public static void Check(Model model, LoadCase cse)
{
var n = model.Nodes.Count;
var ft = new Vector();
var fs = new Vector[n];
var mt = new Vector();
model.Solve();
model.LastResult.AddAnalysisResultIfNotExists(cse);
var css = model.LastResult.ConcentratedForces[cse]; //concentrated s
var ess = model.LastResult.ElementForces[cse]; //elements
for (var i = 0; i < n; i++)
{
var loc = model.Nodes[i].Location;
var cs = Force.FromVector(css, 6 * i);
var es = Force.FromVector(ess, 6 * i);
var ss = model.Nodes[i].GetSupportReaction(cse);
var fi = (cs + es + ss).Move(-(Vector)loc);
fs[i] = fi.Forces;
ft += fi.Forces;
mt += fi.Moments;
}
Console.WriteLine("Total Force: {0}", ft);
Console.WriteLine("Total Moment: {0}", mt);
}
/// <summary>
/// Gets the internal force at <see cref="x" /> position.
/// </summary>
/// <param name="x">The position (from start point).</param>
/// <param name="cmb">The <see cref="LoadCombination" />.</param>
/// <returns></returns>
/// <exception cref="System.NotImplementedException"></exception>
/// <remarks>
/// Will calculate the internal forces of member regarding the <see cref="cmb" /> <see cref="LoadCombination" />
/// </remarks>
public override Force GetInternalForceAt(double x, LoadCombination cmb)
{
var gStartDisp = StartNode.GetNodalDisplacement(cmb);
var gEndDisp = EndNode.GetNodalDisplacement(cmb);
var lStartDisp = new Displacement(
TransformGlobalToLocal(gStartDisp.Displacements),
TransformGlobalToLocal(gStartDisp.Rotations));
var lEndDisp = new Displacement(
TransformGlobalToLocal(gEndDisp.Displacements),
TransformGlobalToLocal(gEndDisp.Rotations));
var displVector = new double[]
{
lStartDisp.DX, lStartDisp.DY, lStartDisp.DZ,
lStartDisp.RX, lStartDisp.RY, lStartDisp.RZ,
lEndDisp.DX, lEndDisp.DY, lEndDisp.DZ,
lEndDisp.RX, lEndDisp.RY, lEndDisp.RZ
};
var lStartForces = GetLocalStiffnessMatrix().Multiply(displVector);
var startForce = Force.FromVector(lStartForces, 0);
var forceAtX = -startForce.Move(new Vector(x, 0, 0));
foreach (var ld in loads)
{
if (!cmb.ContainsKey(ld.Case))
{
continue;
}
var frc = ((Load1D)ld).GetInternalForceAt(this, x);
forceAtX += cmb[ld.Case] * frc;
}
return(forceAtX);
}
public static ValidationResult Validation_1()
{
var nx = 2;
var ny = 2;
var nz = 2;
#region model definition
var grd = StructureGenerator.Generate3DBarElementGrid(nx, ny, nz);
//StructureGenerator.SetRandomiseConstraints(grd);
StructureGenerator.SetRandomiseSections(grd);
StructureGenerator.AddRandomiseNodalLoads(grd, LoadCase.DefaultLoadCase);//random nodal loads
//StructureGenerator.AddRandomiseBeamUniformLoads(grd, LoadCase.DefaultLoadCase);//random elemental loads
StructureGenerator.AddRandomDisplacements(grd, 0.1);
#endregion
grd.Solve_MPC();
#region solve & compare
var res = OpenseesValidator.OpenseesValidate(grd, LoadCase.DefaultLoadCase, false);
var disp = res[0];
var reac = res[1];
var dispAbsErrIdx = disp.Columns.Cast <DataColumn>().ToList().FindIndex(i => i.ColumnName.ToLower().Contains("absolute"));
var dispRelErrIdx = disp.Columns.Cast <DataColumn>().ToList().FindIndex(i => i.ColumnName.ToLower().Contains("relative"));
var reacAbsErrIdx = reac.Columns.Cast <DataColumn>().ToList().FindIndex(i => i.ColumnName.ToLower().Contains("absolute"));
var reacRelErrIdx = reac.Columns.Cast <DataColumn>().ToList().FindIndex(i => i.ColumnName.ToLower().Contains("relative"));
