OS-V: 0415 Deep Simply-Supported Beam

Test No. FV5 OptiStruct tests the repeated eigenvalues, shear deformation, and rotary inertia. The possibility of missing extensional modes is also investigated.

Benchmark Model

The 2-node beam elements are used to model the simply-supported beam which consists of five elements. The displacements in x, y, and z direction, as well as the rotation in x direction are fixed at the end A. In addition, the displacements in y and z direction are constrained at end B.

The material properties are:

E: 200 x 10⁹ N/m²
$υ$: 0.3
$ρ$: 8000 kg/m³

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution.

f*: Closed form solution.

Modes 1 and 2 Flexural		Mode 3 Torsional		Mode 4 Extensional
`f*` CBEAM 42.649 Hz	42.649 Hz 1.0124	`f*` CBEAM 77.542 Hz	77.542 Hz 0.9157	`f*` CBEAM	125.00 Hz 1.0000

Modes 5 and 6 Flexural		Mode 7 Torsional		Modes 8 and 9 Flexural
`f*` CBEAM 42.649 Hz	148.31 Hz 1.0409	`f*` CBEAM	233.10 Hz 0.8840	`f*` CBEAM	284.55 Hz 1.0725

Model Files

The model files used in this problem include:

<install_directory>/hwsolvers/demos/optistruct/verification/fv5.fem

Reference

NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.