private static void FrameElementForce(double[] s, List <Vec3Float> xyz, double L, double Le, int n1, int n2,
float Ax, float Asy, float Asz, float J, float Iy, float Iz, float E, float G, float p, double[] fT, double[] fM,
double[] D, bool shear, bool geom, double axialStrain)//return s
{
double d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11, d12,
delta = 0.0, /* stretch in the frame element */
Ksy, Ksz, Dsy, Dsz, /* shear deformation coeff's */
T = 0.0; /* axial force for geometric stiffness */
double f1 = 0, f2 = 0, f3 = 0, f4 = 0, f5 = 0, f6 = 0,
f7 = 0, f8 = 0, f9 = 0, f10 = 0, f11 = 0, f12 = 0;
double[] t = Coordtrans.coordTrans(xyz, L, n1, n2, p);
n1 = 6 * n1; n2 = 6 * n2;
d1 = D[n1 + 0]; d2 = D[n1 + 1]; d3 = D[n1 + 2];
d4 = D[n1 + 3]; d5 = D[n1 + 4]; d6 = D[n1 + 5];
d7 = D[n2 + 0]; d8 = D[n2 + 1]; d9 = D[n2 + 2];
d10 = D[n2 + 3]; d11 = D[n2 + 4]; d12 = D[n2 + 5];
if (shear)
{
Ksy = 12.0 * E * Iz / (G * Asy * Le * Le);
Ksz = 12.0 * E * Iy / (G * Asz * Le * Le);
Dsy = (1 + Ksy) * (1 + Ksy);
Dsz = (1 + Ksz) * (1 + Ksz);
}
else
{
Ksy = Ksz = 0.0;
Dsy = Dsz = 1.0;
}
delta = (d7 - d1) * t[0] + (d8 - d2) * t[1] + (d9 - d3) * t[2];
axialStrain = delta / Le; // log(Ls/Le);
s[0] = -(Ax * E / Le) * ((d7 - d1) * t[0] + (d8 - d2) * t[1] + (d9 - d3) * t[2]);
if (geom)
{
T = -s[0];
}
s[1] = -(12.0 * E * Iz / (Le * Le * Le * (1.0 + Ksy)) +
T / L * (1.2 + 2.0 * Ksy + Ksy * Ksy) / Dsy) *
((d7 - d1) * t[3] + (d8 - d2) * t[4] + (d9 - d3) * t[5])
+ (6.0 * E * Iz / (Le * Le * (1.0 + Ksy)) + T / 10.0 / Dsy) *
((d4 + d10) * t[6] + (d5 + d11) * t[7] + (d6 + d12) * t[8]);
s[2] = -(12.0 * E * Iy / (Le * Le * Le * (1.0 + Ksz)) +
T / L * (1.2 + 2.0 * Ksz + Ksz * Ksz) / Dsz) *
((d7 - d1) * t[6] + (d8 - d2) * t[7] + (d9 - d3) * t[8])
- (6.0 * E * Iy / (Le * Le * (1.0 + Ksz)) + T / 10.0 / Dsz) *
((d4 + d10) * t[3] + (d5 + d11) * t[4] + (d6 + d12) * t[5]);
s[3] = -(G * J / Le) * ((d10 - d4) * t[0] + (d11 - d5) * t[1] + (d12 - d6) * t[2]);
s[4] = (6.0 * E * Iy / (Le * Le * (1.0 + Ksz)) + T / 10.0 / Dsz) *
((d7 - d1) * t[6] + (d8 - d2) * t[7] + (d9 - d3) * t[8])
+ ((4.0 + Ksz) * E * Iy / (Le * (1.0 + Ksz)) +
T * L * (2.0 / 15.0 + Ksz / 6.0 + Ksz * Ksz / 12.0) / Dsz) *
(d4 * t[3] + d5 * t[4] + d6 * t[5])
+ ((2.0 - Ksz) * E * Iy / (Le * (1.0 + Ksz)) -
T * L * (1.0 / 30.0 + Ksz / 6.0 + Ksz * Ksz / 12.0) / Dsz) *
(d10 * t[3] + d11 * t[4] + d12 * t[5]);
s[5] = -(6.0 * E * Iz / (Le * Le * (1.0 + Ksy)) + T / 10.0 / Dsy) *
((d7 - d1) * t[3] + (d8 - d2) * t[4] + (d9 - d3) * t[5])
+ ((4.0 + Ksy) * E * Iz / (Le * (1.0 + Ksy)) +
T * L * (2.0 / 15.0 + Ksy / 6.0 + Ksy * Ksy / 12.0) / Dsy) *
(d4 * t[6] + d5 * t[7] + d6 * t[8])
+ ((2.0 - Ksy) * E * Iz / (Le * (1.0 + Ksy)) -
T * L * (1.0 / 30.0 + Ksy / 6.0 + Ksy * Ksy / 12.0) / Dsy) *
(d10 * t[6] + d11 * t[7] + d12 * t[8]);
s[6] = -s[0];
s[7] = -s[1];
s[8] = -s[2];
s[9] = -s[3];
s[10] = (6.0 * E * Iy / (Le * Le * (1.0 + Ksz)) + T / 10.0 / Dsz) *
((d7 - d1) * t[6] + (d8 - d2) * t[7] + (d9 - d3) * t[8])
+ ((4.0 + Ksz) * E * Iy / (Le * (1.0 + Ksz)) +
T * L * (2.0 / 15.0 + Ksz / 6.0 + Ksz * Ksz / 12.0) / Dsz) *
(d10 * t[3] + d11 * t[4] + d12 * t[5])
+ ((2.0 - Ksz) * E * Iy / (Le * (1.0 + Ksz)) -
T * L * (1.0 / 30.0 + Ksz / 6.0 + Ksz * Ksz / 12.0) / Dsz) *
(d4 * t[3] + d5 * t[4] + d6 * t[5]);
s[11] = -(6.0 * E * Iz / (Le * Le * (1.0 + Ksy)) + T / 10.0 / Dsy) *
((d7 - d1) * t[3] + (d8 - d2) * t[4] + (d9 - d3) * t[5])
+ ((4.0 + Ksy) * E * Iz / (Le * (1.0 + Ksy)) +
T * L * (2.0 / 15.0 + Ksy / 6.0 + Ksy * Ksy / 12.0) / Dsy) *
(d10 * t[6] + d11 * t[7] + d12 * t[8])
+ ((2.0 - Ksy) * E * Iz / (Le * (1.0 + Ksy)) -
T * L * (1.0 / 30.0 + Ksy / 6.0 + Ksy * Ksy / 12.0) / Dsy) *
(d4 * t[6] + d5 * t[7] + d6 * t[8]);
// add fixed end forces to internal element forces
// 18oct[1]012, 14may1204, 15may2014
// add temperature fixed-end-forces to variables f1-f12
// add mechanical load fixed-end-forces to variables f1-f12
// f1 ... f12 are in the global element coordinate system
f1 = fT[0] + fM[0]; f2 = fT[1] + fM[1]; f3 = fT[2] + fM[2];
f4 = fT[3] + fM[3]; f5 = fT[4] + fM[4]; f6 = fT[5] + fM[5];
f7 = fT[6] + fM[6]; f8 = fT[7] + fM[7]; f9 = fT[8] + fM[8];
f10 = fT[9] + fM[9]; f11 = fT[10] + fM[10]; f12 = fT[11] + fM[11];
// transform f1 ... f12 to local element coordinate system and
// add local fixed end forces (-equivalent loads) to internal loads
// {Q} = [T]{f}
s[0] -= (f1 * t[0] + f2 * t[1] + f3 * t[2]);
s[1] -= (f1 * t[3] + f2 * t[4] + f3 * t[5]);
s[2] -= (f1 * t[6] + f2 * t[7] + f3 * t[8]);
s[3] -= (f4 * t[0] + f5 * t[1] + f6 * t[2]);
s[4] -= (f4 * t[3] + f5 * t[4] + f6 * t[5]);
s[5] -= (f4 * t[6] + f5 * t[7] + f6 * t[8]);
s[6] -= (f7 * t[0] + f8 * t[1] + f9 * t[2]);
s[7] -= (f7 * t[3] + f8 * t[4] + f9 * t[5]);
s[8] -= (f7 * t[6] + f8 * t[7] + f9 * t[8]);
s[9] -= (f10 * t[0] + f11 * t[1] + f12 * t[2]);
s[10] -= (f10 * t[3] + f11 * t[4] + f12 * t[5]);
s[11] -= (f10 * t[6] + f11 * t[7] + f12 * t[8]);
}