var maxDispAbsError = disp.Rows.Cast <DataRow>().Max(ii => (double)ii.ItemArray[dispAbsErrIdx]);
var maxDispRelError = disp.Rows.Cast <DataRow>().Max(ii => (double)ii.ItemArray[dispRelErrIdx]);
var maxReacAbsError = reac.Rows.Cast <DataRow>().Max(ii => (double)ii.ItemArray[reacAbsErrIdx]);
var maxReacRelError = reac.Rows.Cast <DataRow>().Max(ii => (double)ii.ItemArray[reacRelErrIdx]);
var maxInternalDisplacementAbsErr = 0.0;
var maxInternalForceResidual = 0.0;
foreach (var elm in grd.Elements)
{
var bar = elm as BarElement;
if (bar == null)
{
continue;
}
var tr = bar.GetTransformationManager();
var L = (bar.StartNode.Location - bar.EndNode.Location).Length;
var d1 = bar.GetInternalDisplacementAt(-1, LoadCase.DefaultLoadCase);
var d2 = bar.GetInternalDisplacementAt(+1, LoadCase.DefaultLoadCase);
var dn1 = tr.TransformGlobalToLocal(bar.StartNode.GetNodalDisplacement(LoadCase.DefaultLoadCase));
var dn2 = tr.TransformGlobalToLocal(bar.EndNode.GetNodalDisplacement(LoadCase.DefaultLoadCase));
var diff1 = dn1 - d1;
var diff2 = dn2 - d2;
var dd = Math.Max(diff1.Displacements.Length, diff2.Displacements.Length);
var dr = Math.Max(diff1.Rotations.Length, diff2.Rotations.Length);
maxInternalDisplacementAbsErr = Math.Max(maxInternalDisplacementAbsErr, dd);
maxInternalDisplacementAbsErr = Math.Max(maxInternalDisplacementAbsErr, dr);
//yet internal force
var n = 10;
var stf = bar.GetLocalStifnessMatrix();//.GetGlobalStifnessMatrix();
var u1 = Displacement.ToVector(dn1);
var u2 = Displacement.ToVector(dn2);
var u = new Matrix(12, 1);
u1.CopyTo(u.CoreArray, 0);
u2.CopyTo(u.CoreArray, 6);
var endFrc = stf * u;
var stFc = Force.FromVector(endFrc.CoreArray, 0);
var endFc = Force.FromVector(endFrc.CoreArray, 6);
for (var i = 0; i < n; i++)
{
var xi = i / (n - 1.0) * 2.0 + -1;
var x = bar.IsoCoordsToLocalCoords(xi)[0];
var fc = bar.GetInternalForceAt(xi);
var toBegin = fc.Move(new Vector(-x, 0, 0));
var toEnd = fc.Move(new Vector(L - x, 0, 0));
var stResid = stFc + toBegin;
var endResid = endFc - toEnd;
var errs = new double[]
{
stResid.Forces.Length,
stResid.Moments.Length,
endResid.Forces.Length,
endResid.Moments.Length
}.Max();
maxInternalForceResidual = Math.Max(maxInternalForceResidual, errs);
}
}
#endregion
var span = new HtmlTag("span");
span.Add("p").Text("Validate 3D frame nodal displacement and reactions");
span.Add("h3").Text("Validate with");
span.Add("paragraph").Text("OpenSEES (the Open System for Earthquake Engineering Simulation) software (available via http://opensees.berkeley.edu/)");
span.Add("h3").Text("Validate objective");
span.Add("paragraph").Text("compare nodal displacement from BFE.net library and OpenSEES for a model consist of random 3d bars");
span.Add("h3").Text("Model Definition");
span.Add("paragraph").Text($"A {nx}x{ny}x{nz} grid, with {grd.Nodes.Count} nodes and {grd.Elements.Count} bar elements.").AddClosedTag("br");
span.Add("paragraph").Text("Every node in the model have a random load on it, random displacement in original location.").AddClosedTag("br");
span.Add("paragraph").Text("Every element in the model have a random uniform distributed load on it.").AddClosedTag("br");
span.Add("h3").Text("Validation Result");
#region nodal disp
{//nodal displacements
span.Add("h4").Text("Nodal Displacements");
span.Add("paragraph")
.Text(string.Format("Validation output for nodal displacements:"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}<br/>-Max RELATIVE Error: {1:e3}", maxDispAbsError, maxDispRelError));
