public IEnumerable <Tetrahedral> MakeTetrahedra(Voxel voxel)
{
var c = voxel.GetCorners().ToArray();
var t = new[, ]
{
{ c[0], c[1], c[2], c[4] },
{ c[3], c[1], c[2], c[7] },
{ c[1], c[2], c[4], c[7] },
{ c[4], c[5], c[7], c[1] },
{ c[4], c[7], c[6], c[2] }
};
for (int i = 0; i < 5; i++)
{
var tetra = new Tetrahedral()
{
E = 210e9, Nu = 0.33
};
for (int j = 0; j < 4; j++)
{
tetra.Nodes[j] = (t[i, j] as FeaCorner).Node;
}
yield return(tetra);
}
}
/// <summary>
/// Gets the global equivalent nodal loads for <see cref="Tetrahedral"/> element.
/// </summary>
/// <param name="elm">The elm.</param>
/// <returns>global equivalent nodal loads for <see cref="Tetrahedral"/> element</returns>
private Force[] GetGlobalEquivalentNodalLoads(Tetrahedral elm)
{
//p.263 of Structural Analysis with the Finite Element Method Linear Statics, ISBN: 978-1-4020-8733-2
//formula (8.37c) : the total body force is distributed in equal parts between the four nodes, as expected!
elm.UpdateGeoMatrix();
var v = elm.det / 6;
var f = new Force();
f.Fx = v / 4 * _vx;
f.Fy = v / 4 * _vy;
f.Fz = v / 4 * _vz;
return(new[] { f, f, f, f });
}
private void AddTetrahedronElement(MeshBuilder bldr, Tetrahedral elm)
{
PolygonYz section = null;
var r = ElementVisualThickness / 2;
var p1 = elm.Nodes[0].Location;
var p2 = elm.Nodes[1].Location;
var p3 = elm.Nodes[2].Location;
var p4 = elm.Nodes[3].Location;
bldr.AddTriangle(p1, p3, p4);
bldr.AddTriangle(p3, p2, p4);
bldr.AddTriangle(p1, p2, p4);
bldr.AddTriangle(p1, p2, p3);
}
/// <summary>
/// Gets the global equivalent nodal loads for <see cref="Tetrahedral"/> element.
/// </summary>
/// <param name="element">The element.</param>
/// <returns></returns>
public Force[] GetGlobalEquivalentNodalLoads(Tetrahedral element)
{
//p.264 of Structural Analysis with the Finite Element Method Linear Statics, ISBN: 978-1-4020-8733-2
//formula (8.39) - (8.42) : Uniform surface tractions are distributed in equal parts between the three nodes of the linear tetrahedron face affected by the loading.
//area of triangle in 3D: S = | AB x AC |/2
//using cross product of two lines of three lines of triangle
var p1 = _surfaceNodes[0].Location;
var p2 = _surfaceNodes[1].Location;
var p3 = _surfaceNodes[2].Location;
var v1 = p2 - p1;
var v2 = p3 - p1;
var s = v1.Cross(v2).Length / 2;
var f = new Force {
Fx = this.Sx * s / 3, Fy = this.Sy * s / 3, Fz = this.Sz * s / 3
};
return(new[] { f, f, f });
}
public static Model Generate3DTet4Grid(int m, int n, int l)
{
var buf = new Model();
var dx = 1.0;
var dy = 1.0;
var dz = 1.0;
var nodes = new Node[m, n, l];
for (int k = 0; k < l; k++)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
var pos = new Point(i * dx, j * dy, k * dz);
var nde = new Node()
{
Location = pos
};
buf.Nodes.Add(nde);
nde.Constraints = Constraint.RotationFixed;
nodes[j, i, k] = nde;
}
}
}
var elm = new Func <Node, Node, Node, Node, Tetrahedral>((n1, n2, n3, n4) =>
{
var buff = new Tetrahedral();
buff.Nodes[0] = n1;
buff.Nodes[1] = n2;
buff.Nodes[2] = n3;
buff.Nodes[3] = n4;
buff.E = 210e9;
buff.Nu = 0.33;
return(buff);
});
var elms = new List <Element>();
for (int i = 0; i < m - 1; i++)
{
for (int j = 0; j < n - 1; j++)
{
for (int k = 0; k < l - 1; k++)
{
var ns = new Node[] {
nodes[i, j, k],
nodes[i + 1, j, k],
nodes[i + 1, j + 1, k],
nodes[i, j + 1, k],
nodes[i, j, k + 1],
nodes[i + 1, j, k + 1],
nodes[i + 1, j + 1, k + 1],
nodes[i, j + 1, k + 1],
};
elms.Add(elm(ns[0], ns[1], ns[3], ns[4]));
elms.Add(elm(ns[2], ns[1], ns[3], ns[6]));
