Basic Truss Example

This example is of a linear-elastic three bar truss, as shown in the figure, subject to static loads.

Model

The model consists of four nodes, three truss elements, a single load pattern with a load acting at node 4, and constraints fixing the movement at the other three nodes in the model. As each Truss element has the same Young's Modulus, a single elastic material is created.

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# Remove existing model
wipe

# Create ModelBuilder (with two-dimensions and 2 DOF/node)
model BasicBuilder -ndm 2 -ndf 2

# Create nodes
# ------------
# Create nodes & add to Domain - command: node nodeId xCrd yCrd
node 1   0.0  0.0
node 2 144.0  0.0
node 3 168.0  0.0
node 4  72.0 96.0
    
# Set the boundary conditions - command: fix nodeID xResrnt? yRestrnt?
fix 1 1 1 
fix 2 1 1
fix 3 1 1
    
# Define materials for truss elements
# -----------------------------------
# Create Elastic material prototype - command: uniaxialMaterial Elastic matID E
uniaxialMaterial Elastic 1 3000

# 
# Define elements
#

# Create truss elements - command: element truss trussID node1 node2 A matID
element Truss 1 1 4 10.0 1
element Truss 2 2 4 5.0 1
element Truss 3 3 4 1
    
    
# Define loads
# ------------
#

# create a Linear TimeSeries with a tag of 1
timeSeries Linear 1
    
# Create a Plain load pattern associated with the TimeSeries: command pattern Plain $patternTag $timeSeriesTag { load commands }

pattern Plain 1 1 {
	
   # Create the nodal load - command: load nodeID xForce yForce
   load 4 100 -50
}

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Analysis

We will now show the commands to perform a static analysis using a linear solution algorithm The model is linear, so we use a solution Algorithm of type Linear. Even though the solution is linear, we have to select a procedure for applying the load which is called an Integrator. For this problem, a LoadControl integrator advances the solution. The equations are formed using a banded system so the System is BandSPD, banded symmetric positive definite This is a good choice for most small size models. The equations have to be numbered so the widely used RCM (Reverse Cuthill-McKee) numberer is used. The constraints are most easily represented with a Plain constraint handler. Once all the components of an analysis are defined, the Analysis object itself is created. For this problem, a Static Analysis object is used.

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# Create the system of equation
system BandSPD
    
# Create the DOF numberer, the reverse Cuthill-McKee algorithm
numberer RCM
    
# Create the constraint handler, a Plain handler is used as homo constraints
constraints Plain

# Create the integration scheme, the LoadControl scheme using steps of 1.0
integrator LoadControl 1.0

# Create the solution algorithm, a Linear algorithm is created
algorithm Linear

# create the analysis object 
analysis Static

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Output Specification

For this analysis, we will record the displacement at node 4, and all the element forces expressed both in the global coordinate system and the local system.

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# create a Recorder object for the nodal displacements at node 4
recorder Node -file example.out -time -node 4 -dof 1 2 disp

# create a Recorder for element forces, one for global system and the other for local system
recorder Element -file eleGlobal.out -time -ele 1 2 3 forces
recorder Element -file eleLocal.out  -time -ele 1 2 3 basicForces