3. Modeling A#

3.1. Characteristics of modeling#

The modeling consists of:

  • « POUTA »: a « SEG2 » between nodes \(A\) and \(B\) with a « POU_D_E » pattern.

  • « POUTB »: a « SEG2 » between nodes \(A\) and \(C\) with a « POU_D_E » pattern.

  • « DISCA »: a « SEG2 » between nodes \(A\) and \(B\) with a « DIS_TR » pattern.

  • « DISCB »: a « SEG2 » between nodes \(A\) and \(C\) with a « DIS_TR » pattern.

Node \(A\) is embedded.

For elements in the \(AB\) direction, the effort at node \(B\) in the global coordinate system: \(Fb_x = F\)

For elements in the \(AC\) direction, the effort at node \(C\) in the global coordinate system:

\(\left\{ \begin{array}{l}Fc_x = F \cos(\beta)\cos(\alpha)\\Fc_y = F \cos(\beta)\sin(\alpha)\\Fc_z = F \sin(\beta)\end{array}\right.\)

The temperature load is a field at the nodes:

Tableau 3.1 :width: 50%#

Instants

Temperature [°C]

0

\(T_0 = T_{ref} = 20.0°C\)

1

\(T_1 = 50°C\)

2

\(T_2 = 75°C\)

3

\(T_3 = 100°C\)

3.2. Characteristics of the mesh#

The mesh consists of a single « SEG2 » mesh per element.

3.3. Tested sizes and results#

The theoretical solutions are written, in the command file, according to the parameters:

  • linked to the mesh: \(L, \alpha, \beta\)

  • linked to the geometry of the beams: \(H_y, H_z\)

  • linked to the characteristics of discretes: \(K_x\)

  • related to the material: \(E, \alpha_{th}\)

The sizes tested:

  • at nodes \(B\) and \(C\): the movements, field « DEPL ».

  • at node \(A\): nodal reactions, field « REAC_NODA ».

  • on beams and discretes: internal forces, field « EFGE_ELNO ».