// See slides p.44
public void GetLocalNodeCoordinates(out Matrix xel, out Matrix Tg)
{
Vector3D v1 = Nodes[1].Pos - Nodes[0].Pos;
Vector3D _v2 = Nodes[2].Pos - Nodes[0].Pos;
Vector3D v3 = Vector3D.CrossProduct(v1, _v2);
Vector3D v2 = Vector3D.CrossProduct(v3, v1);
if (v1.IsZeroVector() || v2.IsZeroVector() || v3.IsZeroVector())
{
throw new Exception("Bad element, ID: " + this.Id.ToString());
}
Vector3D e1 = v1.Normalize(false);
Vector3D e2 = v2.Normalize(false);
Vector3D e3 = v3.Normalize(false);
Matrix xeg = new Matrix(3, 3);
xeg.SetRow(v1.ToMatrix().Transpose(), 1);
xeg.SetRow(_v2.ToMatrix().Transpose(), 2);
Matrix T = new Matrix(3, 3);
T.SetCol(e1.ToMatrix(), 0);
T.SetCol(e2.ToMatrix(), 1);
T.SetCol(e3.ToMatrix(), 2);
xel = xeg * T;
Tg = new Matrix(18, 18);
int[] pos1 = SF.intSrs(0, 2);
int[] pos2 = SF.intSrs(3, 5);
int[] pos3 = SF.intSrs(6, 8);
int[] pos4 = SF.intSrs(9, 11);
int[] pos5 = SF.intSrs(12, 14);
int[] pos6 = SF.intSrs(15, 17);
Tg[pos1, pos1] = T;
Tg[pos2, pos2] = T;
Tg[pos3, pos3] = T;
Tg[pos4, pos4] = T;
Tg[pos5, pos5] = T;
Tg[pos6, pos6] = T;
}
//Only verified to MATLAB-cod with configurations: 4 laminas (all 0 degrees), 4 laminas (45,30,30,45) degrees
public static void eqModulus(ShellElement shell, out Matrix D, out List <Matrix> Qtot, out List <double> zValues)
{
//Just used for the shorter name
List <double> E1s = shell.Section.Exs;
List <double> E2s = shell.Section.Eys;
List <double> angles = shell.Section.angles;
List <double> thickness = shell.Section.thickness;
List <double> v12s = shell.Section.vs;
List <double> Gxys = shell.Section.Gxys;
List <double> densitys = shell.Section.densitys;
double totThick = shell.Section.totalThickness;
//Used for gravity load
//double gravity = 9.81;
//Global stiffness matrices for the laminate
Matrix AA = new Matrix(3, 3); //Extensional or membrane stiffness terms of a laminate
Matrix BB = new Matrix(3, 3); //Coupling stiffness terms of a laminate
Matrix DD = new Matrix(3, 3); //Bending stiffness n therms of a laminate
//Testing stresses
Qtot = new List <Matrix>();
zValues = new List <double>();
//Global bodyforces matrices for the laminate (not used now)
double II0 = 0;
//double II1 = 0;
//double II2 = 0;
//Get the maximum of the different inputs
int[] lengths = { E1s.Count, E2s.Count, angles.Count, thickness.Count, v12s.Count };
int listLength = lengths.Max();
//Check if number of inputs is one or the same as the maximum And make the lists same length
E1s = SF.checkPlyListLength(E1s, listLength);
E2s = SF.checkPlyListLength(E2s, listLength);
angles = SF.checkPlyListLength(angles, listLength);
thickness = SF.checkPlyListLength(thickness, listLength);
v12s = SF.checkPlyListLength(v12s, listLength);
Gxys = SF.checkPlyListLength(Gxys, listLength);
//if odd numbers of numbers
double iterations = Math.Ceiling(listLength / 2.0);
iterations = listLength;
