Esempio n. 1
0
        public void ContinuumElement3DNonLinearVonMisesMaterialDynamicConsistent()
        {
            IList <Node> nodes = new List <Node>();

            // Create Model
            var model = new Model();

            // Create Subdomain
            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));

            // Create von Mises Plastic Material
            var solidMaterial = new VonMisesMaterial3D(youngModulus, poissonRatio, yieldStress, plasticModulus);

            // Create Dynamic Material
            var dynamicMaterial = new DynamicMaterial(density, 0, 0, true);

            DefineContinuumElement3DNonLinear(model, solidMaterial, dynamicMaterial);

            BoundaryConditionsNLM(model);

            // Choose linear equation system solver
            var           solverBuilder = new SkylineSolver.Builder();
            SkylineSolver solver        = solverBuilder.BuildSolver(model);

            // Choose the provider of the problem -> here a structural problem
            var provider = new ProblemStructural(model, solver);

            // Choose child analyzer -> Child: NewtonRaphson - LoadControl
            var subdomainUpdaters    = new[] { new NonLinearSubdomainUpdater(model.SubdomainsDictionary[subdomainID]) };
            var childAnalyzerBuilder = new LoadControlAnalyzer.Builder(model, solver, provider, increments)
            {
                MaxIterationsPerIncrement     = 50,
                NumIterationsForMatrixRebuild = 1,
                ResidualTolerance             = 1E-06,
            };
            var childAnalyzer = childAnalyzerBuilder.Build();

            // Choose parent analyzer -> Parent: Static
            var parentAnalyzerBuilder = new NewmarkDynamicAnalyzer.Builder(model, solver, provider, childAnalyzer, 1.0, 100.0);

            parentAnalyzerBuilder.SetNewmarkParametersForConstantAcceleration();
            NewmarkDynamicAnalyzer parentAnalyzer = parentAnalyzerBuilder.Build();

            // Request output
            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { monitorDof });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log           = (DOFSLog)childAnalyzer.Logs[subdomainID][0];
            double  computedValue = log.DOFValues[monitorDof];
            double  expectedValue = 1.93737;

            Assert.Equal(expectedValue, computedValue, 2);
        }
Esempio n. 2
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        public void ContinuumElement3DElasticMaterialDynamicConsistent()
        {
            IList <Node> nodes = new List <Node>();

            // Create Model
            var model = new Model();

            // Create Subdomain
            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));

            // Create Elastic Material
            var solidMaterial = new ElasticMaterial3D()
            {
                YoungModulus = youngModulus,
                PoissonRatio = poissonRatio,
            };

            // Create Dynamic Material
            var dynamicMaterial = new DynamicMaterial(density, 0, 0, true);

            DefineContinuumElement3DLinear(model, solidMaterial, dynamicMaterial);

            BoundaryConditions(model);

            // Choose linear equation system solver
            var           solverBuilder = new SkylineSolver.Builder();
            SkylineSolver solver        = solverBuilder.BuildSolver(model);

            // Choose the provider of the problem -> here a structural problem
            var provider = new ProblemStructural(model, solver);

            // Choose child analyzer -> Linear
            var childAnalyzer = new LinearAnalyzer(model, solver, provider);

            // Choose parent analyzer -> Parent: Static
            var parentAnalyzerBuilder = new NewmarkDynamicAnalyzer.Builder(model, solver, provider, childAnalyzer, 1.0, 100.0);

            parentAnalyzerBuilder.SetNewmarkParametersForConstantAcceleration();
            NewmarkDynamicAnalyzer parentAnalyzer = parentAnalyzerBuilder.Build();

            // Request output
            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { monitorDof });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log           = (DOFSLog)childAnalyzer.Logs[subdomainID][0];
            double  computedValue = log.DOFValues[monitorDof];
            double  expectedValue = 0.531178; // consistent: 0.531178 // lumped: 0.894201

