Skip to content

Download MATLAB script

Restrained beam under thermal expansion¤

This live script is written as a guided walkthrough for a thermal-loading example. It shows how restrained thermal expansion is represented and how the resulting forces and deformations are interpreted. Read the text cells first, then run each code cell in order so that the variables, model state, and recorded results are available for the later sections.

1
2
opsMAT = OpenSeesMatlab();
ops = opsMAT.opensees;

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
ops.wipe()
ops.model('basic', '-ndm', 2, '-ndf', 3);
% nodes
ops.node(1, 0.0, 0.0);
ops.node(2, 2.0, 0.0);
ops.node(3, 1.0, 0.0);

% boundary conditions
ops.fix(1, 1, 1, 1);
ops.fix(2, 1, 1, 1);
ops.fix(3, 0, 1, 1);

% material
matTag = 1;
ops.uniaxialMaterial('Steel01Thermal', matTag, 2e11, 2e11, 0.01);

% fiber section
secTag = 1;
ops.section('FiberThermal', secTag);
ops.fiber(-0.025, 0.0, 0.005, matTag);
ops.fiber( 0.025, 0.0, 0.005, matTag);

% coordinate transformation
transfTag = 1;
ops.geomTransf('Linear', transfTag);

% beam integration
np = 3;
biTag = 1;
ops.beamIntegration('Lobatto', biTag, secTag, np);

% elements
ops.element('dispBeamColumnThermal', 1, 1, 3, transfTag, biTag);
ops.element('dispBeamColumnThermal', 2, 3, 2, transfTag, biTag);

% time series
tsTag = 1;
ops.timeSeries('Linear', tsTag);

% load pattern
patternTag = 1;
maxtemp = 1000.0;
ops.pattern('Plain', patternTag, tsTag);
ops.eleLoad('-ele', 1, '-type', '-beamThermal', 1000.0, -0.05, 1000.0, 0.05);
% ops.eleLoad('-ele', 2, '-type', '-beamThermal', 0.0, -0.05, 0.0, 0.05);

% analysis
incrtemp = 0.01;
ops.system('BandGeneral');
ops.constraints('Plain');
ops.numberer('Plain');
ops.test('NormDispIncr', 1.0e-6, 100);
ops.algorithm('Newton');
ops.integrator('LoadControl', incrtemp);
ops.analysis('Static');

% run analysis
nstep = 100;
temp = zeros(nstep + 1, 1);
disp = zeros(nstep + 1, 1);

temp(1) = 0.0;
disp(1) = 0.0;

for i = 1:nstep
    ok = ops.analyze(1);
    if ok < 0
        temp = temp(1:i);
        disp = disp(1:i);
        break;
    end

    temp(i + 1) = ops.getLoadFactor(patternTag) * maxtemp;
    disp(i + 1) = ops.nodeDisp(3, 1);
end

1
2
3
4
5
6
% plot
figure;
plot(temp, disp, '-o');
xlabel('Temperature');
ylabel('Nodal displacement');
grid on;
figure_0.png