public static void Input(ref List <Point3d> gp, ref List <Curve> tp, ref List <Curve> sp, ref List <int> lp, ref List <Vector3d> lv, ref int[] fix, ref int[] free, ref ln.Vector <double> Pfix, ref ln.Matrix <double> C, ref int[] istart, ref int[] iend, ref double[] rfload)
{
int nk = gp.Count; //number of nodes
int nm = tp.Count; //number of members
C = ln.Matrix <double> .Build.Dense(nm, nk);
istart = new int[nm];
iend = new int[nm];
for (int i = 0; i < nm; i++)
{
istart[i] = Rhino.Collections.Point3dList.ClosestIndexInList(gp, tp[i].PointAtStart);
iend[i] = Rhino.Collections.Point3dList.ClosestIndexInList(gp, tp[i].PointAtEnd);
C[i, istart[i]] = -1;
C[i, iend[i]] = 1;
}
///definition of support input
///supports are defined by curve objects
int nsp = sp.Count;
///fix0 is an index of supported & loaded points
System.Collections.ArrayList fix0 = new System.Collections.ArrayList();
//add supported points' indices into fix0
for (int i = 0; i < nk; i++)
{
for (int j = 0; j < nsp; j++)
{
double t = new double();
bool scparam = sp[j].ClosestPoint(gp[i], out t);
Point3d scp = sp[j].PointAt(t);
if ((gp[i] - scp).IsTiny())
{
fix0.Add(i);
}
}
}
//add loaded points' indices into fix0
int nl = lp.Count;//number of nodal loads
for (int i = 0; i < nl; i++)
{
fix0.Add(lp[i]);
}
fix0.Sort();//maybe unnecessary??
//convert to integer array "fix1"
int[] fix1 = (int[])fix0.ToArray(typeof(int));
//convert to HashSet(HashSet can remove overlapping values and sort automatically and quickly)
HashSet <int> fix2 = new HashSet <int>(fix1);
//convert to integer array "fix"
fix = new int[fix2.Count];
//int[] fix = new int[fix2.Count];
fix2.CopyTo(fix, 0);
int nfix = fix.Length;
int ifix = 0;
free = new int[nk - nfix];
int nfree = 0;
for (int i = 0; i < nk; i++)
{
if (ifix != nfix)
{
if (i == fix[ifix])
{
ifix++;
}
else
{
free[nfree] = i;
nfree++;
}
}
else
{
free[nfree] = i;
nfree++;
}
}
Pfix = ln.Vector <double> .Build.Dense(nfix * 3);
int iload = 0;
for (int i = 0; i < nfix; i++)
{
if (iload == nl)
{
break;
}
if (fix[i] == lp[iload])
{
Pfix[i] = lv[iload].X;
Pfix[nfix + i] = lv[iload].Y;
Pfix[nfix * 2 + i] = lv[iload].Z;
iload++;
}
}
rfload = new double[nl * 3];
}
/// <summary>
/// free nodal coordinates as a function of force density method
/// </summary>
public static void Sens(ref double[] q, ref List <Point3d> gp, ref List <Curve> tp, ref List <int> lp, ref double[] cs, ref double compliance, ref double[] rfload, ref int[] fix, ref int[] free, ref ln.Vector <double> Pfix, ref ln.Matrix <double> C, ref int[] istart, ref int[] iend, ref double[] scompliance, ref List <double[]> srfload)
{
int nk = gp.Count;
int nm = tp.Count;
int nfree = free.Length;
int nfix = fix.Length;
ln.Matrix <double> Ct = C.Transpose();
double[] x = new double[nk];
double[] y = new double[nk];
double[] z = new double[nk];
for (int i = 0; i < nk; i++)
{
x[i] = gp[i].X;
y[i] = gp[i].Y;
z[i] = gp[i].Z;
}
ln.Matrix <double> qd = ln.Matrix <double> .Build.DenseOfDiagonalArray(q);
List <ln.Matrix <double> > sqd = new List <ln.Matrix <double> >(nm);
for (int i = 0; i < nm; i++)
{
var sq = ln.Vector <double> .Build.Dense(nm);
sq[i] = 1.0;
sqd.Add(ln.Matrix <double> .Build.DenseOfDiagonalVector(sq));