var id = "tbl_" + Guid.NewGuid().ToString("N").Substring(0, 5);
span.Add("button").Attr("type", "button").Text("Toggle Details").AddClasses("btn btn-primary")
.Attr("onclick", $"$('#{id}').collapse('toggle');");
var div = span.Add("div").AddClasses("panel-collapse", "collapse", "out").Id(id);
var tbl = div.Add("table").AddClass("table table-striped table-inverse table-bordered table-hover");
tbl.Id(id);
var trH = tbl.Add("Thead").Add("tr");
foreach (DataColumn column in disp.Columns)
{
trH.Add("th").Attr("scope", "col").Text(column.ColumnName);
}
var tbody = tbl.Add("tbody");
for (var i = 0; i < disp.Rows.Count; i++)
{
var tr = tbody.Add("tr");
for (var j = 0; j < disp.Columns.Count; j++)
{
tr.Add("td").Text(disp.Rows[i][j].ToString());
}
}
}
#endregion
#region nodal reaction
{//nodal reactions
span.Add("h4").Text("Nodal Support Reactions");
span.Add("paragraph")
.Text(string.Format("Validation output for nodal support reactions:"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}<br/>-Max RELATIVE Error: {1:e3}", maxReacAbsError, maxReacRelError));
var id = "tbl_" + Guid.NewGuid().ToString("N").Substring(0, 5);
span.Add("button").Attr("type", "button").Text("Toggle Details").AddClasses("btn btn-primary")
.Attr("onclick", $"$('#{id}').collapse('toggle');");
var div = span.Add("div").AddClasses("panel-collapse", "collapse", "out").Id(id);
var tbl = div.Add("table").AddClass("table table-striped table-inverse table-bordered table-hover");
tbl.Id(id);
var trH = tbl.Add("Thead").Add("tr");
foreach (DataColumn column in reac.Columns)
{
trH.Add("th").Attr("scope", "col").Text(column.ColumnName);
}
var tbody = tbl.Add("tbody");
for (var i = 0; i < reac.Rows.Count; i++)
{
var tr = tbody.Add("tr");
for (var j = 0; j < reac.Columns.Count; j++)
{
tr.Add("td").Text(reac.Rows[i][j].ToString());
}
}
}
#endregion
#region internal displacement
{//internal displacements
span.Add("h4").Text("Internal Displacements");
span.Add("paragraph")
.Text(string.Format("Validation output for internal displacements (Displacement at each end node of bar elements should be equal to bar element's internal displacement of bar element at that node)"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}", maxInternalDisplacementAbsErr));
}
#endregion
#region internal force
{//internal force
span.Add("h4").Text("Internal Force");
span.Add("paragraph")
.Text(string.Format("Validation output for internal force (forces retrived by K.Δ formula should be in equiblirium with internal force of bar elements at any location within element):"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}", maxInternalForceResidual));
}
#endregion
var buf = new ValidationResult();
buf.Span = span;
buf.Title = "3D Grid Validation";
return(buf);
}
public static ValidationResult Validation_2()
{
var nx = 5;
var ny = 5;
var nz = 5;
var grd = StructureGenerator.Generate3DBarElementGrid(nx, ny, nz);
//StructureGenerator.SetRandomiseConstraints(grd);
StructureGenerator.SetRandomiseSections(grd);
StructureGenerator.AddRandomiseNodalLoads(grd, LoadCase.DefaultLoadCase);//random nodal loads
//StructureGenerator.AddRandomiseBeamUniformLoads(grd, LoadCase.DefaultLoadCase);//random elemental loads
StructureGenerator.AddRandomDisplacements(grd, 0.1);
grd.Solve_MPC();
var maxInternalDisplacementAbsErr = 0.0;
