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 the Normal Modes Analysis is examined using OptiStruct.

Benchmark Model

The 4-node quad elements with 16x8 mesh configuration are used in test FV32. Displacements in the z-direction are fixed on all nodes and the x- and y-translation displacements are fixed for the nodes along the y-axis.

The material properties are:
Property
Value
E
200 x 109 N/m2
$\upsilon$
0.3
$\rho$
8000 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*

CQUAD4

44.623 Hz

0.9092

f*

CQUAD4

130.03 Hz

1.0265

f*

CQUAD4

162.70 Hz

0.9104

Mode 4 Mode 5 Mode 6
f*

CQUAD4

246.05 Hz

1.0766

f*

CQUAD4

379.90 Hz

1.0070

f*

CQUAD4

391.44 Hz

1.0479

Model Files

The model file used in this problem includes:

fv32.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis