//[TestMethod]
public void LoadInternalForce_trapezoidload_eulerbernoullybeam_dirY()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
//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.(LoadCase.DefaultLoadCase, -Vector.K, w, CoordinationSystem.Global);
new Loads.PartialNonUniformLoad();
u1.CoordinationSystem = CoordinationSystem.Global;
u1.Direction = -Vector.K;
// u1.StartLocation = new double[] { };
// u1.EndLocation = new double[] { };
//u1.StartMagnitude
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.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 = w / 12 * (6 * length * x - 6 * x * x - length * length);
var vi = w * (length / 2 - x);
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 d = testFrc.FirstOrDefault(i => i.Item1 == DoF.Ry).Item2 + exactFrc.My;
Assert.IsTrue(d < 1e-5, "invalid value");
}
}
public void LoadEquivalentNodalLoads_partialnonuniformload_eulerbernoullybeam_dirY()
{
//internal force of 2 node beam beam with uniform load and both ends fixed
var w = 2.0;
var x1 = -1;
var x2 = 1;
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.PartialNonUniformLoad();
u1.Direction = -Vector.K;
u1.CoordinationSystem = CoordinationSystem.Global;
u1.SeverityFunction = Mathh.Polynomial.FromPoints(1.0, w);
u1.StartLocation = new IsoPoint(x1);
u1.EndLocation = new IsoPoint(x2);
var hlpr = new ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Y, elm);
var loads = hlpr.GetLocalEquivalentNodalLoads(elm, u1);
var L = (elm.Nodes[1].Location - elm.Nodes[0].Location).Length;
var m1 = w * L * L / 12;
var m2 = -w * L * L / 12;
var v1 = -w * L / 2;
var v2 = -w * L / 2;
Assert.IsTrue(Math.Abs(loads[0].Fz - v1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[0].My - m1) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].Fz - v2) < 1e-5, "invalid value");
Assert.IsTrue(Math.Abs(loads[1].My - m2) < 1e-5, "invalid value");
}
public static ValidationResult Test_Trapezoid_1()
{
var buff = new ValidationResult();
buff.Title = "Test #2 for Trapezoid Load on BarElement";
buff.Span = new HtmlTag("span");
buff.Span.Add("p").Text("endforces from Trapezoidal load with 0 offset and same start and end should be same as uniform load");
var elm = new BarElement(new Node(0, 0, 0), new Node(1, 0, 0));
elm.Behavior = BarElementBehaviours.BeamZ;
var direction = Vector.K + Vector.I + Vector.J;
var ld_u = new Loads.UniformLoad();
ld_u.Magnitude = 1;//*Math.Sqrt(2);
ld_u.Direction = direction;
ld_u.CoordinationSystem = CoordinationSystem.Global;
var ld_t = new Loads.PartialNonUniformLoad();
//ld_t.EndLocation = ld_t.StartLocation = new double[] { 0 };
//ld_t.StartMagnitude = ld_t.EndMagnitude = new double[] { 1 };
ld_t.Direction = direction;
ld_t.CoordinationSystem = CoordinationSystem.Global;
var loads = elm.GetGlobalEquivalentNodalLoads(ld_u);
var loads2 = elm.GetGlobalEquivalentNodalLoads(ld_t);
var epsilon = 1e-9;
{//test 1 : equality betweeb above
var resid = new Force[loads.Length];
for (var i = 0; i < loads.Length; i++)
{
var f = resid[i] = loads[i] - loads2[i];
buff.ValidationFailed = Math.Abs(f.Forces.Length) > epsilon || Math.Abs(f.Moments.Length) > epsilon;
}
}
return(buff);
}
public static void ValidateLoadInternalForce_B_z()
{
var load = new Loads.PartialNonUniformLoad();
load.Direction = Vector.J;
var w = 1;
//load.StartLocation = new double[] { -1 };
//load.EndLocation = new double[] { 1 };
//load.StartMagnitude = new double[] { w };
//load.EndMagnitude = new double[] { w };
var elm = new BarElement(new Node(0, 0, 0), new Node(2, 0, 0));
var hlpr = new BriefFiniteElementNet.ElementHelpers.EulerBernoulliBeamHelper(ElementHelpers.BeamDirection.Z, elm);
var l = (elm.Nodes[0].Location - elm.Nodes[1].Location).Length;
var v = new Func <double, double>(x => w * (l / 2 - x));
var m = new Func <double, double>(x => - (w / 12.0) * (6 * l * x - l * l - 6 * x * x));
var rdn = new Random(0);
for (var i = 0; i < 10; i++)
{
var x_t =
rdn.NextDouble()
//0.125
* l;
var xi = hlpr.Local2Iso(elm, x_t);
var frc = hlpr.GetLoadInternalForceAt(elm, load, xi);
var rv = v(x_t);
var rm = m(x_t);
//var dv = v(x_t) - frc.MembraneTensor.S13;
//var dm = m(x_t) - frc.BendingTensor.M12;
}
}
public static void Run1()
{
///https://user-images.githubusercontent.com/10573467/111787314-781d7d00-88c7-11eb-869d-d8d7d40db005.png
var model = new Model();