            Assert.Equal(expectedValue, computedValue, 3);
        }
Esempio n. 3
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        public void EmbeddedElementTechniqueExample()
        {
            var model = new Model();

            model.SubdomainsDictionary.Add(1, new Subdomain(1));

            // Choose model
            EmbeddedExamplesBuilder.ExampleWithEmbedded(model);

            // Choose linear equation system solver
            SkylineSolver solver = (new SkylineSolver.Builder()).BuildSolver(model);

            // Choose the provider of the problem -> here a structural problem
            var provider = new ProblemStructural(model, solver);

            // Choose child analyzer -> Child: NewtonRaphsonNonLinearAnalyzer
            int increments                    = 10;
            var loadControlBuilder            = new LoadControlAnalyzer.Builder(model, solver, provider, increments);
            LoadControlAnalyzer childAnalyzer = loadControlBuilder.Build();

            // Choose parent analyzer -> Parent: Static
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            // Request output
            childAnalyzer.LogFactories[1] = new LinearAnalyzerLogFactory(new int[] { 11 });
            //childAnalyzer.LogFactories[1] = new LinearAnalyzerLogFactory(new int[] {
            //    model.GlobalDofOrdering.GlobalFreeDofs[model.NodesDictionary[5], DOFType.X],
            //    model.GlobalDofOrdering.GlobalFreeDofs[model.NodesDictionary[5], DOFType.Y],
            //    model.GlobalDofOrdering.GlobalFreeDofs[model.NodesDictionary[5], DOFType.Z]});

            // Run
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log           = (DOFSLog)childAnalyzer.Logs[1][0];   //There is a list of logs for each subdomain and we want the first one (index = 0) from subdomain id = 1
            var     computedValue = log.DOFValues[11];

            Assert.Equal(11.584726466617692, computedValue, 3);
        }
Esempio n. 4
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        private static void SolveBuildingInNoSoilSmallDynamic()
        {
            var model = new Model();

            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
            BeamBuildingBuilder.MakeBeamBuilding(model, 20, 20, 20, 5, 4, model.NodesDictionary.Count + 1,
                                                 model.ElementsDictionary.Count + 1, subdomainID, 4, false, false);

            // Solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            // Structural problem provider
            var provider = new ProblemStructural(model, solver);

            // Linear static analysis
            var childAnalyzer         = new LinearAnalyzer(model, solver, provider);
            var parentAnalyzerBuilder = new NewmarkDynamicAnalyzer.Builder(model, solver, provider, childAnalyzer, 0.01, 0.1);

            parentAnalyzerBuilder.SetNewmarkParametersForConstantAcceleration(); // Not necessary. This is the default
            NewmarkDynamicAnalyzer parentAnalyzer = parentAnalyzerBuilder.Build();

            // Request output
            int monitorDof = 420;

            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { monitorDof });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Write output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[subdomainID][0]; //There is a list of logs for each subdomain and we want the first one

            Console.WriteLine($"dof = {monitorDof}, u = {log.DOFValues[monitorDof]}");

            //TODO: No loads have been defined so the result is bound to be 0.
        }
Esempio n. 5
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        private static void SolveBuildingInNoSoilSmall()
        {
            var model = new Model();

            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
            BeamBuildingBuilder.MakeBeamBuilding(model, 20, 20, 20, 5, 4, model.NodesDictionary.Count + 1,
                                                 model.ElementsDictionary.Count + 1, subdomainID, 4, false, false);
            model.Loads.Add(new Load()
            {
                Amount = -100, Node = model.Nodes[21], DOF = StructuralDof.TranslationX
            });

            // Solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            // Structural problem provider
            var provider = new ProblemStructural(model, solver);

            // Linear static analysis
            var childAnalyzer  = new LinearAnalyzer(model, solver, provider);
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            // Request output
            int monitorDof = 420;

            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { monitorDof });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Write output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[subdomainID][0]; //There is a list of logs for each subdomain and we want the first one

