VM22

VM22
Small Deflection of a Belleville Spring

Overview

Reference:	S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 143, problem 2.
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	2-Node Finite Strain Axisymmetric Shell (SHELL208)
Input Listing:	vm22.dat

Test Case

The conical ring shown below represents an element of a Belleville spring. Determine the deflection y produced by a load F per unit length on the inner edge of the ring.

Figure 28: Belleville Spring Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.0

a = 1 in

b = 1.5 in

t = 0.2 in

β = 7° = 0.12217 rad

F = 100 lb/in

Analysis Assumptions and Modeling Notes

The input force, -2 πF = -628.31853 lb., is applied per full circumference.

Results Comparison

	Target	Mechanical APDL	Ratio
y, in	-0.0028205	-0.0028571	1.013