VM60

VM60
Natural Frequency of a Cross-ply Laminated Shell

Overview

Reference:	J. N. Reddy, "Exact Solutions of Moderately Thick Laminated Shells", ASCE Journal Engineering Mechanics, Vol. 110 No. 5, 1972, pg. 806, tab. 6.
Analysis Type(s):	Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):	8-Node Finite Strain Shell Elements (SHELL281)
Input Listing:	vm60.dat

Test Case

Determine the first mode natural frequency f of a simply-supported equal-sided sector of a spherical shell of radius r. The shell sector consists of a 0°/90° cross-ply laminate (2 layers of equal thickness, t).

Figure 84: Laminated Spherical Shell Problem Sketch

Material Properties

Geometric Properties

ρ = 1 gm/mm³

E_x = 25 x 10⁶ Pa

E_y = 1 x 10⁶ Pa

G_xy = G_xz = 5 x 10⁵ Pa

G_yz = 2 x 10⁵ Pa

υ_yx = .25 (major Poisson's ratio)

r = 300 mm

a = 100 mm

t = 0.5 mm

Analysis Assumptions and Modeling Notes

Four elements are chosen along each edge of area 1. The reduced method of eigenvalue solution is chosen and the first five modes are extracted. The input value for υ_xy is calculated from:

The geometric input in spherical coordinates is calculated as:

The alternate method of Poisson's ratio input (PRXY) could also have been used.

The model is solved using layered finite-strain shell elements (SHELL281).

Results Comparison

	Target	Mechanical APDL	Ratio
SHELL281
f, Hz	0.73215	0.73534	1.004