elms.Add(elm(ns[1], ns[3], ns[4], ns[6]));
elms.Add(elm(ns[4], ns[5], ns[6], ns[1]));
elms.Add(elm(ns[4], ns[6], ns[7], ns[3]));
}
}
}
buf.Elements.Add(elms.ToArray());
for (int i = 0; i < n * m; i++)
{
buf.Nodes[i].Constraints = Constraint.Fixed;
}
return(buf);
}
public static void Test3()
{
var model = new BriefFiniteElementNet.Model();
var p = new Point[20];
var ns = new Node[20];
p[0] = new Point(x: 0, y: 1, z: 0);
p[1] = new Point(x: 0, y: 0, z: 0);
p[2] = new Point(x: 0.20, y: 0, z: 0);
p[3] = new Point(x: 0.20, y: 0, z: 0.20);
p[4] = new Point(x: 0.20, y: 1, z: 0);
p[5] = new Point(x: 0.20, y: 1, z: 0.20);
p[6] = new Point(x: 0, y: 1, z: 0.20);
p[7] = new Point(x: 0, y: 0, z: 0.20);
p[8] = new Point(x: 0, y: 0.50, z: 0);
p[9] = new Point(x: 0.20, y: 0.50, z: 0);
p[10] = new Point(x: 0, y: 0.50, z: 0.20);
p[11] = new Point(x: 0.20, y: 0.50, z: 0.20);
p[12] = new Point(x: 0.20, y: 0.25, z: 0.20);
p[13] = new Point(x: 0, y: 0.25, z: 0.20);
p[14] = new Point(x: 0, y: 0.25, z: 0);
p[15] = new Point(x: 0.20, y: 0.25, z: 0);
p[16] = new Point(x: 0.20, y: 0.75, z: 0.20);
p[17] = new Point(x: 0.20, y: 0.75, z: 0);
p[18] = new Point(x: 0, y: 0.75, z: 0);
p[19] = new Point(x: 0, y: 0.75, z: 0.20);
for (var i = 0; i < 20; i++)
{
model.Nodes.Add(ns[i] = new Node(p[i]));
ns[i].Label = "n" + i.ToString(CultureInfo.CurrentCulture);
ns[i].Constraints = Constraints.RotationFixed;
}
var mesh = new int[24][];
mesh[0] = new int[] { 0, 4, 16, 17 };
mesh[1] = new int[] { 8, 15, 12, 14 };
mesh[2] = new int[] { 8, 16, 17, 18 };
mesh[3] = new int[] { 10, 8, 11, 12 };
mesh[4] = new int[] { 5, 19, 0, 16 };
mesh[5] = new int[] { 1, 15, 14, 12 };
mesh[6] = new int[] { 8, 10, 11, 16 };
mesh[7] = new int[] { 3, 13, 1, 7 };
mesh[8] = new int[] { 3, 13, 12, 1 };
mesh[9] = new int[] { 8, 12, 13, 14 };
mesh[10] = new int[] { 1, 15, 12, 2 };
mesh[11] = new int[] { 9, 8, 11, 16 };
mesh[12] = new int[] { 10, 8, 12, 13 };
mesh[13] = new int[] { 5, 0, 4, 16 };
mesh[14] = new int[] { 5, 19, 6, 0 };
mesh[15] = new int[] { 8, 19, 16, 18 };
mesh[16] = new int[] { 8, 19, 10, 16 };
mesh[17] = new int[] { 0, 19, 18, 16 };
mesh[18] = new int[] { 1, 3, 2, 12 };
mesh[19] = new int[] { 8, 15, 9, 12 };
mesh[20] = new int[] { 13, 12, 1, 14 };
mesh[21] = new int[] { 8, 9, 11, 12 };
mesh[22] = new int[] { 9, 8, 16, 17 };
mesh[23] = new int[] { 16, 0, 17, 18 };
foreach (var elm in mesh)
{
var felm = new Tetrahedral();
felm.Nodes[0] = ns[elm[0]];
felm.Nodes[1] = ns[elm[1]];
felm.Nodes[2] = ns[elm[2]];
felm.Nodes[3] = ns[elm[3]];
felm.E = 210e9;
felm.Nu = 0.33;
model.Elements.Add(felm);
}
var relm = new BriefFiniteElementNet.MpcElements.RigidElement_MPC();
relm.Nodes = new NodeList()
{
ns[0], ns[4], ns[5], ns[6]
};
relm.UseForAllLoads = true;
//model.MpcElements.Add(relm);
ns[1].Constraints = ns[2].Constraints = ns[3].Constraints = ns[7].Constraints = Constraints.Fixed;
var load = new BriefFiniteElementNet.NodalLoad();
var frc = new Force();
frc.Fz = 1000;// 1kN force in Z direction
load.Force = frc;
ns[5].Loads.Add(load);
ns[6].Loads.Add(load);
model.Solve_MPC();
var d5 = ns[5].GetNodalDisplacement();
var d6 = ns[6].GetNodalDisplacement();
Console.WriteLine("Nodal displacement in Z direction is {0} meters (thus {1} mm)", d5.DZ, d5.DZ * 1000);
Console.WriteLine("Nodal displacement in Z direction is {0} meters (thus {1} mm)", d6.DZ, d6.DZ * 1000);
var tetra = model.Elements[0] as Tetrahedral;
var stress = tetra.GetInternalForce(LoadCombination.DefaultLoadCombination);
}
