3. Modeling A#

3.1. Characteristics of modeling#

The symmetry of revolution of the problem allows axisymmetric modeling: The sphere and the block are represented respectively by a half disk and the section of half of the block, meshed with axisymmetric 2D elements.

A node-mesh contact is defined between the two structures.

An imposed displacement load is applied to the upper part of the sphere, which is rigidified by a high Young’s modulus.

_images/1000000000000179000001D8DC22DCCDBD5A4E55.png

Boundary condition:

  • symmetry of revolution: the nodes located on the \(Y\) axis (group of nodes \(«\mathrm{LB}»\) and \(«\mathrm{LS}»\)) are blocked in the direction \(X\) (DX = 0),

  • embedding the base: the nodes in group \(«\mathrm{PLANX}»\) are blocked in the directions \(X\) and \(Y\) (DX = DY = 0),

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

Loads:

An imposed displacement is applied to the upper part of the sphere (group of nodes \(«\mathrm{NDPL}»\)) in the direction \(Y\): Loading from 0 to \(–100.\mathrm{mm}\)

3.2. Characteristics of the mesh#

Number of knots: 916

Number of meshes and type: 625 QUAD4 and 289 SEG2

3.3. Tested values#

Identification

Movement \((\mathrm{mm})\)

Reference

Aster

% tolerance

Reaction \((N)\)

20

—2.03804E+06

—2.06806E+06

5

Reaction \((N)\)

40

—4.07608E+06

—4.04698E+06

5

Reaction \((N)\)

60

—6.11412E+06

—5.82730E+06

5

Reaction \((N)\)

80

—8.15217E+06

—7.66632E+06

10

Reaction \((N)\)

100

—1.01902E+07

—9.11899E+06

15

3.4. notes#

The most important error is for the last result. Nevertheless, it is still acceptable.

We illustrated the deformation of the massif at the final time step:

_images/10000000000000A50000008B0476BC635C00FE07.png