VM63

VM63
Static Hertz Contact Problem

Overview

Reference:

S. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd Edition, McGraw-Hill Book Co., Inc., New York, NY, 1970, pg. 409-413, article 140.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D 8-Node Structural Solid Elements (PLANE82 )

2D 8-Node Structural Solid Elements (PLANE183)

3D Node-to-Node Contact Elements (CONTA178)

Input Listing:

vm63.dat

Test Case

A sphere of radius r is pressed against a rigid flat plane. Determine the contact radius, a, for a given load F.

Figure 87: Static Hertz Problem

Material Properties

Geometric Properties

E = 1000 N/mm²

υ = 0.3

r = 8 mm

F = (30 x 2 π) N

Analysis Assumptions and Modeling Notes

An axisymmetric model is used. A node is placed near the expected radius of contact. Midside nodes are removed along the surface where contact is likely to occur. The model has both PLANE82 and PLANE183 for verification purposes, but could be solved using either element type alone. The model is solved using 3D node-to-node contact elements (CONTA178).

Results

a, mm	Target	Mechanical APDL	Ratio
CONTA178	1.010	1.011	1.001