Truss.m

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namespace models{
namespace beam{


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class Truss
  :public models.beam.StructureElement {
    public: /* ( Constant ) */

        static const PlotSplitFactor = 5;

        
    public: /* ( Constant ) */

        Truss(models.BaseFullModel model,material,pointsidx) {
            this = this@models.beam.StructureElement(model, material, pointsidx);
            this.initialize;
        }


        function globIdx = getGlobalIndices() {
            data = this.Model.data;
            p = this.PointsIdx;
            index_0_glob = 7*data.knot_index(p(1))-6 : 7*data.knot_index(p(1))-4;
            index_l_glob = 7*data.knot_index(p(2))-6 : 7*data.knot_index(p(2))-4;
            globIdx = [index_0_glob index_l_glob];
        }
        function M = getLocalMassMatrix() {

            M = zeros(6);
            M([1 4], [1 4]) = this.c(2) * [2 1; 1 2];

            M = this.TG * M * this.TG^t;
        }
        function K = getLocalStiffnessMatrix() {

            K = zeros(6);
            K([1 4], [1 4]) = this.c(1) * [1 -1; -1 1];

            K = this.TG * K * this.TG^t;
        }
        function f = getLocalForceMatrix() {
            q_lok = this.Material.rho * this.Material.A * this.T^t;
            f = zeros(6, 3);
            f([1 4],1) = 0.5 * this.Length;
            f = this.TG * f * q_lok;
        }
        function [K , R ] = getLocalTangentials(u) {

            L = this.Length;
            c = this.c;                 

            /*  lokale Verschiebungen des Elements */
            u_lok  = this.TG^t * u;
            /*  lokale Ableitungen */
            u_lok_prime = (u_lok(4:6) - u_lok(1:3)) / L;
            /*  Lokales Spannungsmaß */
            E_11 = u_lok_prime(1) + 0.5 * (u_lok_prime^t * u_lok_prime);
            S_x = L*c(1) * E_11;

            R = S_x * [-u_lok_prime - [1;0;0]; u_lok_prime + [1;0;0]];

            A1 = c(1) * (u_lok_prime + [1;0;0]) * (u_lok_prime + [1;0;0])^t;
            A2 = S_x/L * eye(3);
            B = A1 + A2;
            K = [B -B; -B B];

            K = this.TG * K * this.TG^t;
            R = this.TG * R;
        }
        function  plot(p,u_elem,plot_options) {
            s = 0 : this.Length/(4*this.PlotSplitFactor) : this.Length;

            u_p = plot_options.multiplier * (u_elem(2,:)"  * s/this.Length + u_elem(1,:) " * (1 - s/this.Length));
            /*  Parametrisierung des Viertelkreises in lokalen Koords */
            y = (this.Length/(2*this.PlotSplitFactor)) * sin( 2*pi*s / (this.Length/this.PlotSplitFactor) );
            x = s;
            z = 0*s;
            /*  Umrechnung in globale Koords und Verschiebung um globale Koords des
             * lokalen Ursprungs KR(i).pc */
            COR = this.T * [x; y; z];
            plot3( p(this.PointsIdx(1), 1) + COR(1,:) + u_p(1,:), ...
                p(this.PointsIdx(1), 2) + COR(2,:) + u_p(2,:), ...
                p(this.PointsIdx(1), 3) + COR(3,:) + u_p(3,:), " k " );
        }

    
    private: /* ( Constant ) */

        function  initialize() {
            m = this.Model;
            /*  Längenberechnung */
            dp = (m.Points(this.PointsIdx(2), :) - m.Points(this.PointsIdx(1), :));
            l = norm(dp);
            this.Length= l;

            /*  Lokales Koordinatensystem */
            e_x = dp^t / l;
            e_y = [-e_x(2) e_x(1) 0]^t;
            if norm(e_y) == 0
                e_y = [0 e_x(3) -e_x(2)]^t;
            end
            e_z = [e_x(2)*e_y(3) - e_x(3)*e_y(2);
                e_x(3)*e_y(1) - e_x(1)*e_y(3);
                e_x(1)*e_y(2) - e_x(2)*e_y(1)];
            e_y = e_y / norm(e_y);
            e_z = e_z / norm(e_z);
            this.T= [e_x e_y e_z];

            /*  Transformationsmatrix: natürliche Koords -> glob. Koords
             * Sortierung der Variablen:
             * u0, v0, w0, u1, v1, w1
             *  1   2   3   4   5   6 */
            this.TG= zeros(6);
            this.TG([1 2 3], [1 2 3]) = this.T;      /*  Verschiebung links */

            this.TG([4 5 6], [4 5 6]) = this.T;    /*  Verschiebung rechts */


            /*      Effektive Konstanten */
            m = this.Material;
            this.c(1) = m.E * m.A / l;          /*  c1 = E*A/L      (Federhärte) */

            this.c(2) = m.rho * m.A * l / 6;    /*  c2 = rho*A*L/6 */


/*              this.c_theta = material(9);
 *             this.kappa = material(10);
 *             this.alphaA = material(11); */
        }

    

};
}
}