReadOnlyList <double[]> strainsAtGPs, IReadOnlyList <double[]> stressesAtGPs) =
tri3.UpdateStrainsStressesAtGaussPoints(displacements);
IReadOnlyList <double[]> strainsAtNodes =
tri3.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(strainsAtGPs, tri3.Interpolation);
IReadOnlyList <double[]> stressesAtNodes =
tri3.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(stressesAtGPs, tri3.Interpolation);
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtGPs, strainsAtGPs, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtGPs, stressesAtGPs, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtNodes, strainsAtNodes, 1e-4));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtNodes, stressesAtNodes, 1e-3));
}
private static void TestStiffness0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, dynamicMaterial);
ContinuumElement2D tri3 = factory.CreateElement(CellType.Tri3, nodeSet0);
IMatrix K = tri3.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 43303.16742081400, 5294.11764705880, -43778.28054298600, -44796.38009049800, 475.11312217194, 39502.26244343900 },
{ 5294.11764705880, 122361.99095023000, -39027.14932126700, -104660.63348416000, 33733.03167420800, -17701.35746606300 },
{ -43778.28054298600, -39027.14932126700, 151866.51583710000, 66176.47058823500, -108088.23529412000, -27149.32126696800 },
{ -44796.38009049800, -104660.63348416000, 66176.47058823500, 127601.80995475000, -21380.09049773800, -22941.17647058800 },
{ 475.11312217194, 33733.03167420800, -108088.23529412000, -21380.09049773800, 107613.12217195000, -12352.94117647100 },
{ 39502.26244343900, -17701.35746606300, -27149.32126696800, -22941.17647058800, -12352.94117647100, 40642.53393665200 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
private static void TestStiffness2()
{
var factory = new ContinuumElement2DFactory(thickness, material1, dynamicMaterial);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet1);
IMatrix K = quad4.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 879120.87912088, 357142.85714286, -109890.10989011, -27472.527472527, -439560.43956044, -357142.85714286, -329670.32967033, 27472.527472527 },
{ 357142.85714286, 1593406.5934066, 27472.527472528, 604395.60439560, -357142.85714286, -796703.29670329, -27472.527472528, -1401098.9010989 },
{ -109890.10989011, 27472.527472528, 879120.87912088, -357142.85714286, -329670.32967033, -27472.527472527, -439560.43956044, 357142.85714286 },
{ -27472.527472527, 604395.60439560, -357142.85714286, 1593406.5934066, 27472.527472528, -1401098.9010989, 357142.85714286, -796703.29670329 },
{ -439560.43956044, -357142.85714286, -329670.32967033, 27472.527472528, 879120.87912088, 357142.85714286, -109890.10989011, -27472.527472527 },
{ -357142.85714286, -796703.29670329, -27472.527472527, -1401098.9010989, 357142.85714286, 1593406.5934066, 27472.527472528, 604395.60439560 },
{ -329670.32967033, -27472.527472528, -439560.43956044, 357142.85714286, -109890.10989011, 27472.527472528, 879120.87912088, -357142.85714286 },
{ 27472.527472527, -1401098.9010989, 357142.85714286, -796703.29670329, -27472.527472527, 604395.60439560, -357142.85714286, 1593406.5934066 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
private static void TestStiffness4()
{
var factory = new ContinuumElement2DFactory(thickness, material1, dynamicMaterial);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet3);
IMatrix K = quad4.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 0.2592059570522744, -0.005023279657148771, -0.1906544880785286, -0.017628995948735127, 0.06474697564228854, -0.12002962865455298, -0.13329844461603435, 0.1426819042604369 },
{ -0.005023279657148771, 0.42886928984872097, 0.049037670717931546, 0.11055696733570626, -0.12002962865455298, -0.022348176556173396, 0.0760152375937702, -0.5170780806282538 },
{ -0.1906544880785286, 0.049037670717931546, 1.3012408988907096, -0.5920791398890163, -0.33356025755449087, 0.15332067182282197, -0.77702615325769, 0.3897207973482628 },