//For the moment only half of the layers are iterated thorough (and then doubled), it is necessary that the
//layers are symmetrical. A check is done for this in Section GH-component. Should be changed later
for (int i = 0; i < iterations; i++)
{
double v21 = v12s[i] * E2s[i] / E1s[i]; // Stiffness and strength analysis (Bokmärke) 4.2
//Reduced stiffness terms (EUROCOMP eq4.50)
double Q11 = E1s[i] / (1 - v12s[i] * v21);
double Q12 = v21 * E1s[i] / (1 - v12s[i] * v21); //= Q21
double Q22 = E2s[i] / (1 - v12s[i] * v21);
double Q66 = Gxys[i];
//Take local coordinate system into account
double angle = angles[i] + shell.MaterialOrientationAngle;
//angle in degree
double m = Math.Cos(angle * 2 * Math.PI / 360); //Math.Cos uses radians
double n = Math.Sin(angle * 2 * Math.PI / 360); //Math.Cos uses radians
//EUROCOMP, fast första är fel där (m^4) (Step 2)
double Q_11 = Q11 * Math.Pow(m, 4) + Q22 * Math.Pow(n, 4) + Q12 * 2 * Math.Pow(m, 2) * Math.Pow(n, 2) + Q66 * 4 * Math.Pow(m, 2) * Math.Pow(n, 2);
double Q_22 = Q11 * Math.Pow(n, 4) + Q22 * Math.Pow(m, 4) + Q12 * 2 * Math.Pow(m, 2) * Math.Pow(n, 2) + Q66 * 4 * Math.Pow(m, 2) * Math.Pow(n, 2);
double Q_66 = (Q11 + Q22 - 2 * Q12) * Math.Pow(m, 2) * Math.Pow(n, 2) + Q66 * Math.Pow(Math.Pow(m, 2) - Math.Pow(n, 2), 2);
double Q_12 = (Q11 + Q22 - 4 * Q66) * Math.Pow(n, 2) * Math.Pow(m, 2) + Q12 * (Math.Pow(n, 4) + Math.Pow(m, 4));
double Q_16 = Q11 * Math.Pow(m, 3) * n - Q22 * Math.Pow(n, 3) * m + Q12 * (Math.Pow(n, 3) * m - Math.Pow(m, 3) * n) + Q66 * 2 * (Math.Pow(n, 3) * m - Math.Pow(m, 3) * n);
double Q_26 = Q11 * Math.Pow(n, 3) * m - Q22 * Math.Pow(m, 3) * n + Q12 * (Math.Pow(m, 3) * n - Math.Pow(n, 3) * m) + Q66 * 2 * (Math.Pow(m, 3) * n - Math.Pow(n, 3) * m);
Matrix Q_ = new Matrix(new double[, ] {
{ Q_11, Q_12, Q_16 }, { Q_12, Q_22, Q_26 }, { Q_16, Q_26, Q_66 }
});
//Determine distances from the mid-plane
//Good picture in laminatedComposite PDF
double hkNew = totThick / 2.0;
double hkMinus1New = totThick / 2.0 - thickness[i];
for (int j = 0; j < i; j++)
{
hkNew -= thickness[j];
hkMinus1New -= thickness[j];
}
//Ändra till +=
AA = AA + (hkNew - hkMinus1New) * Q_;
BB = BB + (Math.Pow(hkNew, 2) - Math.Pow(hkMinus1New, 2)) * Q_;
DD = DD + (Math.Pow(hkNew, 3) - Math.Pow(hkMinus1New, 3)) * Q_;
//Same but for the masses
II0 = II0 + thickness[i];
//For stresses
Matrix Qlarge = new Matrix(6, 6);
Qlarge[new int[] { 0, 1, 2 }, new int[] { 0, 1, 2 }] = Q_;
Qtot.Add(Qlarge);
zValues.Add(hkNew - thickness[i] / 2);
}
BB = (1.0 / 2.0) * BB;
DD = (1.0 / 3.0) * DD;
// II2 = (1.0 / 3.0) * II2;
// II0 = II0 * density * gravity;
//Step 5 i euroCOMP
// Matrix a = AA.Invert();
//TEMPORARY. THEY GET SINGULAR
// Matrix b = B.Invert();
// Matrix d = DD.Invert();
//Step 6 euroCOMP
/* double totalThick = listLength * thickLam;
* double Ex = 1 / (totalThick * a[0, 0]);
* double Ey = 1 / (totalThick * a[1, 1]);
* double Gxy = 1 / (totalThick * a[2, 2]);
* double vxy = -a[0, 1] / a[0, 0];
