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.

図 1. FE Model of Twisted Beam with Boundary and Loading Conditions

Benchmark Model

As shown in 図 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.
表 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

図 2. Deformed Shapes of the Twisted Beam

Model Files


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.