9. G modeling#

9.1. Characteristics of modeling#

The symmetry of the problem makes it possible to represent only a quarter of the model in 3D: the sphere and the block are represented respectively by the contact surface of the sphere and a quarter of a cylinder, meshed with 3D solid elements CUB8.

A node-mesh contact is defined between the sphere and the block.

An imposed displacement load is applied to the entire surface of the sphere, which is rigidified by kinematic conditions.

_images/10000000000001720000018532F7F696FB8E16D1.png

Boundary condition:

  • Symmetry conditions:

the nodes located in plane \((O,y,z)\) (group of nodes \(«\mathrm{SBYZ}»\)) are blocked in the direction \(X\) (DX = 0),

the nodes located in plane \((O,x,y)\) (group of nodes \(«\mathrm{SBXY}»\)) are blocked in the direction \(Z\) (DZ = 0),

the nodes of the sphere (group of nodes \(«\mathit{SMAI}»\)) are blocked in the directions \(X\) and \(Z\) (DX = DZ = 0)

  • Base embedding:

the nodes in group \(«\mathit{BASE}»\) (plane \(Y=0.\)) are blocked in the directions \(X\), \(Y\), and \(Z\) (DX = DY = DZ = 0).

  • Rigid body movements are suppressed by imposing a following link y between node \(E\) belonging to the sphere and node \(S\) belonging to the massif.

Loads:

An imposed displacement is applied to the entire surface representing the sphere (group of nodes \(«\mathit{SMAI}»\)) in the direction \(Y\): Loading from 0 to \(–100.\mathrm{mm}\)

9.2. Characteristics of the mesh#

Number of knots: 2157

Number of meshes and type: 1496 HEXA8, 108 PENTA6, 108, 988 QUAD4, 12 TRIA3 and 8 PYRAM5.

9.3. Tested values#

Identification

Movations

Reference

Aster

% tolerance

Reaction \((N)\)

\(d=–20\mathrm{mm}\)

—3.201351E+05

-3.6492888E+05

20