{ -0.017628995948735127, 0.11055696733570626, -0.5920791398890163, 1.5350381195234322, 0.21998733848948865, -0.7683820415727372, 0.3897207973482628, -0.8772130452864011 },
{ 0.06474697564228854, -0.12002962865455298, -0.33356025755449087, 0.21998733848948865, 0.3475567568780642, -0.03912861828761283, -0.07874347496586184, -0.060829091547322856 },
{ -0.12002962865455298, -0.022348176556173396, 0.15332067182282197, -0.7683820415727372, -0.03912861828761283, 0.5397386843830521, 0.005837575119343828, 0.25099153374585864 },
{ -0.13329844461603435, 0.0760152375937702, -0.77702615325769, 0.3897207973482628, -0.07874347496586184, 0.005837575119343828, 0.9890680728395862, -0.4715736100613768 },
{ 0.1426819042604369, -0.5170780806282538, 0.3897207973482628, -0.8772130452864011, -0.060829091547322856, 0.25099153374585864, -0.4715736100613768, 1.1432995921687963 }
}; // from Solverize
//Assert.True(Utilities.AreMatricesEqual(K, new Matrix(expectedK), 1e-10));
}
private static void TestStiffness0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, dynamicMaterial);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet0);
IMatrix K = quad4.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 181603.19122884000, -89089.52288016200, -4991.10465483030, 7519.91442892909, -126789.16986973000, 70773.21914644800, -49822.91670427800, 10796.38930478500 },
{ -89089.52288016200, 210532.99196037000, 13289.14519816000, -85869.32985046300, 70773.21914644800, -146868.68100448000, 5027.15853555400, 22205.01889457400 },
{ -4991.10465483030, 13289.14519816000, 73155.65851293700, 4056.21872780570, -66433.22620703800, 10577.55360637600, -1731.32765106900, -27922.91753234200 },
{ 7519.91442892909, -85869.32985046300, 4056.21872780570, 85360.61861633800, 16346.78437560700, 2912.80345339600, -27922.91753234200, -2404.09221927070 },
{ -126789.16986973000, 70773.21914644800, -66433.22620703800, 16346.78437560700, 200705.04715702000, -95472.47721160800, -7482.65108024430, 8352.47368955240 },
{ 70773.21914644800, -146868.68100448000, 10577.55360637600, 2912.80345339600, -95472.47721160800, 232719.03971773000, 14121.70445878300, -88763.16216664000 },
{ -49822.91670427800, 5027.15853555400, -1731.32765106900, -27922.91753234200, -7482.65108024430, 14121.70445878300, 59036.89543559100, 8774.05453800470 },
{ 10796.38930478500, 22205.01889457400, -27922.91753234200, -2404.09221927070, 8352.47368955240, -88763.16216664000, 8774.05453800470, 68962.23549133600 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
private static void TestStiffness3()
{
var factory = new ContinuumElement2DFactory(thickness, material1, dynamicMaterial);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet3);
IMatrix K = quad4.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 514198.06499808, -10764.170693892, -403744.28140248, 6179.6240659003, 136202.13267487, -257206.34711690, -246655.91627047, 261790.89374489 },
{ -10764.170693892, 877762.34956189, 61124.679010955, 241708.83734231, -257206.34711690, -50430.336321830, 206845.83879984, -1069040.8505824 },
{ -403744.28140248, 61124.679010955, 2618366.6203953, -1268741.0140479, -648721.49301375, 372500.34071924, -1565900.8459791, 835115.99431770 },
{ 6179.6240659003, 241708.83734231, -1268741.0140479, 3119360.6646083, 427445.39566429, -1580482.4587671, 835115.99431770, -1780587.0431835 },
{ 136202.13267487, -257206.34711690, -648721.49301375, 427445.39566429, 691579.93709070, -83847.039187745, -179060.57675182, -86392.009359646 },
{ -257206.34711690, -50430.336321830, 372500.34071924, -1580482.4587671, -83847.039187745, 1103398.3531728, -31446.954414592, 527514.44191615 },
{ -246655.91627047, 206845.83879984, -1565900.8459791, 835115.99431770, -179060.57675182, -31446.954414592, 1991617.3390014, -1010514.8787030 },
{ 261790.89374489, -1069040.8505824, 835115.99431770, -1780587.0431835, -86392.009359646, 527514.44191615, -1010514.8787030, 2322113.4518497 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
private static void TestStiffness1()
{
var factory = new ContinuumElement2DFactory(thickness, material1, dynamicMaterial);
