# 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.

## 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 are used for each model; extension, in-plane bending, transverse bending, and twist. 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 |

## Model Files

The model files used in this problem include:

- /SCBhex8.fem
- /SCBhex20.fem
- /SCBquad4.fem
- /SCBquad8.fem
- /SCBtri3.fem
- /SCBtri6.fem

## 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.