Static Load on a Truss Structure

Model Description

Model location: <altair>\utility\mbd\nlfe\validationmanual\model4.mdl

This model consists of a truss structure composed of seven straight beams of a 0.01m*0.01m cross section as shown in Figure 1 below.

Figure 1. A Truss Structure Attached to the Ground via Pin (Revolute) Joint and Inplane Joint

A load of 2000000N and 1000000N is applied in the downward direction at point A and B respectively.

Multibody Model

Each beam member is modeled using a single NLFE beam element in MotionSolve. Gravity is turned off for this model. The truss is attached to the ground via revolute joint at point C and via Inplane joint at point E. The joints between the beams are all revolute joints.

Figure 2. The Truss Structure Modeled in MotionView
The load of 2000000N and 1000000N is applied in the negative Y direction at points A and B. The following material properties are used for the NFLE beam:
1 m2
7860 kg/m3
2.1 x 1011 N/m2
0.3 (Poisson ratio)
For the above values, the theoretical axial stress (force/area) in each of the beam members is:
Theoretical Axial Stress N/m2
1500 x 103
5250 x 103
2500 x 103
2500 x 103
3750 x 103
8750 x 103
3000 x 103

This model is simulated with an end time of 5 seconds, for a quasi-static analysis.

Numerical Results

Figure 3 below depicts the final state of the truss structure under the load. The contours depict the axial stresses in each beam member (ignoring the local values at the joint locations).

Figure 3. Axial Stresses in the Beam Members of the Truss
The axial stresses are written to the H3D file and their contours can be visualized in HyperView as shown in Figure 3. The numerical values of these axial stresses are summarized below.
Numerical Axial Stress N/m2
1505 x 103
5255 x 103
2501 x 103
2501 x 103
3749 x 103
8752 x 103
3001 x 103


The NLFE model with 7 BEAM12 elements show close agreement to the theoretical results for this case.

Beam Theoretical Axial Stress N/m2 Numerical Axial Stress N/m2 % error
AB 1500 x 103 1505 x 103 0.33
BC 5250 x 103 5255 x 103 0.1
AD 2500 x 103 2501 x 103 0.04
DB 2500 x 103 2501 x 103 0.04
BE 3750 x 103 3749 x 103 0.03
EC 8750 x 103 8752 x 103 0.02
DE 3000 x 103 3001 x 103 0.03

The results presented use the default solver settings present in MotionView.