ContinuumElement2D quad4 = factory.CreateElement(CellType.Quad4, nodeSet2);
IMatrix K = quad4.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 989010.98901099, 357142.85714286, -604395.60439561, -27472.527472528, -494505.49450549, -357142.85714286, 109890.10989011, 27472.527472528 },
{ 357142.85714286, 989010.98901099, 27472.527472528, 109890.10989011, -357142.85714286, -494505.49450549, -27472.527472528, -604395.60439561 },
{ -604395.60439561, 27472.527472528, 989010.98901099, -357142.85714286, 109890.10989011, -27472.527472528, -494505.49450549, 357142.85714286 },
{ -27472.527472528, 109890.10989011, -357142.85714286, 989010.98901099, 27472.527472528, -604395.60439561, 357142.85714286, -494505.49450549 },
{ -494505.49450549, -357142.85714286, 109890.10989011, 27472.527472528, 989010.98901099, 357142.85714286, -604395.60439561, -27472.527472528 },
{ -357142.85714286, -494505.49450549, -27472.527472528, -604395.60439561, 357142.85714286, 989010.98901099, 27472.527472528, 109890.10989011 },
{ 109890.10989011, -27472.527472528, -494505.49450549, 357142.85714286, -604395.60439561, 27472.527472528, 989010.98901099, -357142.85714286 },
{ 27472.527472528, -604395.60439561, 357142.85714286, -494505.49450549, -27472.527472528, 109890.10989011, -357142.85714286, 989010.98901099 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-10));
}
private static void TestConsistentMassParametric(IReadOnlyList <Node> nodeSet, IQuadrature2D quadratureForMass,
bool reducedQuadrature)
{
var materialsAtGaussPoints = new List <IContinuumMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var tri3 = new ContinuumElement2D(thickness, nodeSet, InterpolationTri3.UniqueInstance,
TriangleQuadratureSymmetricGaussian.Order1Point1, quadratureForMass,
ExtrapolationGaussTriangular1Point.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = tri3.BuildConsistentMassMatrix();
// Reference: http://kis.tu.kielce.pl/mo/COLORADO_FEM/colorado/IFEM.Ch31.pdf, (eq 31.27)
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 2, 0, 1, 0, 1, 0 },
{ 0, 2, 0, 1, 0, 1 },
{ 1, 0, 2, 0, 1, 0 },
{ 0, 1, 0, 2, 0, 1 },
{ 1, 0, 1, 0, 2, 0 },
{ 0, 1, 0, 1, 0, 2 }
});
double area = CalcTriangleArea(nodeSet);
double scalar = dynamicMaterial.Density * thickness * area / 12.0;
expectedM.ScaleIntoThis(scalar);
if (reducedQuadrature)
{
Assert.False(M.Equals(expectedM, 1e-10));
}
else
{
Assert.True(M.Equals(expectedM, 1e-10));
}
}
private static void TestConsistentMass0()
{
IQuadrature2D quadratureForMass = GaussLegendre2D.GetQuadratureWithOrder(3, 3);
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var quad8 = new ContinuumElement2D(thickness, nodeSet0, InterpolationQuad8.UniqueInstance,
GaussLegendre2D.GetQuadratureWithOrder(3, 3), quadratureForMass,
ExtrapolationGaussLegendre3x3.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = quad8.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 9.115245555556, 0.000000000000, 1.881383333333, 0.000000000000, 3.914882222222, 0.000000000000, 2.417800000000, 0.000000000000, -7.376906666667, 0.000000000000, -11.056637777778, 0.000000000000, -9.104604444445, 0.000000000000, -7.444940000000, 0.000000000000 },
{ 0.000000000000, 9.115245555556, 0.000000000000, 1.881383333333, 0.000000000000, 3.914882222222, 0.000000000000, 2.417800000000, 0.000000000000, -7.376906666667, 0.000000000000, -11.056637777778, 0.000000000000, -9.104604444445, 0.000000000000, -7.444940000000 },
{ 1.881383333333, 0.000000000000, 9.727545555556, 0.000000000000, 2.239866666667, 0.000000000000, 3.841615555556, 0.000000000000, -6.727973333334, 0.000000000000, -6.701806666667, 0.000000000000, -9.031337777778, 0.000000000000, -11.077571111111, 0.000000000000 },
{ 0.000000000000, 1.881383333333, 0.000000000000, 9.727545555556, 0.000000000000, 2.239866666667, 0.000000000000, 3.841615555556, 0.000000000000, -6.727973333334, 0.000000000000, -6.701806666667, 0.000000000000, -9.031337777778, 0.000000000000, -11.077571111111 },
