how to perform Newmark method for fixed beam?
5 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
hi,
i am new to matlab. i am doing dynamic analysis of a beam using newmark method with different time steps at the midpoint point of node 6 of the beam. the outputs are not correct as i expected. Displacement is linear and not parabloic. could anyone help me out where did i do the mistake.
% Beam properties
L=10; %length in m length 10m
A=0.00767; %area in m^2
E=2.1e12; %youngs modulus in N/m^2
n=10; %no of elements
I=0.000636056; %moment of inertia in m^4
nn=n+1; %no of node points
Le=L\n; %length of each element
m = 588.42; % 60kg/m
P=10000; %Force in 10kN
p = 7800;
%ks = 4.5e+11; %stiffness
Gamma=1/2;
Beta=1/4; % average acceleration method
C=0; %damping
%global stiffness and mass matrix for fixed beam
Ka = E*I/Le^3 *[24 -12 0 0 0 0 0 0 0;
-12 24 -12 0 0 0 0 0 0;
0 -12 12 -12 0 0 0 0 0;
0 0 -12 12 -12 0 0 0 0;
0 0 0 -12 12 -12 0 0 0;
0 0 0 0 -12 12 -12 0 0;
0 0 0 0 0 -12 12 -12 0;
0 0 0 0 0 0 -12 24 -12;
0 0 0 0 0 0 0 -12 24];
Ma = p*A*Le/2 * [588.42 0 0 0 0 0 0 0 0;
0 588.42 0 0 0 0 0 0 0;
0 0 588.42 0 0 0 0 0 0;
0 0 0 588.42 0 0 0 0 0;
0 0 0 0 588.42 0 0 0 0;
0 0 0 0 0 588.42 0 0 0;
0 0 0 0 0 0 588.42 0 0;
0 0 0 0 0 0 0 588.42 0;
0 0 0 0 0 0 0 0 588.42];
%C = Dalpha * Ka + Dbeta * Ma;
% integration constant
c1 = 1/Beta/dt^2;
c2 = Gamma/Beta/dt;
c3 = 1/Beta/dt;
c4 = 1/2/Beta-1;
c5 = Gamma/Beta-1;
c6 = (Gamma/2/Beta-1)*dt;
c7 = (1-Gamma)*dt;
c8 = Gamma*dt;
% % Time step
t = linspace(1,10,11); % 10 timestep
dt = 1;
nt = length(t);
P =zeros(9);
P(:,1) = 10000;
%intial conditions
Fbar = zeros(9);
Dv = zeros(9);
veldv = zeros(9);
accldv = zeros(9);
D = zeros(9);
V = zeros(9);
Aa = zeros(9);
D(:,1) = 0;
V(:,1) = 0;
Aa(:,1) = (Ma^-1)*(P(:,1) - C*V(:,1) - Ka*D(:,1));
Kbar = c1*Ma+c2*C+Ka;
%A = Ma /(Beta*dt) + Gamma*C/beta;
%B = Ma /(2*Beta) +dt*C*((0.5*Gamma/Beta)-1)*C;
for i = 1:(nt-1)
Fbar(:,i+1) = P(:,1) + Ma * (c1 * D(:,i) + c3 * V(:,i) + c4 * Aa(:,i)) + C * (c2 * D(:,i) + c5 * V(:,i) + c6 * Aa(:,i));
Dv(:,i+1) = Kbar^-1 * Fbar(:,i+1);
D(:,i+1) = D(:,i) + Dv(:,i+1);
accldv(:,i+1) = ((c1 * D(:,i+1)) - D(:,i)) - (c3 *V(:,i)) - (c4 * Aa(:,i));
Aa(:,i+1) = Aa(:,i) + accldv(:,i+1);
veldv(:,i+1) = V(:,i) + (c7 * Aa(:,i)) + (c8 * Aa(:,i+1));
V(:,i+1) = V(:,i) + veldv(:,i+1);
end
0 commentaires
Réponses (0)
Voir également
Catégories
En savoir plus sur Data Import and Analysis dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!