Tracé fonction

[invitef0337726]

Bonsoir je voudrai savoir comment tracé ces fonctions du code ci-joint sur matlab ?

Merci beaucoup
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[invitef0337726]

voila le code:

function [L2_error_w] = beam_loadsteps(N,LS)

    % problem parameters
    param.L  = 1; 
    param.EA = 10^5; 
    param.EI = 20;
    param.p1 = 0; 
    param.p3 = 10; 
    

    param.num_load_steps = linspace(0,1,LS);
    

    F1crit=403.814571;
    F1=0.50*F1crit;


    % problem kinematic and static boundary conditions
    bc.u_idx   = [1 ]; 
    bc.u_val   = [0 ]; 
    bc.w_idx   = [2 3*N-1]; 
    bc.w_val   = [0 0]; 
    bc.phi_idx = [3]; 
    bc.phi_val = [0]; 
    bc.F1_idx  = [3*N-2]; 
    bc.F1_val  = [-F1];
    bc.F3_idx  = [ ];
    bc.F3_val  = [ ];
    bc.M_idx   = [ ];
    bc.M_val   = [ ];
    

    % define number of points for evaluating exact solution
    E = N*100;

     % obtain exact and approximate solution
    %[x_exact ,U_exact ] = beam_exact(E, param, bc);
    [x_exact ,U_exact ] = beam_exact_loadsteps(E, param, bc);
    [x_approx,U_approx] = beam_approx_loadsteps(N, param, bc);

    % prepare plotting
    close all hidden; figure('DefaultAxesFontSize',18); clf; hold on;
    set(gca,'Ydir','reverse');

    % get sub-element values (for plotting and error computation)
    u_exact = U_exact(1,:);
    w_exact = U_exact(2,:);
    u_approx_m = interp1       (x_approx,U_approx(1,:,end),                  x_exact);
    w_approx_m = interp1hermite(x_approx,U_approx(2,:,end),U_approx(3,:,end),x_exact);

    % plot exact and approximate solution graph
    plot(x_exact ,u_exact   , 'b--');
    plot(x_exact ,u_approx_m, 'b-' );
    plot(x_exact ,w_exact   , 'r--');
    plot(x_exact ,w_approx_m, 'r-' );

    plot(x_approx,U_approx(1,:,end),'bo');
    plot(x_approx,U_approx(2,:,end),'ro');

    axis([0 param.L -0.005 +0.015]);
    xlabel('coordinate x [m]');
    ylabel('displacement [m]');
    title('beam 2nd order theory');
    legend('u_{exact}^{2nd order}', 'u_{approx}^{2nd order}', 'w_{exact}^{2nd order}', 'w_{approx}^{2nd order}', 'Location','SouthWest');
    grid on;
    print('beam_2ndorder.png','-dpng');

    % plot lambda-deformation curve
    figure('DefaultAxesFontSize',18); clf; hold on;
    phi = squeeze(U_approx(3,end,:));
    plot(phi, param.num_load_steps, 'b-*');
    xlabel('deformation value (end point rotation) [rad]');
    ylabel('load factor [-]');
    set(gca,'Xdir','reverse');
    title('beam 2nd order theory: load-deformation curve');
    grid on;
    print('beam_2ndorder_loadcurve.png','-dpng');

    % compute L_2 error w
    L2_error_w = sqrt( trapz( (w_approx_m - w_exact).^2 ) / trapz(w_exact.^2) );
end