VM187

VM187
Bending of a Curved Beam

Overview

Reference:R. J. Roark, Formulas for Stress and Strain, 4th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1965, pg. 166, example.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):
3D Coupled-Field Solid Elements (SOLID5)
3D 10-Node Tetrahedral Structural Solid Elements (SOLID92)
Tetrahedral Coupled-Field Solid Elements (SOLID98)
3D 10-Node Tetrahedral Structural Solid Elements (SOLID187)
Input Listing:vm187.dat

Test Case

A curved beam spans a 90° arc as shown. A shear load F is applied to the top end while the bottom end is built-in. Determine the deflection d at the free end.

Figure 288: Bending of a Curved Beam Problem Sketch

Bending of a Curved Beam Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 10 x 106 psi
υ = 0.25
ri = 4.12 in
ro = 4.32 in
h = 0.1 in
F = 1 lb

Analysis Assumptions and Modeling Notes

The problem is solved in four different ways:

  • using Coupled-Field Solid Elements (SOLID5)

  • using Tetrahedral Solid Elements (SOLID92)

  • using Tetrahedral Coupled-Field Solid Elements (SOLID98)

  • using Tetrahedral Solid Elements (SOLID187)

For the tetrahedral elements, the nodes at the free end are coupled and the shear force applied to the prime node.

Postprocessing is used to directly obtain the difference between the target solution and the Ansys results in the form of a ratio.

Results Comparison

TargetMechanical APDLRatio
Deflection, in (SOLID5)0.088540.0881360.995
Deflection, in (SOLID92)0.088540.0883330.998
Deflection, in (SOLID98)0.088540.0883330.998
Deflection, in (SOLID187)0.088540.0883330.998