}
ln.Matrix <double> Q0 = Ct * qd * C;
var sQ0 = new List <ln.Matrix <double> >(nm);
for (int i = 0; i < nm; i++)
{
sQ0.Add(Ct * sqd[i] * C);
}
///Qfree & sQfree
var Qfree0 = Q0.Clone();
for (int i = nfix - 1; i >= 0; i--)
{
Qfree0 = Qfree0.RemoveColumn(fix[i]).RemoveRow(fix[i]);
}
var sQfree0 = new List <ln.Matrix <double> >(nm);
foreach (ln.Matrix <double> m in sQ0)
{
sQfree0.Add(m);
}
for (int j = 0; j < nm; j++)
{
for (int i = nfix - 1; i >= 0; i--)
{
sQfree0[j] = sQfree0[j].RemoveColumn(fix[i]).RemoveRow(fix[i]);
}
}
///Qfix & sQfix
var Qfix0 = Q0.Clone();
for (int i = nfree - 1; i >= 0; i--)
{
Qfix0 = Qfix0.RemoveColumn(free[i]).RemoveRow(free[i]);
}
var sQfix0 = new List <ln.Matrix <double> >(nm);
foreach (ln.Matrix <double> m in sQ0)
{
sQfix0.Add(m);
}
for (int j = 0; j < nm; j++)
{
for (int i = nfree - 1; i >= 0; i--)
{
sQfix0[j] = sQfix0[j].RemoveColumn(free[i]).RemoveRow(free[i]);
}
}
///Qlink & sQlink
var Qlink0 = Q0.Clone();
for (int i = nfree - 1; i >= 0; i--)
{
Qlink0 = Qlink0.RemoveColumn(free[i]);
}
for (int i = nfix - 1; i >= 0; i--)
{
Qlink0 = Qlink0.RemoveRow(fix[i]);
}
var sQlink0 = new List <ln.Matrix <double> >(nm);
foreach (ln.Matrix <double> m in sQ0)
{
sQlink0.Add(m);
}
for (int j = 0; j < nm; j++)
{
for (int i = nfree - 1; i >= 0; i--)
{
sQlink0[j] = sQlink0[j].RemoveColumn(free[i]);
}
for (int i = nfix - 1; i >= 0; i--)
{
sQlink0[j] = sQlink0[j].RemoveRow(fix[i]);
}
}
var Qfree = ln.Matrix <double> .Build.Dense(nfree * 3, nfree * 3);
var Qfix = ln.Matrix <double> .Build.Dense(nfix * 3, nfix * 3);
var Qlink = ln.Matrix <double> .Build.Dense(nfree * 3, nfix * 3);
for (int i = 0; i < 3; i++)
{
Qfree.SetSubMatrix(nfree * i, nfree * i, Qfree0);
Qfix.SetSubMatrix(nfix * i, nfix * i, Qfix0);
Qlink.SetSubMatrix(nfree * i, nfix * i, Qlink0);
}
var sQfree = new List <ln.Matrix <double> >(nm);
var sQfix = new List <ln.Matrix <double> >(nm);
var sQlink = new List <ln.Matrix <double> >(nm);
for (int i = 0; i < nm; i++)
{
sQfree.Add(ln.Matrix <double> .Build.Dense(nfree * 3, nfree * 3));
sQfix.Add(ln.Matrix <double> .Build.Dense(nfix * 3, nfix * 3));
sQlink.Add(ln.Matrix <double> .Build.Dense(nfree * 3, nfix * 3));
}
for (int j = 0; j < nm; j++)
{
for (int i = 0; i < 3; i++)
{
sQfree[j].SetSubMatrix(nfree * i, nfree * i, sQfree0[j]);
sQfix[j].SetSubMatrix(nfix * i, nfix * i, sQfix0[j]);
sQlink[j].SetSubMatrix(nfree * i, nfix * i, sQlink0[j]);
}
}
var Xfree = ln.Vector <double> .Build.Dense(nfree * 3);
var Xfix = ln.Vector <double> .Build.Dense(nfix * 3);
for (int i = 0; i < nfix; i++)
{
Xfix[i] = gp[fix[i]].X;
Xfix[nfix + i] = gp[fix[i]].Y;
Xfix[nfix * 2 + i] = gp[fix[i]].Z;
}
Xfree = -(Qfree).Inverse() * Qlink * Xfix;
var sQfreeXfree = ln.Matrix <double> .Build.Dense(nfree * 3, nm);
for (int i = 0; i < nm; i++)
{
sQfreeXfree.SetColumn(i, sQfree[i] * Xfree);
}
var sQlinkXfix = ln.Matrix <double> .Build.Dense(nfree * 3, nm);
for (int i = 0; i < nm; i++)
{
sQlinkXfix.SetColumn(i, sQlink[i] * Xfix);
}
var sXfree = ln.Matrix <double> .Build.Dense(nfree * 3, nm);
sXfree = -Qfree.Inverse() * (sQfreeXfree + sQlinkXfix);
///return nodal coordinates
for (int i = 0; i < nfree; i++)
{
x[free[i]] = Xfree[i];
y[free[i]] = Xfree[nfree + i];
