public static void Validate()
{
var dim = 42;
var B = Matrix.RandomMatrix(dim, dim);// elm.GetLocalStifnessMatrix();
var A = Matrix.RandomMatrix(3, 3);
var sp = System.Diagnostics.Stopwatch.StartNew();
sp.Restart();
var at_b_a_mgr = TransformManagerL2G.At_B_A(A, B);
var a_b_at_mgr = TransformManagerL2G.A_B_At(A, B);
sp.Stop();
System.Console.WriteLine("Optimised took {0} ms", sp.ElapsedMilliseconds);
var AA = Matrix.DiagonallyRepeat(A, dim / 3);
sp.Restart();
var at_b_a_dir = AA.Transpose() * B * AA;
var a_b_at_dir = AA * B * AA.Transpose();
System.Console.WriteLine("Non optimised took {0} ms", sp.ElapsedMilliseconds);
var d1 = (at_b_a_mgr - at_b_a_dir).ToArray().Max(i => Math.Abs(i));
var d2 = (a_b_at_mgr - a_b_at_dir).ToArray().Max(i => Math.Abs(i));
System.Console.WriteLine("ERR = {0} for {1}x{1} matrix", d1, dim);
System.Console.WriteLine("ERR = {0} for {1}x{1} matrix", d2, dim);
}
/// <summary>
/// Gets the local to global (and vice versa) transformation manager for this element.
/// </summary>
/// <returns>the trasformation manager related to this element</returns>
public TransformManagerL2G GetTransformationManager()
{
if (this.lastNodalLocations == null)
{
lastNodalLocations = new Point[this.nodes.Length];
}
var flag = true;
for (var i = 0; i < this.nodes.Length; i++)
{
if (lastNodalLocations[i] != nodes[i].Location)
{
flag = false;
break;
}
}
if (flag)
{
return(TransformManagerL2G.MakeFromLambdaMatrix(lastLambdaMatrix));
}
else
{
for (var i = 0; i < this.nodes.Length; i++)
{
lastNodalLocations[i] = nodes[i].Location;
}
return(TransformManagerL2G.MakeFromLambdaMatrix(lastLambdaMatrix = GetLambdaMatrix()));
}
}
/// <summary>
/// Gets the local to global (and vice versa) transformation manager for this element.
/// </summary>
/// <returns>the trasformation manager related to this element</returns>
public TransformManagerL2G GetTransformationManager()
{
/*
* if (this.lastNodalLocations == null)
* lastNodalLocations = new Point[this.nodes.Length];
*
* var flag = true;
*
* for (var i = 0; i < this.nodes.Length; i++)
* {
* if (lastNodalLocations[i] != nodes[i].Location)
* {
* flag = false;
* break;
* }
* }
*
* if (flag)
* return TransformManagerL2G.MakeFromLambdaMatrix(lastLambdaMatrix);
*
*
* else*/
{
//for (var i = 0; i < this.nodes.Length; i++)
// lastNodalLocations[i] = nodes[i].Location;
var lambda = GetLambdaMatrix();
return(TransformManagerL2G.MakeFromLambdaMatrix(lambda, MatrixPool));
}
}
public override Matrix GetGlobalStifnessMatrix()
{
var local = GetLocalStifnessMatrix();
var t = GetTransformationMatrix();
var mgr = TransformManagerL2G.MakeFromTransformationMatrix(t);
var buf = mgr.TransformLocalToGlobal(local);
return(buf);
}
/// <summary>
/// convert abaqus iso coords to bfe coords
/// </summary>
/// <param name="elm">target triangle element</param>
/// <param name="elementTransformation">target triangle element</param>
/// <param name="v">coordinations in <see cref="elm"/>'s local coordination system (abaqus)</param>
/// <returns></returns>
public static double[] AbaqusCoord2BfeCoord(TriangleElement elm, Vector v)
{
///abaqus local coordination def: comment from https://engineering.stackexchange.com/questions/48285/abaqus-stri3-element-local-coordination-system?noredirect=1#comment87622_48285
///bfe local coordination def: comment from
{
//abaqus
var v12 = elm.Nodes[1].Location - elm.Nodes[0].Location; //from node 2 to node 1
var v13 = elm.Nodes[2].Location - elm.Nodes[0].Location; //from node 3 to node 1
var n = Vector.Cross(v12, v13).GetUnit(); //unit of positive normal
var cosOneTenth = Math.Cos(0.1 * Math.PI / 180); //cos(0.1 deg)
var takeI = false; //take projection of I vector as local x dir
var cos_normal_i = Vector.Dot(n, Vector.I); //cos angle between I and positive normal unit
var angle_n_i = Math.Acos(cos_normal_i) * 180.0 / Math.PI;
//due to Math.Acos documentation, 0° ≤ angle_n_i ≤ 180°
if (angle_n_i < 179.9 && angle_n_i > 0.1)
{
takeI = true;
}
else
{
takeI = false;
}
var _1Axis = takeI ? Vector.I : Vector.J;//needs to be projected on the plane with normal of `n`
//vector to plane project https://www.maplesoft.com/support/help/maple/view.aspx?path=MathApps%2FProjectionOfVectorOntoPlane
var alpha = Vector.Dot(n, _1Axis) / n.Length;
var proj1 = _1Axis - alpha * n; //it is local x axis
var local1 = proj1; //local x axis in global 3d
var local3 = n; //local y axis in global 3d
var local2 = Vector.Cross(local3, local1); //local z axis in global 3d
var lamX = local1.GetUnit(); //Lambda_X
var lamY = local2.GetUnit(); //Lambda_Y
var lamZ = local3.GetUnit(); //Lambda_Z
var lambda = Matrix.OfJaggedArray(new[] //eq. 5.13
{
new[] { lamX.X, lamY.X, lamZ.X },
new[] { lamX.Y, lamY.Y, lamZ.Y },
new[] { lamX.Z, lamY.Z, lamZ.Z }
});
var tr = TransformManagerL2G.MakeFromLambdaMatrix(lambda.AsMatrix());
//lambda for transform between abaqus local coordination system <> global system
//first need to convert v from element coord system to
//TODO: these are right only if both abaqus and bfe local system origins are same
Vector local;
{//transform from abaus local to bfe local
var abaqusLocal = v;
var global = tr.TransformLocalToGlobal(abaqusLocal);
var bfeLocal = elm.GetTransformationManager().TransformGlobalToLocal(global);
local = bfeLocal;
}
return(new double[] { local.X, local.Y, local.Z });
}
}
