exd_beam2_b¶

Purpose:

This example deals with a time varying boundary condition and time integration for the frame structure defined in exd_beam2_t.

Description:

Suppose that the support of the vertical beam is moving in the horizontal direction. The commands below prepare the model for time integration. Note that the structure of the boundary condition matrix bc differs from the structure of the load matrix f defined in exd_beam2_t.

Time dependent boundary condition at the support, DOF 1.

dt=0.002;    T=1;
% --- boundary condition, initial condition ------------------
G=[0 0; 0.1 0.02; 0.2 -0.01; 0.3 0.0; T 0]; [t,g]=gfunc(G,dt);
bc=zeros(4, 1 + length(g));
bc(1,:)=[1 g];  bc(2,1)=2;  bc(3,1)=3;  bc(4,1)=14;
a0=zeros(15,1);               da0=zeros(15,1);
% --- output parameters --------------------------------------
times=[0.1:0.1:1];           dofs=[1 4 11];
% --- time integration parameters ----------------------------
ip=[dt T 0.25 0.5];
% --- time integration ---------------------------------------
k=sparse(K);                  m=sparse(M);
[a,da,d2a,ahist,dahist,d2ahist]...
=step2(k,[],m,[],a0,da0,bc,ip,times,dofs);

The time history plots are generated by the following commands:

% --- plot time history for two DOF:s ------------------------
figure(1), plot(t,ahist(1,:),'-',t,ahist(2,:),'--',t,ahist(3,:),'-.')
grid, xlabel('time (sec)'), ylabel('displacement (m)')
title('Displacement(time) at the 1st, 4th and 11th'...
      ' degree-of-freedom')
text(0.2,0.022,'solid line = bottom, vertical beam,'...
               ' x-direction')
text(0.2,0.017,'dashed line = center, vertical beam,'...
               ' x-direction')
text(0.2,0.012,'dashed-dotted line = center,'...
               ' horizontal beam, y-direction')

The snapshots of the deformed geometry are visualized by the following commands:

% --- plot displacement for some time increments -------------
figure(2),clf, axis('equal'), hold on, axis off
sfac=20;
title('Snapshots (sec), magnification = 20'); for i=1:5;
  Ext=Ex+(i-1)*3;            eldraw2(Ext,Ey,[2 3 0]);
  Edb=extract_ed(Edof,a(:,i));
  eldisp2(Ext,Ey,Edb,[1 2 2],sfac);
  Time=num2str(times(i));   text(3*(i-1)+.5,1.5,Time);
end;
Eyt=Ey-4;
for i=6:10;
  Ext=Ex+(i-6)*3;            eldraw2(Ext,Eyt,[2 3 0]);
  Edb=extract_ed(Edof,a(:,i));
  eldisp2(Ext,Eyt,Edb,[1 2 2],sfac);
  Time=num2str(times(i));   text(3*(i-6)+.5,-2.5,Time);
end

Snapshots of the deformed geometry for every 0.1 sec.