            Console.WriteLine($"dof = {monitorDof}, u = {log.DOFValues[monitorDof]}");
        }
        public void CantileverYBeam3DQuaternionNonlinearTest()
        {
            double youngModulus     = 21000.0;
            double poissonRatio     = 0.3;
            double nodalLoad        = 20000.0;
            double area             = 91.04;
            double inertiaY         = 2843.0;
            double inertiaZ         = 8091.0;
            double torsionalInertia = 76.57;
            double effectiveAreaY   = 91.04;
            double effectiveAreaZ   = 91.04;
            int    nNodes           = 3;
            int    nElems           = 2;
            int    monitorNode      = 3;

            // Create new 3D material
            var material = new ElasticMaterial3D
            {
                YoungModulus = youngModulus,
                PoissonRatio = poissonRatio,
            };

            // Node creation
            IList <Node> nodes = new List <Node>();
            Node         node1 = new Node(id: 1, x:   0.0, y:  0.0, z: 0.0);
            Node         node2 = new Node(id: 2, x: 100.0, y:  0.0, z: 0.0);
            Node         node3 = new Node(id: 3, x: 200.0, y:  0.0, z: 0.0);

            nodes.Add(node1);
            nodes.Add(node2);
            nodes.Add(node3);

            // Model creation
            Model model = new Model();

            // Add a single subdomain to the model
            model.SubdomainsDictionary.Add(1, new Subdomain(1));

            // Add nodes to the nodes dictonary of the model
            for (int i = 0; i < nodes.Count; ++i)
            {
                model.NodesDictionary.Add(i + 1, nodes[i]);
            }

            // Constrain bottom nodes of the model
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.TranslationX
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.TranslationY
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.TranslationZ
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.RotationX
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.RotationY
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint {
                DOF = StructuralDof.RotationZ
            });

            // Generate elements of the structure
            int iNode = 1;

            for (int iElem = 0; iElem < nElems; iElem++)
            {
                // element nodes
                IList <Node> elementNodes = new List <Node>();
                elementNodes.Add(model.NodesDictionary[iNode]);
                elementNodes.Add(model.NodesDictionary[iNode + 1]);

                // Create new Beam3D section and element
                var beamSection = new BeamSection3D(area, inertiaY, inertiaZ, torsionalInertia, effectiveAreaY, effectiveAreaZ);
                var beam        = new Beam3DCorotationalQuaternion(elementNodes, material, 7.85, beamSection);

                // Create elements
                var element = new Element()
                {
                    ID          = iElem + 1,
                    ElementType = beam
                };

                // Add nodes to the created element
                element.AddNode(model.NodesDictionary[iNode]);
                element.AddNode(model.NodesDictionary[iNode + 1]);

                var a = beam.StiffnessMatrix(element);
                //var writer = new FullMatrixWriter();
                //writer.WriteToFile(a, output);


                // Add beam element to the element and subdomains dictionary of the model
                model.ElementsDictionary.Add(element.ID, element);
                model.SubdomainsDictionary[1].Elements.Add(element);
                iNode++;
            }

            // Add nodal load values at the top nodes of the model
            model.Loads.Add(new Load()
            {
                Amount = nodalLoad, Node = model.NodesDictionary[monitorNode], DOF = StructuralDof.TranslationY
            });

            // Solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            // Problem type
            var provider = new ProblemStructural(model, solver);

            // Analyzers
            int increments           = 10;
            var childAnalyzerBuilder = new LoadControlAnalyzer.Builder(model, solver, provider, increments);

            childAnalyzerBuilder.ResidualTolerance = 1E-3;
            //childAnalyzerBuilder.SubdomainUpdaters = new[] { new NonLinearSubdomainUpdater(model.SubdomainsDictionary[subdomainID]) }; // This is the default
            LoadControlAnalyzer childAnalyzer = childAnalyzerBuilder.Build();
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            // Request output
            childAnalyzer.LogFactories[1] = new LinearAnalyzerLogFactory(new int[] { 7 });

            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[1][0]; //There is a list of logs for each subdomain and we want the first one

            Assert.Equal(148.936792350562, log.DOFValues[7], 2);
        }
        private static void TestBatheImplicitAnalysisExample()
        {
            var model       = new Model();
            int subdomainID = 0;

            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));

            var n = new Node(id: 0, x: double.NaN);
            var e = new Element()
            {
                ID = 0
            };

            e.NodesDictionary.Add(0, n);
            var m = new Mock <IFiniteElement>();

            m.Setup(x => x.StiffnessMatrix(e)).Returns(Matrix.CreateFromArray(new double[, ] {
                { 6, -2, }, { -2, 4 }
            }));
            m.Setup(x => x.MassMatrix(e)).Returns(Matrix.CreateFromArray(new double[, ] {
                { 2, 0, }, { 0, 1 }
            }));
            m.Setup(x => x.DampingMatrix(e)).Returns(Matrix.CreateFromArray(new double[, ] {
                { 0, 0, }, { 0, 0 }
            }));
            //m.Setup(x => x.StiffnessMatrix(e)).Returns(new Numerical.LinearAlgebra.SymmetricMatrix2D(new double[] { 6, -2, 4 }));
            //m.Setup(x => x.MassMatrix(e)).Returns(new Numerical.LinearAlgebra.SymmetricMatrix2D(new double[] { 2, 0, 1 }));
            //m.Setup(x => x.DampingMatrix(e)).Returns(new Numerical.LinearAlgebra.SymmetricMatrix2D(new double[] { 0, 0, 0 }));
            m.Setup(x => x.GetElementDofTypes(e)).Returns(new[] { new[] { StructuralDof.TranslationX, StructuralDof.TranslationY } });
            m.SetupGet(x => x.DofEnumerator).Returns(new GenericDofEnumerator());
            e.ElementType = m.Object;
            model.NodesDictionary.Add(0, n);
            model.ElementsDictionary.Add(0, e);
            model.SubdomainsDictionary[subdomainID].Elements.Add(e);
            model.Loads.Add(new Load()
            {
                Amount = 10, Node = n, DOF = StructuralDof.TranslationY
            });
            var lX = new Mock <IMassAccelerationHistoryLoad>();

            lX.SetupGet(x => x.DOF).Returns(StructuralDof.TranslationX);
            lX.SetupGet(x => x[It.IsAny <int>()]).Returns(0);
            var lY = new Mock <IMassAccelerationHistoryLoad>();

            lY.SetupGet(x => x.DOF).Returns(StructuralDof.TranslationY);
            lY.SetupGet(x => x[0]).Returns(10);
            lY.SetupGet(x => x[It.IsInRange(1, 100, Range.Inclusive)]).Returns(0);
            model.MassAccelerationHistoryLoads.Add(lX.Object);
            model.MassAccelerationHistoryLoads.Add(lY.Object);
            m.Setup(x => x.CalculateAccelerationForces(It.IsAny <Element>(), It.IsAny <IList <MassAccelerationLoad> >()))
            .Returns <Element, IList <MassAccelerationLoad> >((element, loads) =>
            {
                double[] accelerations = { loads[0].Amount, loads[1].Amount };
                var massMatrix         = Matrix.CreateFromArray(new double[, ] {
                    { 2, 0, }, { 0, 1 }
                });
                //var massMatrix = new Numerical.LinearAlgebra.SymmetricMatrix2D(new double[] { 2, 0, 1 });
                return(massMatrix.Multiply(accelerations));
            }
                                                              );

            // Solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            //TODO: These overwrite the corresponding data extracted by the Model. Either set up these or the Model.
            //solver.LinearSystems[subdomainID].SetMatrix(
            //    SkylineMatrix.CreateFromArrays(2, new double[] { 6, 4, -2 }, new int[] { 0, 1, 3 }, true)); // K = [6 -2; -2 4]
            //solver.LinearSystems[subdomainID].RhsVector = Vector.CreateFromArray(new double[] { 0, 10 });

            // Problem type
            var provider = new ProblemStructural(model, solver);

            // Analyzers
            var childAnalyzer         = new LinearAnalyzer(model, solver, provider);
            var parentAnalyzerBuilder = new NewmarkDynamicAnalyzer.Builder(model, solver, provider, childAnalyzer, 0.28, 3.36);

            parentAnalyzerBuilder.SetNewmarkParametersForConstantAcceleration(); // Not necessary. This is the default
            //parentAnalyzerBuilder.SetNewmarkParameters(0.25, 0.5); // Not necessary. This is the default
            NewmarkDynamicAnalyzer parentAnalyzer = parentAnalyzerBuilder.Build();

            // Request output
            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { 0, 1 });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            //Check output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[subdomainID][0]; //There is a list of logs for each subdomain and we want the first one

            Assert.Equal(2.2840249264795207, log.DOFValues[0], 8);
            Assert.Equal(2.4351921891904156, log.DOFValues[1], 8);
        }
        private static void CantileverBeam2DCorotationalNonlinearTest()
        {
            double youngModulus = 21000.0;
            double poissonRatio = 0.3;
            double nodalLoad    = 20000.0;
            double area         = 91.04;
            double inertia      = 8091.0;
            int    nNodes       = 3;
            int    nElems       = 2;
            int    monitorNode  = 3;

            // Create new 2D material
            var material = new ElasticMaterial
            {
                YoungModulus = youngModulus,
                PoissonRatio = poissonRatio,
            };

            // Node creation
            IList <Node> nodes = new List <Node>();
            Node         node1 = new Node(id: 1, x: 0.0, y: 0.0);
            Node         node2 = new Node(id: 2, x: 100.0, y: 0.0);
            Node         node3 = new Node(id: 3, x: 200.0, y: 0.0);

            nodes.Add(node1);
            nodes.Add(node2);
            nodes.Add(node3);

            // Model creation
            var model = new Model();

            // Add a single subdomain to the model
            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));

            // Add nodes to the nodes dictonary of the model
            for (int i = 0; i < nodes.Count; ++i)
            {
                model.NodesDictionary.Add(i + 1, nodes[i]);
            }

            // Constrain bottom nodes of the model
            model.NodesDictionary[1].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationX, Amount = 0.0
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationY, Amount = 0.0
            });
            model.NodesDictionary[1].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.RotationZ, Amount = 0.0
            });

            // Generate elements of the structure
            int iNode = 1;

            for (int iElem = 0; iElem < nElems; iElem++)
            {
                // element nodes
                IList <Node> elementNodes = new List <Node>();
                elementNodes.Add(model.NodesDictionary[iNode]);
                elementNodes.Add(model.NodesDictionary[iNode + 1]);

                // Create new Beam3D section and element
                var beamSection = new BeamSection2D(area, inertia);

                // Create elements
                var element = new Element()
                {
                    ID          = iElem + 1,
                    ElementType = new Beam2DCorotational(elementNodes, material, 7.85, beamSection)
                };

                // Add nodes to the created element
                element.AddNode(model.NodesDictionary[iNode]);
                element.AddNode(model.NodesDictionary[iNode + 1]);

                var a = element.ElementType.StiffnessMatrix(element);

                // Add beam element to the element and subdomains dictionary of the model
                model.ElementsDictionary.Add(element.ID, element);
                model.SubdomainsDictionary[subdomainID].Elements.Add(element);
                iNode++;
            }

            // Add nodal load values at the top nodes of the model
            model.Loads.Add(new Load()
            {
                Amount = nodalLoad, Node = model.NodesDictionary[monitorNode], DOF = StructuralDof.TranslationY
            });

