Nonlinear Truss Pushover Analysis¤

This live script is written as a guided walkthrough for a structural-analysis example. It walks from model definition to analysis setup and then to response checks or plots. 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.

First, instantiate the OpenSeesMatlab interface class. This class provides native OpenSees commands, as well as additional visualization, pre/post-processing, and utility methods.

clc; clear;

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

Create model¤

This section creates the finite-element idealization used by the rest of the example. Check the dimensions, tags, and connectivity here before moving on.

ops.wipe();
ops.model("basic", "-ndm", 2, '-ndf', 2);

% variables
A = 4.0;
E = 29000.0;
alpha = 0.05;
sY = 36.0;
udisp = 2.5;
Nsteps = 1000;
Px = 160.0;
Py = 0.0;

% create nodes
ops.node(1, 0.0, 0.0);
ops.node(2, 72.0, 0.0);
ops.node(3, 168.0, 0.0);
ops.node(4, 48.0, 144.0);

% set boundary condition
ops.fix(1, 1, 1);
ops.fix(2, 1, 1);
ops.fix(3, 1, 1);

% define materials
ops.uniaxialMaterial('Hardening', 1, E, sY, 0.0, alpha / (1 - alpha) * E);

% define elements
ops.element('Truss', 1, 1, 4, A, 1);
ops.element('Truss', 2, 2, 4, A, 1);
ops.element('Truss', 3, 3, 4, A, 1);

% create TimeSeries
ops.timeSeries('Linear', 1);

% create a plain load pattern
ops.pattern('Plain', 1, 1);

% Create the nodal load
ops.load(4, Px, Py);

Start of analysis generation¤

This section configures and runs the analysis. The solver, constraints, convergence test, and step size should be read together because they control numerical robustness.

% create SOE
ops.system('ProfileSPD');
% create DOF number
ops.numberer('Plain');
% create constraint handler
ops.constraints('Plain');
% create integrator
ops.integrator('LoadControl', 1.0 / Nsteps);
% create algorithm
ops.algorithm('Newton');
% create test
ops.test('NormUnbalance', 1e-8, 10, 0);
% create analysis object
ops.analysis("Static");

Finally perform the analysis¤

This section configures and runs the analysis. The solver, constraints, convergence test, and step size should be read together because they control numerical robustness.

data = zeros(Nsteps + 1, 2);

for j = 1:Nsteps
    ops.analyze(1);
    data(j + 1, 1) = ops.nodeDisp(4, 1);
    data(j + 1, 2) = ops.getLoadFactor(1) * Px;
end

Model Visualization¤

This section creates the finite-element idealization used by the rest of the example. Check the dimensions, tags, and connectivity here before moving on.

opsMAT.vis.plotModel();

Output

[OpenSeesMatlab] Model summary
  Nodes: 4
  Truss elements: 3

Plot¤

This section turns the numerical results into plots. Use these figures to check the deformed shape, response pattern, and whether the result is physically reasonable.

figure;
plot(data(:, 1), data(:, 2), 'LineWidth', 1.5);
xlabel('Horizontal Displacement');
ylabel('Horizontal Load');
grid on;