VM141

VM141
Diametral Compression of a Disk

Overview

Reference:S. Timoshenko, J. N. Goodier, Theory of Elasticity, 2nd Edition, McGraw-Hill Book Co., Inc., New York, NY, 1951, pg. 107, article 37.
Analysis Type(s):
Static Analysis (ANTYPE = 0)
Substructure Analysis (ANTYPE = 7)
Element Type(s):
2D 8-Node Structural Solid Plane Stress Elements (PLANE82)
2D 8-Node Structural Solid Elements (PLANE183)
Superelement (or Substructure) (MATRIX50)
4-Node Finite Strain Shell Elements (SHELL181)
8-Node Finite Strain Shell Elements (SHELL281)
Input Listing:vm141.dat

Test Case

Two equal and opposite forces act along the vertical diameter of a disk as shown. Determine the compressive stress at the center of the disk and on the major horizontal diameter at 0.1 in. from the center.

Figure 195: Disk Problem Sketch

Disk Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
d = 2 in
t = 0.2 in
F = 2000 lb

Analysis Assumptions and Modeling Notes

The problem is solved first using plane stress elements (PLANE82 and PLANE183), then using shell elements (SHELL281) with the substructure analysis and expansion pass. In the second case, the model is created as a superelement only to illustrate the procedure for substructure capability. Third and fourth solution is done using finite-strain shell elements SHELL181 and SHELL281.

A one-fourth symmetry model is used. Three element types and the corresponding element type modifications are used only for various printout control purposes. One half of the load is applied because of symmetry. POST1 is used to extract results from the solution phase. Since the midside nodal stresses are not available in POST1, path operations are performed to get the compressive stress at 0.1 in. from the center of the disk.

Results Comparison

 TargetMechanical APDLRatio
PLANE82 and PLANE183Stressy , psi (at x = 0.0, y = 0.0)-9549.-9649.1.010
Stressy , psi (at x = 0.1, y = 0.0)-9298.-9139.0.983
SHELL281- SubstructureStressy , psi (at x = 0.0, y = 0.0)-9549.-9646.1.010
Stressy , psi (at x = 0.1, y = 0.0)-9298.-9130.0.982
SHELL181Stressy , psi (at x = 0.0, y = 0.0)-9549-9593.1.005
Stressy , psi (at x = 0.1, y = 0.0)-9298.-9293.0.999
SHELL281Stressy , psi (at x = 0.0, y = 0.0)-9549.-9646.1.010
Stressy , psi (at x = 0.1, y = 0.0)-9298.-9130.0.982