private static void TestMultinodeBar1()
{
var n = 2;
var bar = new BarElement(n);
var hlp = new EulerBernoulliBeamHelper(BeamDirection.Y, bar);
for (var i = 0; i < n; i++)
{
bar.Nodes[i] = new Node(i * 3, 0, 0);
}
var testXi = -0.66;
//var n1 = hlp.GetNMatrixBar2Node(bar, testXi);
var n2 = hlp.GetNMatrixAt(bar, testXi);
var b = hlp.GetBMatrixAt(bar, testXi);
//var d = n1 - n2;
}
public void barelement_endrelease()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var eI = 210e9 * (0.1 * 0.1 * 0.1 * 0.1) / 12;
var l = 2.0;
var n1 = new Node(0, 0, 0);
var n2 = new Node(l, 0, 0);
var e1 = new BarElement(2);
e1.Nodes[0] = n1;
e1.Nodes[1] = n2;
//e1.NodalReleaseConditions[0] = Constraints.Fixed;
//e1.NodalReleaseConditions[1] = Constraints.MovementFixed;
e1.Material = new UniformIsotropicMaterial(210e9, 0.3);
e1.Section = new UniformParametric1DSection(0.1, 0.01, 0.01, 0.01);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y, e1);
var s1 = hlpr.CalcLocalStiffnessMatrix(e1);
//var d1 = 1.0/s1[3, 3];
var theoricalK = 12 * eI / (l * l * l);
var calculatedK = s1[2, 2];
var ratio = theoricalK / calculatedK;
}
/*
*
* 3 kN/m
* ^^^^^^^^^^^^^^^^^^^^^^^^^^^
* ----------------------------
* /\ 10m /\
*
* n1 n2
*
*/
public static void BeamShapeFunction()
{
var fix = Constraints.Fixed;
var beam1 = new BarElement(3);
beam1.Nodes[0] = new Node(0, 0, 0)
{
Constraints = fix
};
beam1.Nodes[1] = new Node(1, 0, 0)
{
Constraints = fix
};
beam1.Nodes[2] = new Node(2, 0, 0)
{
Constraints = fix
};
var old = beam1.StartReleaseCondition;//.DZ = DofConstraint.Released;
old.DZ = DofConstraint.Released;
//old.RZ = DofConstraint.Released;
beam1.StartReleaseCondition = old;
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y, beam1);
SingleVariablePolynomial[] ns, ms;
hlpr.GetShapeFunctions(beam1, out ns, out ms);
}
public void eulerbernoullybeam_dirZ_diff()
{
var w = 2.0;
var a = 4;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(5.2355, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
var n0 = hlpr.GetNMatrixAt(elm, -1);
var n1 = hlpr.GetNMatrixAt(elm, 1);
var epsilon = 1e-5;
Assert.IsTrue(Math.Abs(n0[1, 1] - L / 2) < epsilon, "invalid value");
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 2.123; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
//foreach (var x in CalcUtil.Divide(length, 10))
{
var x = 2.4;
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = w / (L * L) * (3 * a * a - 2 * a * L);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = 6 * w * a / (L * L * L) * (L - a); //R1
mi = ma + ra * x - ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = Math.Abs(testFrc.My) - Math.Abs(exactFrc.My); //regarding value
var df = Math.Abs(testFrc.Fz) - Math.Abs(exactFrc.Fz); //regarding value
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value"); //regarding sign
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value"); //regarding sign
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirZ_fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, -w, 0, 0, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
//https://www.engineeringtoolbox.com/beams-fixed-both-ends-support-loads-deflection-d_809.html
var mi = 0.0;
var vi = 0.0;
{
var a = forceLocation;
var b = L - a;
var ma = -w * a * b * b / (L * L);
var mb = -w * a * a * b / (L * L);
var mf = 2 * w * a * a * b * b / (L * L * L);
double x0, x1, y0, y1;
if (x < forceLocation)
{
x0 = 0;
x1 = forceLocation;
y0 = ma;
y1 = mf;
}
else
{
x0 = forceLocation;
x1 = L;
y0 = mf;
y1 = mb;
}
var m = (y1 - y0) / (x1 - x0);
mi = m * (x - x0) + y0;
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
if (x < forceLocation)
{
vi = ra;
}
else
{
vi = -rb;
}
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) }).ToForce();
var exactFrc = new Force(fx: 0, fy: vi, fz: 0, mx: 0, my: 0, mz: +mi);
var dm = Math.Abs(testFrc.Mz) - Math.Abs(exactFrc.Mz);
var df = Math.Abs(testFrc.Fy) - Math.Abs(exactFrc.Fy);
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
{
var end1 = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var f0 = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { -1 + 1e-9 }).ToForce();;
var sum = end1[0] + f0;
Assert.IsTrue(Math.Abs(sum.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(sum.Moments.Length) < 1e-5, "invalid value");
}
}
public void LoadInternalForce_concentratedLLoad_eulerbernoullybeam_dirY_My()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var forceLocation = 0.5; //[m]
var L = 4; //[m]
//var model = new Model();
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var u1 = new Loads.ConcentratedLoad();
u1.Case = LoadCase.DefaultLoadCase;
u1.Force = new Force(0, 0, 0, 0, w, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Y);
var length = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
foreach (var x in CalcUtil.Divide(length, 10))
{
var xi = elm.LocalCoordsToIsoCoords(x);
var mi = 0.0;
var vi = 0.0;
{
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
var a = forceLocation;
var b = L - a;
var ma = -w / (L * L) * (L * L - 4 * a * L + 3 * a * a);
var mb = -w / (L * L) * (3 * a * a - 2 * a * L);
//var m = (y1 - y0) / (x1 - x0);
var ra = -6 * w * a / (L * L * L) * (L - a); //R1
var rb = -ra; //R2
mi = ma + ra * x + ((x > forceLocation) ? w : 0.0);
vi = ra;
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: 0, fy: 0, fz: vi, mx: 0, my: -mi, mz: 0);
var dm = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 - exactFrc.My;
var df = testFrc.FirstOrDefault(i => i.Item1 == DoF.Dz).Item2 + exactFrc.Fz;
Assert.IsTrue(Math.Abs(dm) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(df) < 1e-5, "invalid value");
}
}
public void eulerbernoullybeam_dirZ()
{
var w = 2.0;
var a = 4;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(4, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var hlpr = new EulerBernoulliBeamHelper(BeamDirection.Z, elm);
for (var i = 0.0; i <= 1; i += 0.01)
{
var x = i * L;
var iso = elm.LocalCoordsToIsoCoords(x);
var n = hlpr.GetNMatrixAt(elm, iso);
var n1 = n[0, 0];
var m1 = n[0, 1];
var n2 = n[0, 2];
var m2 = n[0, 3];
var n1p = n[1, 0];
var m1p = n[1, 1];
var n2p = n[1, 2];
var m2p = n[1, 3];
var xi = iso[0];
var n1e = 0.25 * (2 - 3 * xi + xi * xi * xi);
var m1e = 0.125 * L * (1 - xi - xi * xi + xi * xi * xi);
var n2e = 0.25 * (2 + 3 * xi - xi * xi * xi);
var m2e = 0.125 * L * (-1 - xi + xi * xi + xi * xi * xi);
var epsilon = 1e-5;
Assert.IsTrue(Math.Abs(n1 - n1e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(n2 - n2e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(m1 - m1e) < epsilon, "invalid value");
Assert.IsTrue(Math.Abs(m2 - m2e) < epsilon, "invalid value");
}
}