            // Choose linear equation system solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            // Choose the provider of the problem -> here a structural problem
            var provider = new ProblemStructural(model, solver);

            // Choose child analyzer -> Child: NewtonRaphsonNonLinearAnalyzer
            int increments                    = 10;
            var childAnalyzerBuilder          = new LoadControlAnalyzer.Builder(model, solver, provider, increments);
            LoadControlAnalyzer childAnalyzer = childAnalyzerBuilder.Build();

            // Choose parent analyzer -> Parent: Static
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            // Request output
            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { 4 });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[subdomainID][0];

            Assert.Equal(146.5587362562, log.DOFValues[4], 3);
        }
Esempio n. 9
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        public static void CNT_4_4_DisplacementControl()
        {
            double youngModulus      = 16710.0;
            double poissonRatio      = 0.034;
            double nodalDisplacement = 23.73;
            double area             = 5.594673861218848e-003;
            double inertiaY         = 2.490804749753243e-006;
            double inertiaZ         = 2.490804749753243e-006;
            double torsionalInertia = inertiaY / 2.0;
            double effectiveAreaY   = area;
            double effectiveAreaZ   = area;

            string workingDirectory     = @"..\..\..\Resources\Beam3DInputFiles";
            string geometryFileName     = "CNT-4-4-L=25-Geometry.inp";
            string connectivityFileName = "CNT-4-4-L=25-ConnMatr.inp";
            int    increments           = 20;

            int nNodes        = File.ReadLines(workingDirectory + '\\' + geometryFileName).Count();
            int nElems        = File.ReadLines(workingDirectory + '\\' + connectivityFileName).Count();
            int monitorNode_1 = nNodes - 1;
            int monitorNode_2 = nNodes;

            // Create new 3D material
            var material_1 = new ElasticMaterial3D
            {
                YoungModulus = youngModulus,
                PoissonRatio = poissonRatio,
            };

            var material_2 = new ElasticMaterial3D
            {
                YoungModulus = 100.0 * youngModulus,
                PoissonRatio = poissonRatio,
            };

            // Model creation
            Model model = new Model();

            // Subdomains
            model.SubdomainsDictionary.Add(1, new Subdomain(1));

            // Node creation
            IList <Node> nodes = new List <Node>();

            using (TextReader reader = File.OpenText(workingDirectory + '\\' + geometryFileName))
            {
                for (int i = 0; i < nNodes; i++)
                {
                    string   text   = reader.ReadLine();
                    string[] bits   = text.Split(',');
                    int      nodeID = int.Parse(bits[0]);
                    double   nodeX  = double.Parse(bits[1]);
                    double   nodeY  = double.Parse(bits[2]);
                    double   nodeZ  = double.Parse(bits[3]);
                    nodes.Add(new Node(id: nodeID, x: nodeX, y:  nodeY, z: nodeZ));
                    model.NodesDictionary.Add(nodeID, nodes[i]);
                }
            }

            // Constraints
            IList <Node> constraintsNodes = new List <Node>();

            constraintsNodes.Add(nodes[1 - 1]);
            constraintsNodes.Add(nodes[2 - 1]);
            constraintsNodes.Add(nodes[617 - 1]);
            constraintsNodes.Add(nodes[618 - 1]);
            constraintsNodes.Add(nodes[1029 - 1]);
            constraintsNodes.Add(nodes[1030 - 1]);
            constraintsNodes.Add(nodes[1441 - 1]);
            constraintsNodes.Add(nodes[1442 - 1]);
            constraintsNodes.Add(nodes[1649 - 1]);

            for (int i = 0; i < 9; i++)
            {
                int iNode = constraintsNodes[i].ID;
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.TranslationX
                });
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.TranslationY
                });
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.TranslationZ
                });
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.RotationX
                });
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.RotationY
                });
                model.NodesDictionary[iNode].Constraints.Add(new Constraint {
                    DOF = StructuralDof.RotationZ
                });
            }

            // Applied displacement
            model.NodesDictionary[monitorNode_2].Constraints.Add(new Constraint {
                DOF = StructuralDof.TranslationY, Amount = nodalDisplacement
            });

            // Create new Beam3D section and element
            var beamSection = new BeamSection3D(area, inertiaY, inertiaZ, torsionalInertia, effectiveAreaY, effectiveAreaZ);

            // Generate elements
            using (TextReader reader = File.OpenText(workingDirectory + '\\' + connectivityFileName))
            {
                for (int i = 0; i < (nElems - 16); i++)
                {
                    string   text      = reader.ReadLine();
                    string[] bits      = text.Split(',');
                    int      elementID = int.Parse(bits[0]);
                    int      node1     = int.Parse(bits[1]);
                    int      node2     = int.Parse(bits[2]);
                    // element nodes
                    IList <Node> elementNodes = new List <Node>();
                    elementNodes.Add(model.NodesDictionary[node1]);
                    elementNodes.Add(model.NodesDictionary[node2]);
                    // create element
                    var beam_1  = new Beam3DCorotationalQuaternion(elementNodes, material_1, 7.85, beamSection);
                    var element = new Element {
                        ID = elementID, ElementType = beam_1
                    };
                    // Add nodes to the created element
                    element.AddNode(model.NodesDictionary[node1]);
                    element.AddNode(model.NodesDictionary[node2]);
                    // beam stiffness matrix
                    var a = beam_1.StiffnessMatrix(element);
                    // Add beam element to the element and subdomains dictionary of the model
                    model.ElementsDictionary.Add(element.ID, element);
                    model.SubdomainsDictionary[1].Elements.Add(element);
                }
                for (int i = (nElems - 16); i < nElems; i++)
                {
                    string   text      = reader.ReadLine();
                    string[] bits      = text.Split(',');
                    int      elementID = int.Parse(bits[0]);
                    int      node1     = int.Parse(bits[1]);
                    int      node2     = int.Parse(bits[2]);
                    // element nodes
                    IList <Node> elementNodes = new List <Node>();
                    elementNodes.Add(model.NodesDictionary[node1]);
                    elementNodes.Add(model.NodesDictionary[node2]);
                    // create element
                    var beam_2  = new Beam3DCorotationalQuaternion(elementNodes, material_2, 7.85, beamSection);
                    var element = new Element {
                        ID = elementID, ElementType = beam_2
                    };
                    // Add nodes to the created element
                    element.AddNode(model.NodesDictionary[node1]);
                    element.AddNode(model.NodesDictionary[node2]);
                    // beam stiffness matrix
                    var a = beam_2.StiffnessMatrix(element);
                    // Add beam element to the element and subdomains dictionary of the model
                    model.ElementsDictionary.Add(element.ID, element);
                    model.SubdomainsDictionary[1].Elements.Add(element);
                }
            }

            // Choose linear equation system solver
            var     solverBuilder = new SkylineSolver.Builder();
            ISolver solver        = solverBuilder.BuildSolver(model);

            // Choose the provider of the problem -> here a structural problem
            var provider = new ProblemStructural(model, solver);

            // Choose child analyzer -> Child: NewtonRaphsonNonLinearAnalyzer
            var subdomainUpdaters    = new[] { new NonLinearSubdomainUpdater(model.SubdomainsDictionary[1]) };
            var childAnalyzerBuilder = new DisplacementControlAnalyzer.Builder(model, solver, provider, increments);
            var childAnalyzer        = childAnalyzerBuilder.Build();

            // Choose parent analyzer -> Parent: Static
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            // Request output
            //int monDOF = linearSystems[1].Solution.Length - 5;  //(6 * monitorNode_2 - 4);
            int monDOF = 9841;

            childAnalyzer.LogFactories[1] = new LinearAnalyzerLogFactory(new int[] { monDOF });

            // Run the analysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[1][0]; //There is a list of logs for each subdomain and we want the first one

            Console.WriteLine($"dof = {monDOF}, u = {log.DOFValues[monDOF]}");
            //Assert.Equal(-21.2328445476855, log.DOFValues[monDOF], 8);
        }
        private static void TestQuad4LinearCantileverExample()
        {
            // Model & subdomains
            var model       = new Model();
            int subdomainID = 0;

            model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));

            // Materials
            double youngModulus = 3.76;
            double poissonRatio = 0.3779;
            double thickness    = 1.0;
            double nodalLoad    = 500.0;
            var    material     = new ElasticMaterial2D(StressState2D.PlaneStress)
            {
                YoungModulus = youngModulus,
                PoissonRatio = poissonRatio
            };

            // Nodes
            var nodes = new Node[]
            {
                new Node(id: 1, x:  0.0, y:   0.0, z: 0.0),
                new Node(id: 2, x: 10.0, y:   0.0, z: 0.0),
                new Node(id: 3, x: 10.0, y:  10.0, z: 0.0),
                new Node(id: 4, x:  0.0, y:  10.0, z: 0.0)
            };

            for (int i = 0; i < nodes.Length; ++i)
            {
                model.NodesDictionary.Add(i, nodes[i]);
            }


            // Elements
            var factory = new ContinuumElement2DFactory(thickness, material, null);

            var elementWrapper = new Element()
            {
                ID          = 0,
                ElementType = factory.CreateElement(CellType.Quad4, nodes)
            };

            elementWrapper.AddNodes(nodes);
            model.ElementsDictionary.Add(elementWrapper.ID, elementWrapper);
            model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);

            //var a = quad.StiffnessMatrix(element);

            // Prescribed displacements
            model.NodesDictionary[0].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationX, Amount = 0.0
            });
            model.NodesDictionary[0].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationY, Amount = 0.0
            });
            model.NodesDictionary[3].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationX, Amount = 0.0
            });
            model.NodesDictionary[3].Constraints.Add(new Constraint()
            {
                DOF = StructuralDof.TranslationY, Amount = 0.0
            });

            // Nodal loads
            model.Loads.Add(new Load()
            {
                Amount = nodalLoad, Node = model.NodesDictionary[1], DOF = StructuralDof.TranslationX
            });
            model.Loads.Add(new Load()
            {
                Amount = nodalLoad, Node = model.NodesDictionary[2], DOF = StructuralDof.TranslationX
            });

            // Solver
            var pcgBuilder = new PcgAlgorithm.Builder();

            pcgBuilder.ResidualTolerance     = 1E-6;
            pcgBuilder.MaxIterationsProvider = new PercentageMaxIterationsProvider(0.5);
            var solverBuilder = new PcgSolver.Builder();

            solverBuilder.PcgAlgorithm = pcgBuilder.Build();
            PcgSolver solver = solverBuilder.BuildSolver(model);

            // Problem type
            var provider = new ProblemStructural(model, solver);

            // Analyzers
            var childAnalyzer  = new LinearAnalyzer(model, solver, provider);
            var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

            //NewmarkDynamicAnalyzer parentAnalyzer = new NewmarkDynamicAnalyzer(provider, childAnalyzer, linearSystems, 0.25, 0.5, 0.28, 3.36);

            // Request output
            childAnalyzer.LogFactories[subdomainID] = new LinearAnalyzerLogFactory(new int[] { 0 });

            // Run the anlaysis
            parentAnalyzer.Initialize();
            parentAnalyzer.Solve();

            // Check output
            DOFSLog log = (DOFSLog)childAnalyzer.Logs[subdomainID][0]; //There is a list of logs for each subdomain and we want the first one

            Assert.Equal(253.132375961535, log.DOFValues[0], 8);
        }