OS-V: 0710 Curved Cantilever Beam

MacNeal-Harder Test This is a curved cantilever beam solved with solid and shell elements. A model is made with each element's type to investigate the effect of distorted elements with a high aspect ratio.

Figure 1. FE Model of the Beam with Boundary Conditions and Loadcases

Benchmark Model

Six types of elements are used for this problem. They are tria-shell, quad-shell, and hexa-solid elements, each with 1st and 2nd order. Two loading cases are used for each model; in-plane bending, transverse bending. For both load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam.

Theoretical solutions for the deflections at the tip, computed by beam theory are:
Load Type Component Value
In-plane bending UY 0.08734
Transverse bending UZ 0.5022

Linear Static Analysis Results

All results are normalized with the target value.
  In-plane Bending Transverse Bending
QUAD4 0.952 0.955
QUAD8 1.015 0.984
TRI3 0.025 0.950
TRI6 1.005 0.961
HEX8 0.880 0.820
HEX20 1.009 0.946

Model Files

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

The model files used in this problem include:
  • CBhex8.fem
  • CBhex20.fem
  • CBquad4.fem
  • CBquad8.fem
  • CBtri3.fem
  • CBtri6.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.