static void TestHingedInternalForce()
{
//test internal force of a beam with partially end release
var model = StructureGenerator.Generate3DBarElementGrid(2, 1, 1);
var bar = model.Elements[0] as BarElement;
bar.StartReleaseCondition = Constraints.MovementFixed & Constraints.FixedRX;
bar.EndReleaseCondition = Constraints.MovementFixed & Constraints.FixedRX;
//var ld = new Loads.UniformLoad() { Direction = Vector.K, Magnitude = -100 };
var ld = new Loads.ConcentratedLoad()
{
Force = new Force(0, 0, -1, 0, 0, 0), ForceIsoLocation = new IsoPoint(0.0)
};
bar.Loads.Add(ld);
model.Solve_MPC();
var func = new Func <double, double>(xi => bar.GetExactInternalForceAt(xi).My);
FunctionVisualizer.VisualizeInNewWindow(func, -1 + 1e-10, 1 - 1e-10, 100);
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_My_End()
{
var l = 4.0;
var w = 2.0;
var a = l;
var nodes = new Node[2];
nodes[0] = (new Node(0, 0, 0)
{
Label = "n0"
});
nodes[1] = (new Node(l, 0, 0)
{
Label = "n1"
});
var elm = new BarElement(nodes[0], nodes[1])
{
Label = "e0"
};
var f = new Force(0, 0, 0, 0, w, 0);
var loc = new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]);
var u1 = new Loads.ConcentratedLoad(f, loc, CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = Force.Zero;
var d1 = loads[1] - f;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirY_My_Start()
{
//equivalent nodal load of a concentrated load applied at start point is same as load itself!
var w = 2.0;
var a = 0;
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(new Force(0, 0, 0, 0, w, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var d0 = loads[0] - u1.Force;
var d1 = Force.Zero;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
private static void testMultySpan()
{
var model = StructureGenerator.Generate3DBarElementGrid(4, 1, 1);
var bar1 = model.Elements[0] as BarElement;
var bar2 = model.Elements[1] as BarElement;
var bar3 = model.Elements[2] as BarElement;
model.Nodes[0].Constraints = Constraints.MovementFixed & Constraints.FixedRY;
model.Nodes[1].Constraints = Constraints.MovementFixed; // & Constraints.FixedRY;
model.Nodes[2].Constraints = Constraints.MovementFixed; // MovementFixed & Constraints.FixedRY;
model.Nodes[3].Constraints = Constraints.MovementFixed & Constraints.FixedRY;
var l = (model.Nodes.Last().Location - model.Nodes[0].Location).Length;
//bar.StartReleaseCondition = Constraints.MovementFixed & Constraints.FixedRX;
//bar.EndReleaseCondition = Constraints.MovementFixed & Constraints.FixedRX;
//var ld = new Loads.UniformLoad() { Direction = Vector.K, Magnitude = -100 };
var ld = new Loads.ConcentratedLoad()
{
Force = new Force(0, 0, -1, 0, 0, 0), CoordinationSystem = CoordinationSystem.Global, ForceIsoLocation = new IsoPoint(0.0)
};
var ld2 = new Loads.UniformLoad()
{
Direction = -Vector.K, Magnitude = 1, CoordinationSystem = CoordinationSystem.Global,
};
bar1.Material = bar2.Material = bar3.Material;
bar1.Section = bar2.Section = bar3.Section;
bar1.Loads.Add(ld2);
//bar2.Loads.Add(ld2);
bar3.Loads.Add(ld2);
model.Solve_MPC();
var r0 = model.Nodes[0].GetSupportReaction();
var st = model.Nodes[0].Location;
var mid = model.Nodes[1].Location;
var en = model.Nodes[2].Location;
var ss = model.Nodes.Select(ii => ii.GetSupportReaction()).ToArray();
var pts = new List <Tuple <double, double> >();
foreach (var elm in model.Elements)
{
var b = elm as BarElement;
if (b == null)
{
continue;
}
for (var ii = -1.0; ii <= 1; ii += 0.001)
{
var global = b.IsoCoordsToGlobalCoords(ii);
try
{
var f1 = b.GetExactInternalForceAt(ii);
var f2 = b.GetInternalForceAt(ii);
var f = f2 - f1;
pts.Add(Tuple.Create(global.Y, -f1.My));
}
catch { }
}
}
pts.Sort((i, j) => i.Item1.CompareTo(j.Item1));
