OS-V: 0440 Cantilevered Tapered Membrane

Test No. FV32 A tapered membrane problem with irregular mesh. The geometry and mesh symmetry are maintained along the x-direction. The shear behavior of membrane elements in Normal Modes Analysis is examined using OptiStruct.

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

fv32.fem

Benchmark Model

In test FV32, 4-node quad elements (CQUAD4 Lower Order Element [LOE]) with 16x8 mesh configuration are used. The taper starts with the model spanning 5.0 m in the y-direction to 1.0 m. Displacements in the z-direction are fixed on all nodes and the x- and y-translation displacements are fixed for the nodes on the 5.0 m edge along the y-axis.

The material properties are:

Property: Value
E: 200.0 x 10⁹ N/m²
$υ$: 0.3
$ρ$: 8000.0 kg/m³

Modal Analysis Results

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

f*: Closed form solution

Mode 1		Mode 2		Mode 3

`f*`=44.61 Hz Normalized=1.001		`f*`=131.120 Hz Normalized=1.008		`f*`=162.813 Hz Normalized=1.001

Mode 4		Mode 5		Mode 6

`f*`=250.666 Hz Normalized=1.001		`f*`=392.555 Hz Normalized=1.033		`f*`=393.157 Hz Normalized=1.004

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis