Quad4 element and simple example

ElasticMaterial2D.cs

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+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using ISAAR.MSolve.PreProcessor.Interfaces;
+using ISAAR.MSolve.Matrices.Interfaces;
+using ISAAR.MSolve.Matrices;
+
+namespace ISAAR.MSolve.PreProcessor.Materials
+{
+    public class ElasticMaterial2D : IFiniteElementMaterial2D
+    {
+        private readonly double[] strains = new double[3];
+        private readonly double[] stresses = new double[3];
+        private double[,] constitutiveMatrix = null;
+        public double YoungModulus { get; set; }
+        public double PoissonRatio { get; set; }
+        public double[] Coordinates { get; set; }
+
+        private double[,] GetConstitutiveMatrix()
+        {
+
+            //Panos Plane Stress
+            //
+            //                    [ 1       v       0   ]
+            // [D] = E/(1-v^2)    [ v       1       0   ]
+            //                    [ 0       0   (1-v)/2 ]
+            //
+
+            double fE1 = YoungModulus / (1 - PoissonRatio*PoissonRatio);
+            double fE2 = (1 - PoissonRatio)/2;
+            double[,] afE = new double[3, 3];
+            afE[0, 0] = fE1;
+            afE[0, 1] = fE1 * PoissonRatio;
+            //afE[0, 2] = 0;
+            afE[1, 0] = fE1 * PoissonRatio;
+            afE[1, 1] = fE1;
+            //afE[1, 2] = 0;
+            //afE[2, 0] = 0;
+            //afE[2, 1] = 0;
+            afE[2, 2] = fE1*fE2;
+
+
+            Vector<double> s = (new Matrix2D<double>(afE)) * (new Vector<double>(strains));
+            s.Data.CopyTo(stresses, 0);
+
+            return afE;
+        }
+
+        #region IFiniteElementMaterial Members
+
+        public int ID
+        {
+            get { return 1; }
+        }
+
+        public bool Modified
+        {
+            get { return false; }
+        }
+
+        public void ResetModified()
+        {
+        }
+
+        #endregion
+
+        #region IFiniteElementMaterial3D Members
+
+        public double[] Stresses { get { return stresses; } }
+
+        public IMatrix2D<double> ConstitutiveMatrix
+        {
+            get
+            {
+                if (constitutiveMatrix == null) UpdateMaterial(new double[3]);
+                return new Matrix2D<double>(constitutiveMatrix);
+            }
+        }
+
+        public void UpdateMaterial(double[] strains)
+        {
+            //throw new NotImplementedException();
+
+            strains.CopyTo(this.strains, 0);
+            constitutiveMatrix = GetConstitutiveMatrix();
+        }
+
+        public void ClearState()
+        {
+            //throw new NotImplementedException();
+        }
+
+        public void SaveState()
+        {
+            //throw new NotImplementedException();
+        }
+
+        public void ClearStresses()
+        {
+            //throw new NotImplementedException();
+        }
+
+        #endregion
+
+        #region ICloneable Members
+
+        public object Clone()
+        {
+            return new ElasticMaterial2D() { YoungModulus = this.YoungModulus, PoissonRatio = this.PoissonRatio };
+        }
+
+        #endregion
+
+    }
+}

GaussQuadrature.cs

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+namespace ISAAR.MSolve.PreProcessor.Elements.SupportiveClasses
+{
+    #region
+
+    using System;
+
+    #endregion
+
+    public class GaussLegendrePoint1D
+    {
+        #region Properties
+
+        public double Coordinate { get; set; }
+
+        public double WeightFactor { get; set; }
+
+        #endregion
+    }
+
+    //Panos Input Start
+    public class GaussLegendrePoint2D
+    {
+        #region Constructors and Destructors
+        public GaussLegendrePoint2D(
+            double xi, double eta, double[,] deformationMatrix, double weightFactor)
+        {
+            this.Xi = xi;
+            this.Eta = eta;
+            this.DeformationMatrix = deformationMatrix;
+            this.WeightFactor = weightFactor;
+        }
+        #endregion
+        #region Properties
+        // Panos - I rearranged the appearce order - If you dont like it, change it...
+        public double Xi { get; private set; }
+        public double Eta { get; private set; }
+        public double WeightFactor { get; private set; }
+        public double[,] DeformationMatrix { get; private set; }
+        //
+        #endregion
+    }
+    //Panos Input End
+    public class GaussLegendrePoint3D
+    {
+        #region Constructors and Destructors
+
+        public GaussLegendrePoint3D(
+            double xi, double eta, double zeta, double[,] deformationMatrix, double weightFactor)
+        {
+            this.Xi = xi;
+            this.Eta = eta;
+            this.Zeta = zeta;
+            this.DeformationMatrix = deformationMatrix;
+            this.WeightFactor = weightFactor;
+        }
+
+        #endregion
+
+        #region Properties
+        // Panos - I rearranged the appearce order - If you dont like it, change it...
+        public double Xi { get; private set; }
+        public double Eta { get; private set; }
+        public double Zeta { get; private set; }
+        public double WeightFactor { get; private set; }
+        public double[,] DeformationMatrix { get; private set; }
+        // 
+        #endregion
+    }
+
+    public class GaussQuadrature
+    {
+        /* For point coordinates, we encounter the following constants:
+         * 0.5773502691896 = 1 / Square Root 3
+         * 0.7745966692415 = (Square Root 15)/ 5
+         * 0.8611363115941 = Square Root( (3 + 2*sqrt(6/5))/7)
+         * 0.3399810435849 = Square Root( (3 - 2*sqrt(6/5))/7)
+         * 
+         * For the weights, we encounter the followings constants:
+         * 0.5555555555556 = 5/9
+         * 0.8888888888889 = 8/9
+         * 0.3478548451375 = (18 - sqrt30)/36
+         * 0.6521451548625 = (18 + sqrt30)/36
+        */
+        #region Constants and Fields
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint1 = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.0, WeightFactor = 2.0 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint2A = new GaussLegendrePoint1D
+            {
+               Coordinate = -0.5773502691896, WeightFactor = 1.0 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint2B = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.5773502691896, WeightFactor = 1.0 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint3A = new GaussLegendrePoint1D
+            {
+               Coordinate = -0.7745966692415, WeightFactor = 0.5555555555556 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint3B = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.0, WeightFactor = 0.8888888888889 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint3C = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.7745966692415, WeightFactor = 0.5555555555556 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint4A = new GaussLegendrePoint1D
+            {
+               Coordinate = -0.86113631159416, WeightFactor = 0.3478548451375 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint4B = new GaussLegendrePoint1D
+            {
+               Coordinate = -0.3399810435849, WeightFactor = 0.6521451548625 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint4C = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.3399810435849, WeightFactor = 0.6521451548625 
+            };
+
+        private static readonly GaussLegendrePoint1D GaussLegendrePoint4D = new GaussLegendrePoint1D
+            {
+               Coordinate = 0.86113631159416, WeightFactor = 0.3478548451375 
+            };
+
+        #endregion
+
+        #region Public Methods
+
+        public static GaussLegendrePoint1D[] GetGaussLegendrePoints(int integrationDegree)
+        {
+            if (integrationDegree < 1)
+            {
+                throw new InvalidOperationException("Integration Degree must be greater or equal to 1. ");
+            }
+
+            switch (integrationDegree)
+            {
+                case 1:
+                    return new[] { GaussLegendrePoint1 };
+                case 2:
+                    return new[] { GaussLegendrePoint2A, GaussLegendrePoint2B };
+                case 3:
+                    return new[] { GaussLegendrePoint3A, GaussLegendrePoint3B, GaussLegendrePoint3C };
+                case 4:
+                    return new[]
+                        {
+                           GaussLegendrePoint4A, GaussLegendrePoint4B, GaussLegendrePoint4C, GaussLegendrePoint4D 
+                        };
+                default:
+                    throw new NotImplementedException("Integration Degree higher than 4 is not implemented yet. ");
+            }
+        }
+
+        #endregion
+    }
+}

IFiniteElementMaterial2D.cs

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+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using ISAAR.MSolve.Matrices.Interfaces;
+
+namespace ISAAR.MSolve.PreProcessor.Interfaces
+{
+    public interface IFiniteElementMaterial2D : IFiniteElementMaterial
+    {
+        double[] Stresses { get; }
+        IMatrix2D<double> ConstitutiveMatrix { get; }
+        void UpdateMaterial(double[] strains);
+        void ClearState();
+        void SaveState();
+        void ClearStresses();
+    }
+}