FunctionVisualizer.VisualizeInNewWindow((x =>
{
var tt = pts.LastOrDefault(j => j.Item1 <= x);
if (tt != null)
{
return(tt.Item2);
}
return(0);
}), 0, l, 1000);
throw new NotImplementedException();
}
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 LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Fy()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
// ^y w
// | ||
// | \/
// ====================================== --> x
// /
// /z
var w = 2.0;
var a = 2;
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(new Force(0, -w, 0, 0, 0, 0), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var b = L - a;
var ma = w * a * b * b / (L * L);
var mb = w * a * a * b / (L * L);
var ra = w * (3 * a + b) * b * b / (L * L * L); //1f
var rb = w * (a + 3 * b) * a * a / (L * L * L); //1g
var expectedF0 = new Force(0, -ra, 0, 0, 0, -ma);
var expectedF1 = new Force(0, -rb, 0, 0, 0, mb);
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] - expectedF0;
var d1 = loads[1] - expectedF1;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadEquivalentNodalLoads_ConcentratedLod_eulerbernoullybeam_dirZ_Mz()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
//https://www.amesweb.info/Beam/Fixed-Fixed-Beam-Bending-Moment.aspx
// ^
// ^m m0 ^
// | /z |
// | / |
// ====================================== --> x
//
var w = 2.0;
var a = 1.234560;
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(new Force(0, 0, 0, 0, 0, w), new IsoPoint(elm.LocalCoordsToIsoCoords(a)[0]), CoordinationSystem.Global);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
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
var expectedR1 = new Force(0, ra, 0, 0, 0, ma); //expected reaction 1
var expectedR2 = new Force(0, rb, 0, 0, 0, -mb); //expected reaction 2
/*
* var m1 = -w * L * L / 12;
* var m2 = w * L * L / 12;
*
* var v1 = -w * L / 2;
* var v2 = -w * L / 2;
*/
var d0 = loads[0] + expectedR1;
var d1 = loads[1] + expectedR2;
Assert.IsTrue(Math.Abs(d0.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d0.Moments.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Forces.Length) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(d1.Moments.Length) < 1e-5, "invalid value");
}
public void LoadInternalForce_concentratedLLoad_Shaft_Mx()
{
//internal force of 2 node truss with concentrated 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, w, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new ShaftHelper(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);
var mi = 0.0;
var vi = 0.0;
{
var a = forceLocation;
var b = L - a;
var ra = (1 - (a / L)) * w;
var rb = (1 - (b / L)) * w;
mi = ra + ((x > forceLocation) ? -w : 0.0);
}
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: -mi, my: 0, mz: 0);
var df = Math.Abs(testFrc.Mx) - Math.Abs(exactFrc.Mx);
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_truss_Fx()
{
//internal force of 2 node truss with concentrated 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(w, 0, 0, 0, 0, 0);
u1.CoordinationSystem = CoordinationSystem.Global;
u1.ForceIsoLocation = new IsoPoint(elm.LocalCoordsToIsoCoords(forceLocation)[0]);
var hlpr = new TrussHelper();
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 ra = (1 - (a / L)) * w;
var rb = (1 - (b / L)) * w;
mi = ra + ((x > forceLocation) ? -w : 0.0);
}
var ends = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var testFrc = hlpr.GetLoadInternalForceAt(elm, u1, new double[] { xi[0] * (1 - 1e-9) });
var exactFrc = new Force(fx: -mi, fy: 0, fz: vi, mx: 0, my: 0, mz: 0);
var df = testFrc.FirstOrDefault(i => i.Item1 == DoF.Dx).Item2 + exactFrc.Fx;
Assert.IsTrue(Math.Abs(df) < 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");
}
}
