The aim of this test case is to validate the following functions:

- remote force

The simulation results of SimScale were compared to the analytical results derived from [Roark]. The meshes used in case (A) and (C) were created with the fully-automatic-tetrahedralization tool on the SimScale platform. The meshes used in case (B) and (D) were created locally.

Import validation project into workspace

The I-beam is L

$L$= 1 m long. The geometry of the cross section is shown below.

B | 0.06 m |

H | 0.08 m |

b | 0.04 m |

h | 0.06 m |

**Tool Type** : Code_Aster

**Analysis Type** : Static

**Mesh and Element types** :

Case | Mesh type | Number of nodes | Element type |
---|---|---|---|

(A) | linear tetrahedral | 5761 | 3D isoparametric |

(B) | linear hexrahedral | 5757 | 3D isoparametric |

(C) | quadratic tetrahedral | 37486 | 3D isoparametric |

(D) | quadratic hexrahedral | 20749 | 3D isoparametric |

Material:

- isotropic: E = 205 GPa, ν

$\nu $= 0.28

Constraints:

- Face A is fixed

Loads:

- A remote force F

$F$= 1000 N in a distance of 1 m is applied to face B

A remote force can be substituted in a parallel force F0

${F}_{0}$with the same magnitude and a momentum M0

${M}_{0}$. This momentum can be calculated with the direction of the force and the distance d

$d$. In this example the connection line between the force and the point of attack is perpendicular to the force and therefore the momentum M0

${M}_{0}$can be calculated as stated in equation (1)

$\text{(1)}$.

M0=F0d(1)

$$\begin{array}{}\text{(1)}& {M}_{0}={F}_{0}d\end{array}$$

w(x)=−M0x22EI−F0EI(12Lx2−16x3)(2)

$$\begin{array}{}\text{(2)}& w(x)=-\frac{{M}_{0}{x}^{2}}{2EI}-\frac{{F}_{0}}{EI}(\frac{1}{2}L{x}^{2}-\frac{1}{6}{x}^{3})\end{array}$$