OS-V: 0720 Straight Cantilever Beam
MacNeal-Harder Test This is a straight cantilever beam solved with solid and shell elements. Three models (rectangular, parallelogram, trapezoidal) are 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
Model Files
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. Four loading cases, extension, in-plane bending, transverse bending, and twist, are used for each model. For the extension and bending load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam. For the twist load cases, a unit moment is applied at the tip.
Load Type | Component | Value |
---|---|---|
Extension | UX | 0.00003 |
In-plane bending | UZ | 0.1081 |
Transverse bending | UY | 0.4321 |
Twist | ROTX | 0.03208 |
Linear Static Analysis Results
In-plane Extension | In-plane Bending | Transverse Bending | Twist | |
---|---|---|---|---|
QUAD4 | 1.000 | 0.992 | 0.981 | 0.941 |
QUAD8 | 1.006 | 1.000 | 1.016 | 0.953 |
TRI3 | 1.000 | 0.032 | 0.973 | 1.072 |
TRI6 | 1.006 | 0.994 | 1.001 | 0.950 |
HEX8 | 0.988 | 0.978 | 0.973 | 0.892 |
HEX20 | 1.008 | 0.992 | 0.992 | 0.905 |
In-plane Extension | In-plane Bending | Transverse Bending | Twist | |
---|---|---|---|---|
QUAD4 | 1.000 | 0.712 | 0.981 | 0.905 |
QUAD8 | 1.008 | 0.999 | 1.015 | 0.937 |
TRI3 | 1.000 | 0.012 | 0.955 | 0.931 |
TRI6 | 1.005 | 0.962 | 0.995 | 0.982 |
HEX8 | 1.012 | 0.624 | 0.529 | 0.820 |
HEX20 | 1.008 | 0.976 | 0.977 | 0.905 |
In-plane Extension | In-plane Bending | Transverse Bending | Twist | |
---|---|---|---|---|
QUAD4 | 1.000 | 0.173 | 0.964 | 0.869 |
QUAD8 | 1.005 | 0.981 | 1.015 | 0.950 |
TRI3 | 1.000 | 0.019 | 0.965 | 1.175 |
TRI6 | 1.006 | 0.972 | 0.999 | 0.947 |
HEX8 | 1.010 | 0.047 | 0.030 | 0.563 |
HEX20 | 1.008 | 0.902 | 0.950 | 0.905 |
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.