{ 3.914882222222, 0.000000000000, 2.239866666667, 0.000000000000, 7.681312222222, 0.000000000000, 2.776283333333, 0.000000000000, -11.082804444445, 0.000000000000, -8.784673333334, 0.000000000000, -6.832640000000, 0.000000000000, -11.150837777778, 0.000000000000 },
{ 0.000000000000, 3.914882222222, 0.000000000000, 2.239866666667, 0.000000000000, 7.681312222222, 0.000000000000, 2.776283333333, 0.000000000000, -11.082804444445, 0.000000000000, -8.784673333334, 0.000000000000, -6.832640000000, 0.000000000000, -11.150837777778 },
{ 2.417800000000, 0.000000000000, 3.841615555556, 0.000000000000, 2.776283333333, 0.000000000000, 7.581878888889, 0.000000000000, -11.009537777778, 0.000000000000, -10.983371111111, 0.000000000000, -6.895440000000, 0.000000000000, -8.941673333334, 0.000000000000 },
{ 0.000000000000, 2.417800000000, 0.000000000000, 3.841615555556, 0.000000000000, 2.776283333333, 0.000000000000, 7.581878888889, 0.000000000000, -11.009537777778, 0.000000000000, -10.983371111111, 0.000000000000, -6.895440000000, 0.000000000000, -8.941673333334 },
{ -7.376906666667, 0.000000000000, -6.727973333334, 0.000000000000, -11.082804444445, 0.000000000000, -11.009537777778, 0.000000000000, 45.023413333334, 0.000000000000, 28.692622222223, 0.000000000000, 20.114142222223, 0.000000000000, 28.734488888889, 0.000000000000 },
{ 0.000000000000, -7.376906666667, 0.000000000000, -6.727973333334, 0.000000000000, -11.082804444445, 0.000000000000, -11.009537777778, 0.000000000000, 45.023413333334, 0.000000000000, 28.692622222223, 0.000000000000, 20.114142222223, 0.000000000000, 28.734488888889 },
{ -11.056637777778, 0.000000000000, -6.701806666667, 0.000000000000, -8.784673333334, 0.000000000000, -10.983371111111, 0.000000000000, 28.692622222223, 0.000000000000, 48.215746666667, 0.000000000000, 24.589688888889, 0.000000000000, 22.134208888889, 0.000000000000 },
{ 0.000000000000, -11.056637777778, 0.000000000000, -6.701806666667, 0.000000000000, -8.784673333334, 0.000000000000, -10.983371111111, 0.000000000000, 28.692622222223, 0.000000000000, 48.215746666667, 0.000000000000, 24.589688888889, 0.000000000000, 22.134208888889 },
{ -9.104604444445, 0.000000000000, -9.031337777778, 0.000000000000, -6.832640000000, 0.000000000000, -6.895440000000, 0.000000000000, 20.114142222223, 0.000000000000, 24.589688888889, 0.000000000000, 28.821013333334, 0.000000000000, 24.924622222223, 0.000000000000 },
{ 0.000000000000, -9.104604444445, 0.000000000000, -9.031337777778, 0.000000000000, -6.832640000000, 0.000000000000, -6.895440000000, 0.000000000000, 20.114142222223, 0.000000000000, 24.589688888889, 0.000000000000, 28.821013333334, 0.000000000000, 24.924622222223 },
{ -7.444940000000, 0.000000000000, -11.077571111111, 0.000000000000, -11.150837777778, 0.000000000000, -8.941673333334, 0.000000000000, 28.734488888889, 0.000000000000, 22.134208888889, 0.000000000000, 24.924622222223, 0.000000000000, 49.869480000000, 0.000000000000 },
{ 0.000000000000, -7.444940000000, 0.000000000000, -11.077571111111, 0.000000000000, -11.150837777778, 0.000000000000, -8.941673333334, 0.000000000000, 28.734488888889, 0.000000000000, 22.134208888889, 0.000000000000, 24.924622222223, 0.000000000000, 49.869480000000 }
}); // from Abaqus
Assert.True(M.Equals(expectedM, 1e-10));
}
private static void TestStiffness0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, dynamicMaterial);
ContinuumElement2D tri6 = factory.CreateElement(CellType.Tri6, nodeSet0);
IMatrix K = tri6.BuildStiffnessMatrix();
double[,] expectedK = new double[, ]
{
{ 51173.75966, -20778.82606, 4273.968122, 6461.400457, 3161.87986, -13008.35802, -16897.34468, -27025.3615, 9688.11919, 8859.762175, -51400.38215, 45491.38295 },
{ -20778.82606, 122356.4459, 4538.323534, 34691.5801, -11085.2811, 5376.486541, -19333.05381, -142941.0483, 8859.762175, 6529.450147, 37799.07526, -26012.91439 },
{ 4273.968122, 4538.323534, 88582.98224, 45240.07515, 32066.51649, 7151.333545, -34941.29312, -27750.00033, -109199.8665, -39522.63295, 19217.69278, 10342.90105 },