* double vyx = -a[0, 1] / a[1, 1]; */
//d and b matrices can be used for the equivalent bending elastic constants (step 6 euroCOMP)
//Total D-matrix D=[AA -BB;-BB DD]
D = new Matrix(6, 6);
D[new int[] { 0, 1, 2 }, new int[] { 0, 1, 2 }] = AA;
D[new int[] { 3, 4, 5 }, new int[] { 3, 4, 5 }] = DD;
D[new int[] { 0, 1, 2 }, new int[] { 3, 4, 5 }] = -BB;
D[new int[] { 3, 4, 5 }, new int[] { 0, 1, 2 }] = -BB;
//Total Gravity load matrix
//q = new Matrix(new double[,] { { 0 } , { 0 }, { -II0 } }); //Gravity works in negative direction
}
//Calculate principal tresses for all the elements
public void CalcStresses()
{
//Folllowing plants in MATlab, each element 15 dofs
//the 15 active dofs used in each element (with 18 dofs in total)
int[] activeDofs = new int[] { 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16 };
PrincipalStresses = new List <Vector3D>();
stresses = new List <Matrix>();
PrincipalAngles = new List <double>();
vonMises = new List <double>();
for (int i = 0; i < elements.Count; i++)
{
//Get all the 18 element dofs from the global
int[] dofsFull = elements[i].GetElementDofs();
//Take the deformations from the element dofs
Matrix aTrans = new Matrix(18, 1);
for (int j = 0; j < dofsFull.Count(); j++)
{
aTrans[j] = a[dofsFull[j]];
}
//Transform the local coordinates to global
aTrans = elements[i].Te.Invert() * aTrans;
//Take the 15 active dofs that should be used from the transformed defrormations
Matrix ed = new Matrix(1, 15);
for (int j = 0; j < activeDofs.Count(); j++)
{
ed[0, j] = aTrans[activeDofs[j]];
}
//Stresses (D*B*a)
// Matrix ss = elements[i].DBe * ed[0, SF.intSrs(0, 14)].Transpose();
// stresses.Add(ss);
double theta = 0;
Vector3D vMax = new Vector3D();
//for every layer
for (int j = 0; j < elements[i].DBe.Count; j++)
{
Matrix ss = new Matrix(6, 1);
ed[3] *= elements[i].zs[j];
ed[4] *= elements[i].zs[j];
ed[8] *= elements[i].zs[j];
ed[9] *= elements[i].zs[j];
ed[13] *= elements[i].zs[j];
ed[14] *= elements[i].zs[j];
ss = elements[i].DBe[j] * ed[0, SF.intSrs(0, 14)].Transpose();
//Make sure there is no errors when this is changed
// theta = 0.5 * Math.Atan(2 * ss[2] / (ss[0] - ss[1]));
// if (ss[0] < ss[1]) theta = theta + Math.PI / 2;
//PrincipalAngles.Add(theta);
//Principle stresses
double p1 = (ss[0] + ss[1]) / 2.0 + Math.Sqrt(Math.Pow((ss[0] - ss[1]) / 2, 2) + Math.Pow(ss[2], 2));
double p2 = (ss[0] + ss[1]) / 2.0 - Math.Sqrt(Math.Pow((ss[0] - ss[1]) / 2, 2) + Math.Pow(ss[2], 2));
Vector3D v = new Vector3D(p1, p2, 0);
if (v.Length > vMax.Length)
{
vMax = v;
theta = 0.5 * Math.Atan(2 * ss[2] / (ss[0] - ss[1]));
if (ss[0] < ss[1])
{
theta = theta + Math.PI / 2;
}
}
}
// PrincipalStresses.Add(new Vector3D(p1, p2, 0));
PrincipalStresses.Add(vMax);
// vonMises.Add(Math.Sqrt(p1 * p1 - p1 * p2 + p2 * p2));
vonMises.Add(Math.Sqrt(vMax.X * vMax.X - vMax.X * vMax.Y + vMax.Y * vMax.Y));
PrincipalAngles.Add(theta);
}
}