//adding nodes
model.Nodes.Add(new Node(0, 0, 0)
{
Label = "n0"
});
model.Nodes.Add(new Node(5, 0, 5)
{
Label = "n1"
});
//adding elements
BarElement elm;
model.Elements.Add(elm = new BarElement(model.Nodes["n0"], model.Nodes["n1"])
{
Label = "e0"
});
//assign constraint to nodes
model.Nodes["n0"].Constraints = Constraints.MovementFixed;
model.Nodes["n1"].Constraints = Constraints.MovementFixed;
//define sections and material
var secAA = new Sections.UniformGeometric1DSection(SectionGenerator.GetISetion(0.24, 0.67, 0.01, 0.006));
var mat = Materials.UniformIsotropicMaterial.CreateFromYoungPoisson(210e9, 0.3);
//assign materials
(model.Elements["e0"] as BarElement).Material = mat;
//assign sections
(model.Elements["e0"] as BarElement).Section = secAA;
//creating loads
var u1 = new Loads.PartialNonUniformLoad()
{
Direction = Vector.K, CoordinationSystem = CoordinationSystem.Local
};
u1.SeverityFunction = Mathh.SingleVariablePolynomial.FromPoints(-1, -6, 1, -4);
u1.StartLocation = new IsoPoint(-1); //set locations of trapezoidal load
u1.EndLocation = new IsoPoint(1); //set locations of trapezoidal load
//assign loads
model.Elements["e0"].Loads.Add(u1);
var cse = new LoadCase("T1", LoadType.Other);
Util.AreaLoad2ConcentratedLoads(elm, u1, cse);
//solve model
model.Solve_MPC(LoadCase.DefaultLoadCase, cse);
//retrieve solve result
var n0reaction = model.Nodes["n0"].GetSupportReaction();
var n0reaction2 = model.Nodes["n0"].GetSupportReaction(cse);
var n1reaction = model.Nodes["n1"].GetSupportReaction();
var n1reaction2 = model.Nodes["n1"].GetSupportReaction(cse);
Console.WriteLine("Support reaction of n0: {0}", n0reaction);
Console.WriteLine("Support reaction of n1: {0}", n1reaction);
var x = 1.0; //need to find internal force at x = 1.0 m
var iso = (model.Elements["e0"] as BarElement).LocalCoordsToIsoCoords(x); //find the location of 1m in iso coordination system
var e4Force = (model.Elements["e0"] as BarElement).GetInternalForceAt(iso[0]); //find internal force
Console.WriteLine("internal force at x={0} is {1}", x, e4Force);
var r1 = new Force(fx: -13.33333333, fy: 0, fz: 13.333333333, mx: 0, my: 0, mz: 0);
var r2 = new Force(fx: -11.666666666, fy: 0, fz: 11.66666666, mx: 0, my: 0, mz: 0);
var d1 = n0reaction - r1;
var d2 = n1reaction - r2;
var epsilon = 1e-3;
Debug.Assert(d1.Forces.Length < epsilon && d1.Moments.Length < epsilon);
Debug.Assert(d2.Forces.Length < epsilon && d2.Moments.Length < epsilon);
}
public static void Run1()
{
var model = new Model();
//adding nodes
model.Nodes.Add(new Node(0, 0, 0)
{
Label = "n0"
});
model.Nodes.Add(new Node(5, 5, 5)
{
Label = "n1"
});
//adding elements
model.Elements.Add(new BarElement(model.Nodes["n0"], model.Nodes["n1"])
{
Label = "e0"
});
//assign constraint to nodes
model.Nodes["n0"].Constraints = Constraints.MovementFixed & Constraints.FixedRX;
model.Nodes["n1"].Constraints = Constraints.MovementFixed;
//define sections and material
var secAA = new Sections.UniformGeometric1DSection(SectionGenerator.GetISetion(0.24, 0.67, 0.01, 0.006));
var mat = Materials.UniformIsotropicMaterial.CreateFromYoungPoisson(210e9, 0.3);
//assign materials
(model.Elements["e0"] as BarElement).Material = mat;
//assign sections
(model.Elements["e0"] as BarElement).Section = secAA;
//creating loads
var u1 = new Loads.PartialNonUniformLoad()
{
Direction = Vector.K, CoordinationSystem = CoordinationSystem.Global
};
u1.SeverityFunction = Mathh.SingleVariablePolynomial.FromPoints(-1, -6, 1, -4);
u1.StartLocation = new IsoPoint(-0.5); //set locations of trapezoidal load
u1.EndLocation = new IsoPoint(0.5); //set locations of trapezoidal load
//assign loads
model.Elements["e0"].Loads.Add(u1);
//solve model
model.Solve_MPC();
//retrieve solve result
var n0reaction = model.Nodes["n0"].GetSupportReaction();
var n1reaction = model.Nodes["n1"].GetSupportReaction();
Console.WriteLine("Support reaction of n0: {0}", n0reaction);
Console.WriteLine("Support reaction of n1: {0}", n1reaction);
var x = 1.0; //need to find internal force at x = 1.0 m
var iso = (model.Elements["e0"] as BarElement).LocalCoordsToIsoCoords(x); //find the location of 1m in iso coordination system
var e4Force = (model.Elements["e0"] as BarElement).GetInternalForceAt(iso[0]); //find internal force
Console.WriteLine("internal force at x={0} is {1}", x, e4Force);
}
