MacNeal-Harder TestA twisted cantilever beam solved
with solid and shell elements using Explicit Analysis. A twisted beam model is made with
each element type to investigate the effect of distorted elements with a high aspect
ratio.
Figure 1. FE Model of Twisted Beam with Boundary and Loading
Conditions
Model Files
Before you begin, copy the file(s) used in this problem
to your working directory.
As shown in Figure 1, the beam is constrained in x, y and z
directions for translational motion. The end of the beam has Force Load applied.
Four types of elements are used for this problem. In-plane bending is used for all
the elements.
Analytical result computed by beam theory for deflection is Uy = 1.754E-04.
Material Properties
Value
Young's modulus
29E+06 psi
Poisson's ratio
0.22
Density
1E-04 lbm/in3
Results
Explicit Analysis results are shown in comparison with the reference result.
Table 1. MacNeal Harder Test Results
Element Type
Analytical Result
OptiStruct Explicit Analysis
Results
Absolute Value
Normalized Value
CQUAD4
1.754E-03
1.895E-03
1.0804
CTRIA3
1.802E-03
1.0274
CHEXA8
1.793E-03
1.022
CTETRA10
1.790E-03
1.020
Figure 2. Deformed Shapes of the Twisted Beam
Reference
MacNeal, R.H., and Harder, R.L., A
Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in
Analysis and Design, 1 (1985) 3-20.
