private static void SolverLinearStatics()
{
SolverFunctions Fun = new SolverFunctions();
Stopwatch sw = new Stopwatch(); sw.Start();
// Others
int inc = 1;
string separator = " ========================================================== ";
// Initialize time 0 and time 1
foreach (Node N in DB.NodeLib.Values)
{
N.Initialize_StepZero();
N.Initialize_NewDisp(inc);
}
foreach (Element E in DB.ElemLib.Values)
{
E.Initialize_StepZero(DB.FELib);
E.Initialize_Increment(inc);
}
// Console paragraph
Console.WriteLine("\n" + separator);
Console.WriteLine(" LINEAR STATIC ANALYSIS ");
Console.WriteLine(separator);
// *****************************************************************************
// ========================= MAIN FINITE ELEMENT CODE ==========================
// *****************************************************************************
// ============================ Essential boundary conditions ======================================
// DoF list with kinematic BC
List <int> Fix_DOF = new List <int>();
foreach (BoundaryCondition BC in DB.BCLib.Values.Where(x => x.Type == "SPC"))
{
foreach (int NID in BC.NodalValues.Keys)
{
if (BC.NodalValues[NID].Get(0, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[0]);
}
if (BC.NodalValues[NID].Get(1, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[1]);
}
if (BC.NodalValues[NID].Get(2, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[2]);
}
}
}
// Sort and remove duplicates of kinematic BC
Fix_DOF = Fix_DOF.Distinct().ToList();
Fix_DOF.Sort();
// Define Row index reduction - rows and columns related to Dirichlet BC are removed from K matrix and F vector
int[] nDOF_reduction = new int[DB.nDOF];
for (int i = 0; i < Fix_DOF.Count; i++)
{
nDOF_reduction[Fix_DOF[i]] = -1;
}
int reduc = 0;
for (int i = 0; i < DB.nDOF; i++)
{
if (nDOF_reduction[i] == -1)
{
reduc++;
}
else
{
nDOF_reduction[i] = reduc;
}
}
// ============================ F (Right hand side) Vector =========================================
double[] F = new double[DB.nDOF - Fix_DOF.Count];
foreach (BoundaryCondition BC in DB.BCLib.Values.Where(x => x.Type == "PointLoad"))
{
foreach (int NID in BC.NodalValues.Keys)
{
for (int dir = 0; dir < 3; dir++)
{
if (nDOF_reduction[DB.NodeLib[NID].DOF[dir]] != -1)
{
if (inc == 1)
{
F[DB.NodeLib[NID].DOF[dir] - nDOF_reduction[DB.NodeLib[NID].DOF[dir]]] +=
BC.NodalValues[NID].Get(dir, 0);
}
}
}
}
}
// ============================== GLOBAL STIFFNESS MATRIX ===================================
alglib.sparsematrix K = Fun.ParallelAssembly_K(DB, nDOF_reduction, inc, "Initial");
// ============================== SOLVING LINEAR SYSTEM ===================================
double[] U = new double[DB.nDOF - Fix_DOF.Count];
if (DB.AnalysisLib.GetLinSolver() == "CG")
{
U = Fun.LinearSolver_CG(K, F, DB.AnalysisLib);
}
if (DB.AnalysisLib.GetLinSolver() == "Cholesky")
{
U = Fun.LinearSolver_Cholesky(K, F);
}
if (DB.AnalysisLib.GetLinSolver() == "LU")
{
U = Fun.LinearSolver_LU(K, F);
}
// ================== U (Left hand side) vector reconstruction =====================================
double[] U_Full = Fun.Include_BC_DOF(U, nDOF_reduction);
// Assign displacements to nodes (replace dU vector and update dU Buffer)
foreach (Node n in DB.NodeLib.Values)
{
n.dU_buffer[0] = U_Full[n.DOF[0]];
n.dU_buffer[1] = U_Full[n.DOF[1]];
n.dU_buffer[2] = U_Full[n.DOF[2]];
//Console.Write("Node " + n.ID + " disp: "); Fun.Print_Vector(n.dU_buffer, 3);
}
// Internal Forces vector
double[] R = new double[DB.nDOF];
Console.Write(" Stress recovery: ");
Parallel.ForEach(DB.ElemLib.Values, Elem =>
{
Elem.Recovery_Stress(DB);
Elem.Compute_NodalForces(DB);
// Assembly Nodal Forces vector
for (int i = 0; i < Elem.NList.Count; i++)
{
for (int j = 0; j < 3; j++)
{
R[DB.NodeLib[Elem.NList[i]].DOF[j]] += Elem.NodalForces.GetFast(3 * i + j, 0);
}
}
});
R = Fun.Exclude_BC_DOF(R, nDOF_reduction);
Console.WriteLine(" Done");
// Update nodal displacement, element stress and strain
foreach (Node n in DB.NodeLib.Values)
{
n.Update_Displacement(inc);
}
foreach (Element E in DB.ElemLib.Values)
{
E.Update_StrainStress(inc);
}
// Print CPU time summary
sw.Stop();
Console.WriteLine("\n" + separator);
Console.WriteLine(" Total CPU time: " + sw.Elapsed.TotalSeconds.ToString("F2", CultureInfo.InvariantCulture) + " s");
Console.WriteLine(separator);
}
private static void SolverNonlinearStatics()
{
SolverFunctions Fun = new SolverFunctions();
Stopwatch sw = new Stopwatch(); sw.Start();
// Analysis settings
double tolerance = 0.001;
// Others
string separator = " ========================================================== ";
// Initialize time 0 and time 1
foreach (Node N in DB.NodeLib.Values)
{
N.Initialize_StepZero();
}
foreach (Element E in DB.ElemLib.Values)
{
E.Initialize_StepZero(DB.FELib);
}
// Console paragraph
Console.WriteLine("\n" + separator);
if (DB.AnalysisLib.GetAnalysisType().StartsWith("Linear"))
{
Console.WriteLine(" LINEAR STATIC ANALYSIS ");
}
if (DB.AnalysisLib.GetAnalysisType().StartsWith("Nonlinear"))
{
Console.WriteLine(" NONLINEAR STATIC ANALYSIS ");
}
Console.WriteLine(separator);
// *****************************************************************************
// ========================= MAIN FINITE ELEMENT CODE ==========================
// *****************************************************************************
// ============================ Essential boundary conditions ======================================
// DoF list with kinematic BC
List <int> Fix_DOF = new List <int>();
foreach (BoundaryCondition BC in DB.BCLib.Values.Where(x => x.Type == "SPC"))
{
foreach (int NID in BC.NodalValues.Keys)
{
if (BC.NodalValues[NID].Get(0, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[0]);
}
if (BC.NodalValues[NID].Get(1, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[1]);
}
if (BC.NodalValues[NID].Get(2, 0) == 1)
{
Fix_DOF.Add(DB.NodeLib[NID].DOF[2]);
}
}
}
// Sort and remove duplicates of kinematic BC
Fix_DOF = Fix_DOF.Distinct().ToList();
Fix_DOF.Sort();
// Define Row index reduction - rows and columns related to Dirichlet BC are removed from K matrix and F vector
int[] nDOF_reduction = new int[DB.nDOF];
for (int i = 0; i < Fix_DOF.Count; i++)
{
nDOF_reduction[Fix_DOF[i]] = -1;
}
int reduc = 0;
for (int i = 0; i < DB.nDOF; i++)
{
if (nDOF_reduction[i] == -1)
{
reduc++;
}
else
{
nDOF_reduction[i] = reduc;
}
}
// >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> INCREMENTAL ANALYSIS <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
for (int inc = 1; inc <= DB.AnalysisLib.GetIncNumb(); inc++)
{
Console.WriteLine("\n" + separator);
Console.WriteLine(" INCREMENT " + inc);
Console.WriteLine(separator);
// Initialize Nodal displacements for new increment
foreach (Node n in DB.NodeLib.Values)
{
n.Initialize_NewDisp(inc);
}
// Initialize Element Strain and Stress for new increment
foreach (Element Elem in DB.ElemLib.Values)
{
Elem.Initialize_Increment(inc);
}
// ============================ F (Right hand side) Vector =========================================
double[] F = new double[DB.nDOF - Fix_DOF.Count];
foreach (BoundaryCondition BC in DB.BCLib.Values.Where(x => x.Type == "PointLoad"))
{
foreach (int NID in BC.NodalValues.Keys)
{
for (int dir = 0; dir < 3; dir++)
{
if (nDOF_reduction[DB.NodeLib[NID].DOF[dir]] != -1)
{
if (inc == 1)
{
F[DB.NodeLib[NID].DOF[dir] - nDOF_reduction[DB.NodeLib[NID].DOF[dir]]] +=
BC.NodalValues[NID].Get(dir, 0) * inc / DB.AnalysisLib.GetIncNumb();
}
}
}
}
}
// ================================ NEWTON-RAPHSON ITERATION =====================================
int iter = 0;
double NormF = Fun.Vector_Norm(F);
double NormRes = 1;
// Iteration zero:
Console.WriteLine(" ITERATION 0: ");
alglib.sparsematrix K = Fun.ParallelAssembly_K(DB, nDOF_reduction, inc, "Initial");
// Newton loop
while (NormRes > tolerance)
//while (iter<1)
{
if (iter > 0)
{
Console.WriteLine(" ITERATION " + iter + ": ");
K = Fun.ParallelAssembly_K(DB, nDOF_reduction, inc, "Tangent");
Fun.Print_Matrix(K, 6, 8);
}
// ============================== SOLVING LINEAR SYSTEM ===================================
double[] U = new double[DB.nDOF - Fix_DOF.Count];
alglib.sparsematrix K1 = (alglib.sparsematrix)K.make_copy();
if (DB.AnalysisLib.GetLinSolver() == "CG")
{
U = Fun.LinearSolver_CG(K1, F, DB.AnalysisLib);
}
if (DB.AnalysisLib.GetLinSolver() == "Cholesky")
{
U = Fun.LinearSolver_Cholesky(K1, F);
}
if (DB.AnalysisLib.GetLinSolver() == "LU")
{
U = Fun.LinearSolver_LU(K1, F);
}
// ================== U (Left hand side) vector reconstruction =====================================
double[] U_Full = Fun.Include_BC_DOF(U, nDOF_reduction);
// Assign displacements to nodes (replace dU vector and update dU Buffer)
foreach (Node n in DB.NodeLib.Values)
{
n.dU[0] = U_Full[n.DOF[0]]; n.dU_buffer[0] += U_Full[n.DOF[0]];
n.dU[1] = U_Full[n.DOF[1]]; n.dU_buffer[1] += U_Full[n.DOF[1]];
n.dU[2] = U_Full[n.DOF[2]]; n.dU_buffer[2] += U_Full[n.DOF[2]];
//Console.Write("Node " + n.ID + " disp: "); Fun.Print_Vector(n.dU_buffer, 3);
}
// Internal Forces vector
double[] R = new double[DB.nDOF];
Console.Write(" Stress recovery: ");
Parallel.ForEach(DB.ElemLib.Values, Elem =>
{
Elem.Recovery_Stress(DB);
Elem.Compute_NodalForces(DB);
// Assembly Nodal Forces vector
for (int i = 0; i < Elem.NList.Count; i++)
{
for (int j = 0; j < 3; j++)
{
R[DB.NodeLib[Elem.NList[i]].DOF[j]] += Elem.NodalForces.GetFast(3 * i + j, 0);
}
}
});
R = Fun.Exclude_BC_DOF(R, nDOF_reduction);
Console.WriteLine(" Done");
Fun.Print_MatrixST(DB.ElemLib[1].dS[0].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[1].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[2].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[3].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[4].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[5].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[6].Transpose(), 1, 6);
Fun.Print_MatrixST(DB.ElemLib[1].dS[7].Transpose(), 1, 6);
Console.WriteLine("\n Nodal forces:");
Fun.Print_Vector(R, R.Length);
Console.WriteLine("\n");
// Calculate Residual Forces
double[] Residual = new double[DB.nDOF - Fix_DOF.Count];
for (int i = 0; i < F.Length; i++)
{
Residual[i] = F[i] - R[i];
}
// Calculate Residual Forces norm and extreme value
NormRes = Fun.Vector_Norm(Residual) / NormF;
double ExtremeResidual = Math.Max(Residual.Max(), Math.Abs(Residual.Min()));
Console.WriteLine(" Residual norm: " + NormRes.ToString("F4"));
Console.WriteLine(" Max residual force: " + ExtremeResidual.ToString("#0.0e+0") + "\n");
//Console.WriteLine("\nOut of balance forces:\n" + string.Join("\n", F.Where(x => x != 0)) + "\n");
// Next iteration
F = Residual;
iter++;
}
Console.WriteLine(" INCREMENT CONVERGED in " + iter + " iterations\n");
// Update nodal displacement, element stress and strain
foreach (Node N in DB.NodeLib.Values)
{
N.Update_Displacement(inc);
}
foreach (Element E in DB.ElemLib.Values)
{
E.Update_StrainStress(inc);
}
}
sw.Stop();
Console.WriteLine("\n" + separator);
Console.WriteLine(" Total CPU time: " + sw.Elapsed.TotalSeconds.ToString("F2", CultureInfo.InvariantCulture) + " s");
Console.WriteLine(separator);
}