public static void ElasticK(double[,] k, List <Vec3Float> xyz, float[] r,
double L, double Le,
int n1, int n2,
double Ax, double Asy, double Asz,
double J, double Iy, double Iz,
double E, double G, float p,
bool shear)
{
double Ksy, Ksz; /* shear deformatn coefficients */
int i, j;
double[] t = Coordtrans.coordTrans(xyz, L, n1, n2, p);
for (i = 0; i < 12; i++)
{
for (j = 0; j < 12; j++)
{
k[i, j] = 0.0;
}
}
if (shear)
{
Ksy = 12.0 * E * Iz / (G * Asy * Le * Le);
Ksz = 12.0 * E * Iy / (G * Asz * Le * Le);
}
else
{
Ksy = Ksz = 0.0;
}
k[0, 0] = k[6, 6] = E * Ax / Le;
k[1, 1] = k[7, 7] = 12.0 * E * Iz / (Le * Le * Le * (1.0 + Ksy));
k[2, 2] = k[8, 8] = 12.0 * E * Iy / (Le * Le * Le * (1.0 + Ksz));
k[3, 3] = k[9, 9] = G * J / Le;
k[4, 4] = k[10, 10] = (4.0 + Ksz) * E * Iy / (Le * (1.0 + Ksz));
k[5, 5] = k[11, 11] = (4.0 + Ksy) * E * Iz / (Le * (1.0 + Ksy));
k[4, 2] = k[2, 4] = -6.0 * E * Iy / (Le * Le * (1.0 + Ksz));
k[5, 1] = k[1, 5] = 6.0 * E * Iz / (Le * Le * (1.0 + Ksy));
k[6, 0] = k[0, 6] = -k[0, 0];
k[11, 7] = k[7, 11] = k[7, 5] = k[5, 7] = -k[5, 1];
k[10, 8] = k[8, 10] = k[8, 4] = k[4, 8] = -k[4, 2];
k[9, 3] = k[3, 9] = -k[3, 3];
k[10, 2] = k[2, 10] = k[4, 2];
k[11, 1] = k[1, 11] = k[5, 1];
k[7, 1] = k[1, 7] = -k[1, 1];
k[8, 2] = k[2, 8] = -k[2, 2];
k[10, 4] = k[4, 10] = (2.0 - Ksz) * E * Iy / (Le * (1.0 + Ksz));
k[11, 5] = k[5, 11] = (2.0 - Ksy) * E * Iz / (Le * (1.0 + Ksy));
k = Coordtrans.Atma(t, k, r[n1], r[n2]);
for (i = 0; i < 12; i++)
{
for (j = i + 1; j < 12; j++)
{
if (k[i, j] != k[j, i])
{
if (Math.Abs(k[i, j] / k[j, i] - 1.0) > 1.0e-6 &&
(Math.Abs(k[i, j] / k[i, i]) > 1e-6 ||
Math.Abs(k[j, i] / k[i, i]) > 1e-6
)
)
{
Console.WriteLine($"elastic_K: element stiffness matrix not symetric ...");
Console.WriteLine($" ... k[{i}][{j}] = {k[i, j]} ");
Console.WriteLine($" ... k[{j}][{i}] = {k[j, i]} ");
Console.WriteLine($" ... relative error = {Math.Abs(k[i, j] / k[j, i] - 1.0)} ");
Console.WriteLine($" ... element matrix saved in file 'kt'");
}
k[i, j] = k[j, i] = 0.5 * (k[i, j] + k[j, i]);
}
}
}
}
public Output Solve(Input input)
{
//Fixed values
int ok = 1;
double rmsResid = 1.0;
double error = 1.0;
int axialStrainWarning = 0;
int axialSign = 1;
int writeMatrix = 0;
string title = input.Title;
IReadOnlyList <Node> nodes = input.Nodes;
IReadOnlyList <FrameElement> frameElements = input.FrameElements;
int nN = input.Nodes.Count;
List <float> rj = input.Nodes.Select(n => n.Radius).ToList();
List <Vec3Float> xyz = input.Nodes.Select(n => n.Position).ToList();