var maxInternalForceResidual = 0.0;
foreach (var elm in grd.Elements)
{
var bar = elm as BarElement;
if (bar == null)
{
continue;
}
var tr = bar.GetTransformationManager();
var L = (bar.StartNode.Location - bar.EndNode.Location).Length;
var d1 = bar.GetInternalDisplacementAt(-1, LoadCase.DefaultLoadCase);
var d2 = bar.GetInternalDisplacementAt(+1, LoadCase.DefaultLoadCase);
var dn1 = tr.TransformGlobalToLocal(bar.StartNode.GetNodalDisplacement(LoadCase.DefaultLoadCase));
var dn2 = tr.TransformGlobalToLocal(bar.EndNode.GetNodalDisplacement(LoadCase.DefaultLoadCase));
var diff1 = dn1 - d1;
var diff2 = dn2 - d2;
var dd = Math.Max(diff1.Displacements.Length, diff2.Displacements.Length);
var dr = Math.Max(diff1.Rotations.Length, diff2.Rotations.Length);
maxInternalDisplacementAbsErr = Math.Max(maxInternalDisplacementAbsErr, dd);
maxInternalDisplacementAbsErr = Math.Max(maxInternalDisplacementAbsErr, dr);
//yet internal force
var n = 10;
var stf = bar.GetLocalStifnessMatrix();//.GetGlobalStifnessMatrix();
var u1 = Displacement.ToVector(dn1);
var u2 = Displacement.ToVector(dn2);
var u = new Matrix(12, 1);
u1.CopyTo(u.CoreArray, 0);
u2.CopyTo(u.CoreArray, 6);
var endFrc = stf * u;
var stFc = Force.FromVector(endFrc.CoreArray, 0);
var endFc = Force.FromVector(endFrc.CoreArray, 6);
for (var i = 0; i < n; i++)
{
var xi = i / (n - 1.0) * 2.0 + -1;
var x = bar.IsoCoordsToLocalCoords(xi)[0];
var fc = bar.GetInternalForceAt(xi);
var toBegin = fc.Move(new Vector(-x, 0, 0));
var toEnd = fc.Move(new Vector(L - x, 0, 0));
var stResid = stFc + toBegin;
var endResid = endFc - toEnd;
var errs = new double[]
{
stResid.Forces.Length,
stResid.Moments.Length,
endResid.Forces.Length,
endResid.Moments.Length
}.Max();
maxInternalForceResidual = Math.Max(maxInternalForceResidual, errs);
}
}
var span = new HtmlTag("span");
span.Add("p").Text("Validate a 3D frame internal force and internal displacement");
span.Add("h3").Text("Validate objective");
span.Add("paragraph").Text("validate internal force and internal displacement of bar elements. ")
.AddClosedTag("br");
span.Add("paragraph").Text("Internal displacement in each element at each end node should be equal to that node's displacement.").AddClosedTag("br");
span.Add("paragraph").Text("End forces and mid force should be in equiblirium with each other.").AddClosedTag("br");
span.Add("h3").Text("Model Definition");
span.Add("paragraph").Text($"A {nx}x{ny}x{nz} grid, with {grd.Nodes.Count} nodes and {grd.Elements.Count} bar elements.").AddClosedTag("br");
span.Add("paragraph").Text("Every node in the model have a random load on it, random displacement in original location.").AddClosedTag("br");
span.Add("h3").Text("Validation Result");
{//internal displacements
span.Add("h4").Text("Internal Displacements");
span.Add("paragraph")
.Text(string.Format("Validation output for internal displacements:"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}", maxInternalDisplacementAbsErr));
}
{//internal force
span.Add("h4").Text("Internal Force");
span.Add("paragraph")
.Text(string.Format("Validation output for internal force (force residuals):"));
span.Add("p").AddClass("bg-info").AppendHtml(string.Format("-Max ABSOLUTE Error: {0:e3}", maxInternalForceResidual));
}
var buf = new ValidationResult();
buf.Span = span;
buf.Title = "Internal force & displacement validation";
return(buf);
}