{ 6461.400457, 34691.5801, 45240.07515, 104048.7171, 5228.256622, 3589.586543, -35442.30802, -149252.8235, -31830.32526, 1377.198943, 10342.90105, 5545.740823 },
{ 3161.87986, -11085.2811, 32066.51649, 5228.256622, 112494.273, -16055.03055, 1567.844178, 1895.723659, -172177.9559, -18317.78738, 22887.44239, 38334.11875 },
{ -13008.35802, 5376.486541, 7151.333545, 3589.586543, -16055.03055, 44329.93416, 1895.723659, 5503.165063, -26010.09507, -38438.07765, 46026.42644, -20361.09466 },
{ -16897.34468, -19333.05381, -34941.29312, -35442.30802, 1567.844178, 1895.723659, 363079.0153, 24675.86222, -73599.74689, 108516.9545, -239208.4748, -80313.17851 },
{ -27025.3615, -142941.0483, -27750.00033, -149252.8235, 1895.723659, 5503.165063, 24675.86222, 449052.1476, 108516.9545, -110192.2562, -80313.17851, -52169.18472 },
{ 9688.11919, 8859.762175, -109199.8665, -31830.32526, -172177.9559, -26010.09507, -73599.74689, 108516.9545, 485631.597, 60752.92074, -140342.1468, -120289.217 },
{ 8859.762175, 6529.450147, -39522.63295, 1377.198943, -18317.78738, -38438.07765, 108516.9545, -110192.2562, 60752.92074, 406726.0715, -120289.217, -266002.3867 },
{ -51400.38215, 37799.07526, 19217.69278, 10342.90105, 22887.44239, 46026.42644, -239208.4748, -80313.17851, -140342.1468, -120289.217, 388845.8685, 106433.9928 },
{ 45491.38295, -26012.91439, 10342.90105, 5545.740823, 38334.11875, -20361.09466, -80313.17851, -52169.18472, -120289.217, -266002.3867, 106433.9928, 358999.8396 }
}; // from Abaqus
Assert.True(K.Equals(Matrix.CreateFromArray(expectedK), 1e-9));
}
/// <summary>
/// Adds a whole mesh, which is defined by its nodes and elements, to the model.
/// </summary>
/// <param name="nodes">The nodes of the mesh.</param>
/// <param name="elements">The elements of the mesh.</param>
/// <param name="material">The common material of all elements in the mesh.</param>
/// <param name="dynamicProperties">Optional material properties for dynamic analysis. Common for all elements in the
/// mesh.</param>
public void AddMesh2D(IReadOnlyList <Node> nodes, IReadOnlyList <CellConnectivity <Node> > elements,
IFiniteElementMaterial material, DynamicMaterial dynamicProperties = null)
{
if (Dimensions == ProblemDimensions.ThreeDimensional)
{
throw new InvalidOperationException(
"This method can be used only for 2D problems (plane strain or plane stress)");
}
// Nodes
int numNodesCurrent = model.NodesDictionary.Count;
for (int i = 0; i < nodes.Count; ++i)
{
model.NodesDictionary.Add(numNodesCurrent + i, nodes[i]);
}
// Elements
int numElementsCurrent = model.Elements.Count;
int numElementsSubdomain = model.Subdomains[0].Elements.Count;
var factory = new ContinuumElement2DFactory(thickness, (ElasticMaterial2D)material, dynamicProperties); //TODO: extend the factory to other materials
for (int i = 0; i < elements.Count; ++i)
{
ContinuumElement2D element = factory.CreateElement(elements[i].CellType, elements[i].Vertices);
var elementWrapper = new Element()
{
ID = numElementsCurrent + i, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(numElementsCurrent + i, elementWrapper);
model.SubdomainsDictionary[0].Elements.Add(elementWrapper); //TODO: let the user decide which subdomain it will be added to.
}
}
private static void TestConsistentMass0()
{
// reduced integration rule - bad idea
IQuadrature2D quadratureForMass = GaussLegendre2D.GetQuadratureWithOrder(1, 1);
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var quad4 = new ContinuumElement2D(thickness, nodeSet1, InterpolationQuad4.UniqueInstance,
GaussLegendre2D.GetQuadratureWithOrder(2, 2), quadratureForMass,
ExtrapolationGaussLegendre2x2.UniqueInstance, materialsAtGaussPoints, dynamicMaterial);
IMatrix M = quad4.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 }
});
double lengthX = nodeSet1[1].X - nodeSet1[0].X;
double lengthY = nodeSet1[2].Y - nodeSet1[1].Y;
// For some reason , only half the thickness is used for Quad4 elements, as shown in Fig. 31.9. Therefore the
// coefficient 1/16 (full thickness) became 1/32 (half thickness). Here 1/16 is used.