int DoF = 6 * nN;
int nR = input.ReactionInputs.Count;
double[] q = new double[DoF];
float[] r = new float[DoF];
for (int i = 0; i < nR; i++)
{
int j = input.ReactionInputs[i].Number; //This index number is decreased by 1 when importing
r[j * 6 + 0] = input.ReactionInputs[i].Position.X;
r[j * 6 + 1] = input.ReactionInputs[i].Position.Y;
r[j * 6 + 2] = input.ReactionInputs[i].Position.Z;
r[j * 6 + 3] = input.ReactionInputs[i].R.X;
r[j * 6 + 4] = input.ReactionInputs[i].R.Y;
r[j * 6 + 5] = input.ReactionInputs[i].R.Z;
}
for (int i = 0; i < DoF; i++)
{
q[i] = (r[i] == (double)1) ? 0 : 1;
}
int nE = input.FrameElements.Count;
List <double> L = input.FrameElements.Select(f =>
Coordtrans.CalculateSQDistance(input.Nodes[f.NodeIdx1].Position, input.Nodes[f.NodeIdx2].Position))
.ToList();
List <double> Le = new List <double>();
for (int i = 0; i < L.Count; i++)
{
Le.Add(L[i] - input.Nodes[input.FrameElements[i].NodeIdx1].Radius -
input.Nodes[input.FrameElements[i].NodeIdx2].Radius);
}
List <int> N1 = input.FrameElements.Select(f => f.NodeIdx1).ToList();
List <int> N2 = input.FrameElements.Select(f => f.NodeIdx2).ToList();
List <float> Ax = input.FrameElements.Select(f => f.Ax).ToList();
List <float> Asy = input.FrameElements.Select(f => f.Asy).ToList();
List <float> Asz = input.FrameElements.Select(f => f.Asz).ToList();
List <float> Jx = input.FrameElements.Select(f => f.Jx).ToList();
List <float> Iy = input.FrameElements.Select(f => f.Iy).ToList();
List <float> Iz = input.FrameElements.Select(f => f.Iz).ToList();
List <float> E = input.FrameElements.Select(f => f.E).ToList();
List <float> G = input.FrameElements.Select(f => f.G).ToList();
List <float> p = input.FrameElements.Select(f => f.Roll).ToList();
List <float> d = input.FrameElements.Select(f => f.Density).ToList();
int nL = input.LoadCases.Count;
List <float> gX = input.LoadCases.Select(l => l.Gravity.X).ToList();
List <float> gY = input.LoadCases.Select(l => l.Gravity.Y).ToList();
List <float> gZ = input.LoadCases.Select(l => l.Gravity.Z).ToList();
List <int> nF = input.LoadCases.Select(l => l.NodeLoads.Count).ToList();
List <int> nU = input.LoadCases.Select(l => l.UniformLoads.Count).ToList();
List <int> nW = input.LoadCases.Select(l => l.TrapLoads.Count).ToList();
float[,,] U = new float[nL, nE, 4];
for (int i = 0; i < nL; i++)
{
for (int j = 0; j < nE; j++)
{
//U[i, j, 0] will store node index, but not all of them will be assigned a value.
//For those not assigned, they are the same value for node index 0.
//This will cause some trouble later, so have to be initialized with another value.
//The problem is caused by converting from 1 based array in the C code to 0 based array in C# here.
U[i, j, 0] = -1;
}
}
float[,,] W = new float[nL, nE *10, 13];
for (int i = 0; i < nL; i++)
{
for (int j = 0; j < nE * 10; j++)
{
W[i, j, 0] = -1;//Same reason for array U
}
}
double[,,] eqFMech = new double[nL, nE, 12];
double[,] FMech = new double[nL, DoF];
bool shear = input.IncludeShearDeformation;
bool geom = input.IncludeGeometricStiffness;
float dx = input.XAxisIncrementForInternalForces;
double[] F = new double[DoF];
double[] dF = new double[DoF];
double[] D = new double[DoF];
double[] dD = new double[DoF];
double[] R = new double[DoF];
double[] dR = new double[DoF];
double[,] Q = new double[nE, 12];
double[,] K = new double[DoF, DoF];
////These are not used
int[] nT = new int[nL];
int[] nP = new int[nL];
int[] nD = new int[nL];
double[,] FTemp = new double[nL, DoF];
double[,,] eqFTemp = new double[nL, nE, 12];
int iter = 0;
double tol = 1.0e-9;
float[,,] P = new float[nL, 10 * nE, 5];
double[,] Dp = new double[nL, DoF];
////
IReadOnlyList <LoadCase> loadCases = input.LoadCases;
Frame3ddIO.AssembleLoads(nN, nE, nL, DoF, xyz, L, Le, N1, N2, Ax, Asy, Asz, Iy, Iz, E, G, p, d, gX, gY, gZ, shear, nF, nU, nW, FMech, eqFMech,
U, W, loadCases);
//ReadMassData()--Not implemented
//ReadCondensationData()--Not implemented
string outputText = Frame3ddIO.InputDataToString(title, nN, nE, nL, nD, nR, nF, nU, nW, nP, nT,
xyz, rj, N1, N2, Ax, Asy, Asz, Jx, Iy, Iz, E, G, p,
d, gX, gY, gZ,
FMech, Dp, r, U, W, P, shear, geom);
////Start anlyz
/* begin load case analysis loop */
List <LoadCaseOutput> loadCaseOutputs = new List <LoadCaseOutput>();
for (int lc = 0; lc < nL; lc++)
{
/* initialize displacements and displ. increment to {0} */
/* initialize reactions and react. increment to {0} */
for (int i = 0; i < DoF; i++)
{
D[i] = dD[i] = R[i] = dR[i] = 0.0;
}
/* initialize internal element end forces Q = {0} */
for (int i = 0; i < nE; i++)
{
for (int j = 0; j < 11; j++)
{
Q[i, j] = 0.0;
}
}
K = Frame3dd.AssembleK(DoF, nE, xyz, r, L, Le, N1, N2, Ax, Asy, Asz, Jx, Iy, Iz, E, G, p, shear, geom, Q);
//if (nT[lc] > 0){
//Aplly temperature loads only --Not implemented
//}
if (nF[lc] > 0 || nU[lc] > 0 || nW[lc] > 0 || nP[lc] > 0 || nD[lc] > 0 ||
gX[lc] != 0 || gY[lc] != 0 || gZ[lc] != 0)
{
for (int i = 0; i < DoF; i++)
{
if (!Common.IsDoubleZero(r[i]))
{
dD[i] = Dp[lc, i];
}
}
}
double[] tempLoadMech = Common.GetRow(FMech, lc);
var solveSystemResult = Frame3dd.SolveSystem(K, dD, tempLoadMech, dR, DoF, q, r, ok, rmsResid);
ok = solveSystemResult.ok;
rmsResid = solveSystemResult.rmsResid;
for (int i = 0; i < DoF; i++)
{
FMech[lc, i] = tempLoadMech[i];
}
for (int i = 0; i < DoF; i++)
{
if (!Common.IsDoubleZero(q[i]))
{
D[i] += dD[i];
}
else
{
D[i] = Dp[lc, i]; dD[i] = 0.0;
}
}
for (int i = 0; i < DoF; i++)
{
if (!Common.IsDoubleZero(r[i]))
{
R[i] += dR[i];
}
}
/* combine {F} = {F_t} + {F_m} */
for (int i = 0; i < DoF; i++)
{
F[i] = FTemp[lc, i] + FMech[lc, i];
}
double[,] tempTArray = Common.GetArray(eqFTemp, lc);
double[,] tempMArray = Common.GetArray(eqFMech, lc);
Frame3dd.ElementEndForces(Q, nE, xyz, L, Le, N1, N2,
Ax, Asy, Asz, Jx, Iy, Iz, E, G, p,
tempTArray, tempMArray, D, shear, geom,
axialStrainWarning);
error = Frame3dd.EquilibriumError(dF, F, K, D, DoF, q, r);
//if (geom && verbose)
// fprintf(stdout, "\n Non-Linear Elastic Analysis ...\n");
if (geom)
{
//Not implemented
}
while (geom && error > tol && iter < 500 && ok >= 0)
{
//Not implemented
}
//Not implemented
/* strain limit failure ... */
//if (axial_strain_warning > 0 && ExitCode == 0) ExitCode = 182;
/* strain limit _and_ buckling failure ... */
//if (axial_strain_warning > 0 && ExitCode == 181) ExitCode = 183;
//if (geom) compute_reaction_forces(R, F, K, D, DoF, r);
if (writeMatrix != 0)/* write static stiffness matrix */
{
//save_ut_dmatrix("Ks", K, DoF, "w");//Not implemented
}
/* display RMS equilibrium error */
//if (verbose && ok >= 0)
// evaluate(error, rms_resid, tol, geom);
var staticResults = Frame3ddIO.GetStaticResults(nN, nE, nL, lc, DoF, N1, N2, F, D, R, r, Q, error, ok, axialSign);
////Not implemented
//if (filetype == 1)
//{ // .CSV format output
// write_static_csv(OUT_file, title,
// nN, nE, nL, lc, DoF, N1, N2, F, D, R, r, Q, error, ok);
//}
//if (filetype == 2)
//{ // .m matlab format output
// write_static_mfile(OUT_file, title, nN, nE, nL, lc, DoF,
// N1, N2, F, D, R, r, Q, error, ok);
//}
float[,] tempU2DArray = Common.GetArray(U, lc);
float[,] tempW2DArray = Common.GetArray(W, lc);
float[,] tempP2DArray = Common.GetArray(P, lc);
List <PeakFrameElementInternalForce> internalForce = Frame3ddIO.GetInternalForces(lc, nL, title, dx, xyz,
Q, nN, nE, L, N1, N2,
Ax, Asy, Asz, Jx, Iy, Iz, E, G, p,
d, gX[lc], gY[lc], gZ[lc],
nU[lc], tempU2DArray, nW[lc], tempW2DArray, nP[lc], tempP2DArray,
D, shear, error);
loadCaseOutputs.Add(new LoadCaseOutput(error, staticResults.nodeDisplacements, staticResults.frameElementEndForces,
staticResults.reactionOutputs, internalForce));
//static_mesh ()
//...
}
outputText += Frame3ddIO.OutputDataToString(loadCaseOutputs);
Output output = new Output(outputText, loadCaseOutputs);
return(output);
}