z[free[i]] = Xfree[nfree * 2 + i];
}
double[,] sx = new double[nk, nm];
double[,] sy = new double[nk, nm];
double[,] sz = new double[nk, nm];
for (int j = 0; j < nm; j++)
{
for (int i = 0; i < nfree; i++)
{
sx[free[i], j] = sXfree[i, j];
sy[free[i], j] = sXfree[nfree + i, j];
sz[free[i], j] = sXfree[nfree * 2 + i, j];
}
}
for (int i = 0; i < nfree; i++)
{
gp[free[i]] = new Point3d(x[free[i]], y[free[i]], z[free[i]]);
}
for (int i = 0; i < nm; i++)
{
tp[i] = new LineCurve(gp[istart[i]], gp[iend[i]]);
}
double[] length = new double[nm];
double[] length2 = new double[nm];
double[,] slength2 = new double[nm, nm];
for (int i = 0; i < nm; i++)
{
length[i] = Math.Sqrt(Math.Pow(x[iend[i]] - x[istart[i]], 2) + Math.Pow(y[iend[i]] - y[istart[i]], 2) + Math.Pow(z[iend[i]] - z[istart[i]], 2));
length2[i] = Math.Pow(length[i], 2);
}
for (int j = 0; j < nm; j++)
{
for (int i = 0; i < nm; i++)
{
slength2[i, j] = 2 * ((x[iend[i]] - x[istart[i]]) * (sx[iend[i], j] - sx[istart[i], j]) + (y[iend[i]] - y[istart[i]]) * (sy[iend[i], j] - sy[istart[i], j]) + (z[iend[i]] - z[istart[i]]) * (sz[iend[i], j] - sz[istart[i], j]));
}
}
var sQlinkXfree = ln.Matrix <double> .Build.Dense(nfix * 3, nm);
var QlinksXfree = ln.Matrix <double> .Build.Dense(nfix * 3, nm);
var sQfixXfix = ln.Matrix <double> .Build.Dense(nfix * 3, nm);
for (int i = 0; i < nm; i++)
{
sQlinkXfree.SetColumn(i, sQlink[i].Transpose() * Xfree);
QlinksXfree.SetColumn(i, Qlink.Transpose() * sXfree.Column(i));
sQfixXfix.SetColumn(i, sQfix[i] * Xfix);
}
///reaction force
var rf = ln.Vector <double> .Build.Dense(nfix * 3);
var srf = ln.Matrix <double> .Build.Dense(nfix * 3, nm);
rf = Qlink.Transpose() * Xfree + (Qfix) * Xfix;
srf = sQlinkXfree + QlinksXfree + sQfixXfix;
int iload = 0;
int nl = lp.Count;
for (int i = 0; i < nfix; i++)
{
if (iload == nl)
{
break;
}
if (fix[i] == lp[iload])
{
rfload[0 + 3 * iload] = rf[i] - Pfix[i];
rfload[1 + 3 * iload] = rf[nfix + i] - Pfix[nfix + i];
rfload[2 + 3 * iload] = rf[nfix * 2 + i] - Pfix[nfix * 2 + i];
iload++;
}
}
iload = 0;
srfload = new List <double[]>(nl * 3);
for (int i = 0; i < nl * 3; i++)
{
srfload.Add(new double[nm]);
}
for (int j = 0; j < nm; j++)
{
for (int i = 0; i < nfix; i++)
{
if (iload == nl)
{
break;
}
if (fix[i] == lp[iload])
{
srfload[0 + 3 * iload][j] = srf[i, j];
srfload[1 + 3 * iload][j] = srf[nfix + i, j];
srfload[2 + 3 * iload][j] = srf[nfix * 2 + i, j];
iload++;
}
}
}
///cross-sectional area
cs = new double[nm];
for (int i = 0; i < nm; i++)
{
cs[i] = Math.Sqrt(Math.Pow(q[i], 2) + .1e-5) * length[i];
}
///volume
double vol = 0;
for (int i = 0; i < nm; i++)
{
vol += Math.Sqrt(Math.Pow(q[i], 2) + .1e-5) * length2[i];
}
///strain energy
double se = 0;
double[] sse = new double[nm];
for (int i = 0; i < nm; i++)
{
se += .5e0 * length2[i] * Math.Sqrt(Math.Pow(q[i], 2) + .1e-5) / ee;
}
for (int j = 0; j < nm; j++)
{
for (int i = 0; i < nm; i++)
{
sse[j] += .5e0 * slength2[i, j] * Math.Sqrt(Math.Pow(q[i], 2) + .1e-5) / ee;
sse[j] += .5e0 * length2[i] * q[i] / Math.Sqrt(Math.Pow(q[i], 2) + .1e-5) * ee;
}
}
///compliance
compliance = se * .2e1;
scompliance = new double[nm];
for (int j = 0; j < nm; j++)
{
scompliance[j] = sse[j] * .2e1;
}
}
