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.


fv32
Figure 1. Overview of FE model with boundary conditions

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
fv32a fv32b fv32c
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
fv32d fv32e
f*=250.666 Hz

Normalized=1.001

 f*=392.555 Hz

Normalized=1.033

 f*=393.157 Hz

Normalized=1.004

Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this problem includes:

fv32.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis