Truss system 3D

To validate the implementation of the truss elements in 3D, the truss system depicted below is analysed.

The members of the truss frame consist of sections of aluminum pipe with a cross-sectional area of \(A=20.7\cdot 10^{-4}\) m². The displacements \(u_{x}\), \(u_{y}\) and \(u_{z}\) at point 4 to be determined.

Analytical solution

Analytically the displacements of node 4 can be computed using the principle of work-energy, yielding:

\(u_{x}\) (mm)	\(u_{y}\) (mm)	\(u_{z}\) (mm)
0.306	0.483	-0.966

Numerical solution

For the numerical solution 2-node linear truss elements are used (u2-truss-3D). The Young's modulus and the cross-sectional areas are prescribed using the *Truss properties keyword of the *Material definition:

*Material, name = truss, phases=1
*Truss properties
20.7e-4, 205e6

Input files

The complete input files can be downloaded here

Results

The results of the numerical simulation are requested using the *Print output option:

*Output, print
*Node, nset=load
U

and yield

\(u_{x}\) (mm)	\(u_{y}\) (mm)	\(u_{z}\) (mm)
0.306	0.483	-0.966

which is in perfect agreement with the analytical solution.