double scalar = dynamicMaterial.Density * thickness * lengthX * lengthY / 16.0;
expectedM.ScaleIntoThis(scalar);
Assert.True(M.Equals(expectedM, 1e-10));
}
public static void WriteStiffnessOfContinuum2DStructure()
{
// ____ ____
// | | |
// |____|____|
// | | |
// |____|____|
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Material
double thickness = 1.0;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = 2.1E7,
PoissonRatio = 0.3
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0, true);
// Generate mesh
double domainLength = 2.0;
double domainHeight = 2.4;
var meshGenerator = new UniformMeshGenerator2D <Node>(0.0, 0.0, domainLength, domainHeight, 10, 10);
(IReadOnlyList <Node> vertices, IReadOnlyList <CellConnectivity <Node> > cells) =
meshGenerator.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < vertices.Count; ++n)
{
model.NodesDictionary.Add(n, vertices[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < cells.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(cells[e].CellType, cells[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Solver
var solverBuilder = new SkylineSolver.Builder();
SkylineSolver solver = solverBuilder.BuildSolver(model);
// Structural problem provider
var provider = new ProblemStructural(model, solver);
// Linear static analysis
var childAnalyzer = new LinearAnalyzer(model, solver, provider);
var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);
// Run the analysis to build the stiffness matrix
parentAnalyzer.Initialize();
parentAnalyzer.BuildMatrices();
// Print the stiffness matrix
//var writer = new MatlabWriter();
var writer = new RawArraysWriter();
writer.WriteToMultipleFiles((SkylineMatrix)solver.LinearSystems[subdomainID].Matrix,
outputDirectory + @"\quad4_20x20_stiffness.txt");
}
public static void TestStrainsStresses0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, null);
ContinuumElement2D tri6 = factory.CreateElement(CellType.Tri6, nodeSet0);
// Abaqus results
double[] displacements =
{
0.0, 0.0, // Node 1
0.0, 0.0, // Node 2
-1.7903E-02, -4.2697E-02, // Node 3
1.5326E-03, -1.0672E-03, // Node 4
-8.8920E-03, -1.1654E-02, // Node 5
3.5728E-03, -1.2996E-02 // Node 6
};
double[][] expectedStrainsAtGPs =
{
new double[] { 3.3735E-03, 8.8893E-04, -4.6302E-03 }, // Gauss point 1
new double[] { -4.4781E-03, 5.7927E-04, 3.6832E-04 }, // Gauss point 2
new double[] { -1.4936E-03, 3.0967E-03, -7.1318E-03 } // Gauss point 3
};
double[][] expectedStressesAtGPs =
{
new double[] { 840.0, 438.7, -374.00 }, // Gauss point 1
new double[] { -993.3, -176.3, 29.75 }, // Gauss point 2
new double[] { -130.3, 611.2, -576.00 } // Gauss point 3
};
// The order of the nodes is the same (at least in this job)
double[][] expectedStrainsAtNodes =
{
new double[] { 7.6130E-03, 2.5621E-04, -5.4625E-03 }, // Node 1
new double[] { -8.0901E-03, -3.6310E-04, 4.5346E-03 }, // Node 2
new double[] { -2.1212E-03, 4.6718E-03, -1.0466E-02 }, // Node 3
new double[] { -2.3853E-04, -5.3446E-05, -4.6399E-04 }, // Node 4
new double[] { -5.1056E-03, 2.1544E-03, -2.9656E-03 }, // Node 5
new double[] { 2.7459E-03, 2.4640E-03, -7.9641E-03 } // Node 6
};
double[][] expectedStressesAtNodes =
{
new double[] { 1775.00, 586.20, -441.20 }, // Node 1
new double[] { -1892.00, -643.90, 366.30 }, // Node 2
new double[] { -166.10, 931.30, -845.30 }, // Node 3
new double[] { -58.74, -28.85, -37.48 }, // Node 4
new double[] { -1029.00, 143.70, -239.50 }, // Node 5
new double[] { 804.30, 758.70, -643.30 } // Node 6
};
(IReadOnlyList <double[]> strainsAtGPs, IReadOnlyList <double[]> stressesAtGPs) =
tri6.UpdateStrainsStressesAtGaussPoints(displacements);
IReadOnlyList <double[]> strainsAtNodes =
tri6.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(strainsAtGPs, tri6.Interpolation);
IReadOnlyList <double[]> stressesAtNodes =
tri6.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(stressesAtGPs, tri6.Interpolation);
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtGPs, strainsAtGPs, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtGPs, stressesAtGPs, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtNodes, strainsAtNodes, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtNodes, stressesAtNodes, 1e-3));
}
public CantileverBeam BuildWithQuad4Elements(int numElementsAlongLength, int numElementsAlongHeight)
{
// Material and section properties
