OS-V: 1205 Twisted Cantilever Beam (Explicit Results)

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

Benchmark Model

As shown in Figure 1, the beam is constrained in x, y and z directions for translational motion. The end of the beam is applied with Force Load. 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
Young's modulus
29E+06 Psi
Poisson's ratio
1E-04 lbm/in3


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

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • CHEXA8.fem
  • CQUAD4.fem
  • CTETRA10.fem
  • CTRIA3.fem


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.