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.

nlfe_static_load_fig1

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.

Multi-Body 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.

nlfe_static_load_fig2

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:

Beam	Theoretical Axial Stress N/m2
AB	1500 x 103
BC	5250 x 103
AD	2500 x 103
DB	2500 x 103
BE	3750 x 103
EC	8750 x 103
DE	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).

nlfe_static_load_fig3

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.

Beam	Numerical Axial Stress N/m2
AB	1505 x 103
BC	5255 x 103
AD	2501 x 103
DB	2501 x 103
BE	3749 x 103
EC	8752 x 103
DE	3001 x 103

Conclusion

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.

Static Load on a Truss Structure

Static Load on a Truss Structure

Static Load on a Truss Structure

Model Description

Multi-Body Model

Beam

Theoretical Axial Stress N/m2

Numerical Results

Beam

Numerical Axial Stress N/m2

Conclusion

Beam

Theoretical Axial Stress N/m2

Numerical Axial Stress N/m2

% error