double thickness = Width;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = this.YoungModulus,
PoissonRatio = this.PoissonRatio
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0);
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Generate mesh
var meshGenerator = new UniformMeshGenerator2D <Node>(0.0, 0.0, Length, Height,
numElementsAlongLength, numElementsAlongHeight);
(IReadOnlyList <Node> vertices, IReadOnlyList <CellConnectivity <Node> > cells) =
meshGenerator.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < vertices.Count; ++n)
{
model.NodesDictionary.Add(n, vertices[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < cells.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(cells[e].CellType, cells[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Clamp boundary condition at one end
double tol = 1E-10; //TODO: this should be chosen w.r.t. the element size along X
foreach (var node in model.Nodes.Where(node => Math.Abs(node.X) <= tol))
{
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationX, Amount = 0.0
});
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = 0.0
});
}
// Apply concentrated load at the other end
Node[] loadedNodes = model.Nodes.Where(node => Math.Abs(node.X - Length) <= tol).ToArray();
foreach (var node in loadedNodes)
{
model.Loads.Add(new Load()
{
Amount = EndPointLoad / loadedNodes.Length, Node = node, DOF = StructuralDof.TranslationY
});
}
return(new CantileverBeam(Length, Height, Width, EndPointLoad, YoungModulus, model, loadedNodes));
}
private static Model CreateModel(IReadOnlyList <Node> nodes, IReadOnlyList <CellConnectivity <Node> > elements)
{
// Initialize
int numNodes = nodes.Count;
int numElements = elements.Count;
// Materials
ElasticMaterial2D material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus,
PoissonRatio = poissonRatio
};
// Subdomains
Model model = new Model();
model.SubdomainsDictionary.Add(0, new Subdomain(0));
// Nodes
for (int i = 0; i < numNodes; ++i)
{
model.NodesDictionary.Add(i, nodes[i]);
}
// Elements
var factory = new ContinuumElement2DFactory(thickness, material, null);
for (int i = 0; i < numElements; ++i)
{
ContinuumElement2D element = factory.CreateElement(elements[i].CellType, elements[i].Vertices);
var elementWrapper = new Element()
{
ID = i, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(i, elementWrapper);
model.SubdomainsDictionary[0].Elements.Add(elementWrapper);
}
// Constraints
double tol = 1E-10;
Node[] constrainedNodes = nodes.Where(node => Math.Abs(node.Y) <= tol).ToArray();
for (int i = 0; i < constrainedNodes.Length; i++)
{
constrainedNodes[i].Constraints.Add(new Constraint {
DOF = StructuralDof.TranslationX
});
constrainedNodes[i].Constraints.Add(new Constraint {
DOF = StructuralDof.TranslationY
});
}
// Loads
Node[] loadedNodes = nodes.Where(
node => (Math.Abs(node.Y - height) <= tol) && ((Math.Abs(node.X) <= tol))).ToArray();
if (loadedNodes.Length != 1)
{
throw new Exception("Only 1 node was expected at the top left corner");
}
model.Loads.Add(new Load()
{
Amount = maxLoad, Node = loadedNodes[0], DOF = StructuralDof.TranslationX
});
return(model);
}
public static void TestStrainsStresses0()
{
var factory = new ContinuumElement2DFactory(thickness, material0, null);
ContinuumElement2D quad8 = factory.CreateElement(CellType.Quad8, nodeSet0);
// Abaqus results
double[] displacements =
{
0.0, 0.0, // Node 1
0.0, 0.0, // Node 2
-6.1872E-03, -1.3677E-02, // Node 3
2.1193E-02, -6.0952E-02, // Node 4
-6.4016E-03, -2.9598E-03, // Node 5
-9.8052E-03, -7.6739E-03, // Node 6
2.0961E-03, -2.4904E-02, // Node 7
1.2842E-02, -2.0029E-02 // Node 8
};
double[][] expectedStrainsAtGPs =
{
new double[] { 5.0483E-03, 9.3636E-04, 1.3684E-03 }, // Gauss point 1
new double[] { 4.4925E-04, 6.0911E-04, -1.1381E-03 }, // Gauss point 2
new double[] { -1.0021E-02, 3.7130E-04, -6.7670E-03 }, // Gauss point 3
new double[] { 3.0367E-03, -4.2664E-03, -6.6618E-03 }, // Gauss point 4
new double[] { 7.6921E-04, -2.1368E-03, -5.1775E-03 }, // Gauss point 5
new double[] { -2.5482E-03, 1.8783E-03, -6.8114E-03 }, // Gauss point 6
new double[] { 1.2133E-03, -2.1843E-05, -1.4123E-02 }, // Gauss point 7
new double[] { -4.6295E-03, -1.0028E-02, -4.5072E-03 }, // Gauss point 8
new double[] { 4.6685E-03, -2.5173E-03, -3.6237E-03 } // Gauss point 9
};
double[][] expectedStressesAtGPs =
{
new double[] { 1230.00, 565.60, 110.50 }, // Gauss point 1
new double[] { 145.80, 171.70, -91.92 }, // Gauss point 2
new double[] { -2287.00, -608.10, -546.60 }, // Gauss point 3
new double[] { 405.40, -774.30, -538.10 }, // Gauss point 4
new double[] { 29.58, -439.80, -418.20 }, // Gauss point 5
new double[] { -458.00, 257.00, -550.20 }, // Gauss point 6
new double[] { 278.50, 78.95, -1141.00 }, // Gauss point 7
new double[] { -1763.00, -2635.00, -364.00 }, // Gauss point 8
new double[] { 903.10, -257.70, -292.70 } // Gauss point 9
};
// The order of the nodes is the same (at least in this job)
double[][] expectedStrainsAtNodes =
{
new double[] { 6.5625E-03, 5.7325E-03, 3.8681E-03 }, // Node 1
new double[] { -1.6562E-02, -1.2399E-03, -8.9890E-03 }, // Node 2
new double[] { 1.4923E-02, 2.1676E-03, -3.8448E-03 }, // Node 3
new double[] { 7.1739E-03, 1.2357E-02, -2.2045E-02 }, // Node 4
new double[] { -7.1803E-04, 4.4174E-04, 9.2207E-04 }, // Node 5
new double[] { -3.7108E-03, 3.4008E-03, -7.8726E-03 }, // Node 6
new double[] { -7.2747E-03, -1.3290E-02, -3.4274E-03 }, // Node 7
new double[] { 3.4993E-03, -4.5319E-03, -7.6795E-03 } // Node 8
};
double[][] expectedStressesAtNodes =
{
new double[] { 1911.0, 1777.00, 312.40 }, // Node 1
new double[] { -3908.0, -1433.00, -726.00 }, // Node 2
new double[] { 3594.0, 1533.00, -310.50 }, // Node 3
new double[] { 2511.0, 3348.00, -1781.00 }, // Node 4
new double[] { -135.1, 52.23, 74.47 }, // Node 5
new double[] { -620.9, 527.90, -635.90 }, // Node 6
new double[] { -2599.0, -3571.00, -276.80 }, // Node 7
new double[] { 493.8, -803.60, -620.30 } // Node 8
};
(IReadOnlyList <double[]> strainsAtGPs, IReadOnlyList <double[]> stressesAtGPs) =
quad8.UpdateStrainsStressesAtGaussPoints(displacements);
IReadOnlyList <double[]> strainsAtNodes =
quad8.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(strainsAtGPs, quad8.Interpolation);
IReadOnlyList <double[]> stressesAtNodes =
quad8.GaussPointExtrapolation.ExtrapolateTensorFromGaussPointsToNodes(stressesAtGPs, quad8.Interpolation);
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtGPs, strainsAtGPs, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtGPs, stressesAtGPs, 0.5e-2));
Assert.True(Utilities.AreTensorsEqual(expectedStrainsAtNodes, strainsAtNodes, 1e-3));
Assert.True(Utilities.AreTensorsEqual(expectedStressesAtNodes, stressesAtNodes, 0.5e-2));
}
private static void TestCantileverBeamGeneral()
{
// Define the materials
double thickness = 1.0;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus, PoissonRatio = 0.3
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0, true);
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Generate mesh
int numElementsX = 32, numElementsY = 20;
double lengthX = numElementsX;
double depthY = numElementsY;
var mesher = new UniformMeshGenerator2D <Node>(0, 0, lengthX, depthY, numElementsX, numElementsY);
(IReadOnlyList <Node> nodes, IReadOnlyList <CellConnectivity <Node> > connectivity) =
mesher.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < nodes.Count; ++n)
{
model.NodesDictionary.Add(n, nodes[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < connectivity.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(connectivity[e].CellType, connectivity[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Clamp boundary condition at left edge
double tol = 1E-10; //TODO: this should be chosen w.r.t. the element size along X
foreach (var node in model.Nodes.Where(node => Math.Abs(node.X) <= tol))
{
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationX, Amount = 0.0
});
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = 0.0
});
}
// Apply concentrated load at the bottom right corner
double load = 1.0;
var cornerNode = model.Nodes.Where(
node => (Math.Abs(node.X - lengthX) <= tol) && (Math.Abs(node.Y - depthY) <= tol));
Assert.True(cornerNode.Count() == 1);
model.Loads.Add(new Load()
{
Amount = load, Node = cornerNode.First(), DOF = StructuralDof.TranslationY
});
// Define the solver
SkylineSolver solver = (new SkylineSolver.Builder()).BuildSolver(model);
// Define the fem analysis and the filter
double filterAreaRadius = 1.2;
var fem = new LinearFemAnalysis2DGeneral(model, solver);
var filter = new ProximityDensityFilter2D(model, filterAreaRadius);
// Run the test
TestCantileverBeam(fem, filter);
}