5. C modeling#

5.1. Characteristics of C modeling#

z

3D, \(\mathrm{H20}\) and \(\mathrm{P15}\) meshes

y, v

F

B

y

x

A, E

B, F

_images/1000000000000E6500000C960E3F99FDBFE68C10.png

x, u

Point position:

\(A,B\) in section \(z=0\)

\(E,F\) in the middle section \(z=L/2\)

Breakdown:

20 elements depending on the length

2 elements according to the radius, 8 elements according to the circumference.

Since the load is symmetric, only half of the cylinder is modelled.

Boundary conditions:

  1. recessed ends section (\(u=v=w=0\))

  2. symmetry conditions in plane \(\mathrm{xz}\): \(v=0\)

Circumference pressure (field \(\mathrm{Up}\)) The surface of the cylinder is divided into 8 rows of elements according to the circumference (1 row of elements represents a sector of \(\pi /8\) radians. Since the pressure is in \(\mathrm{cos}\theta\), it is assumed to be uniform on each row. For any point on the corner surface \(\theta\), (between \({\theta }_{1}\) and and between and \({\theta }_{2}\), \({\theta }_{1}=(n–1)\frac{\pi }{8}\),, \({\theta }_{2}=n\frac{\pi }{8}\), \(1\le n\le 8\)), the pressure value assigned to the row of elements containing this point is taken to be equal to: \(\frac{\mathrm{p0}}{2}(\mathrm{cos}{\theta }_{1}+\mathrm{cos}{\theta }_{2})\).

Vertical gravity next \(x\) (field \(\mathrm{Ug}\))

Node names:

\(A=\mathrm{N845}\)

\(B=\mathrm{N965}\)

\(E=\mathrm{N865}\)

\(F=\mathrm{N995}\)

5.2. Characteristics of the mesh#

Number of knots: 1285

Number of meshes and types: 160 HEXA20, 80 PENTA15

5.3. Tested values#

Location

Value type

Reference

Aster

% difference

Field \(\mathrm{Up}\)

Point E

\(u(m)\) \(v(m)\)

—7.82 x 10—6 10—21

Point \(F\)

\(u(m)\)

\(v(m)\)

—7.816 x 10—6 10—21

Point \(B\)

\({\sigma }_{\mathrm{xx}}(\mathrm{Pa})\)

\({\sigma }_{\mathrm{yy}}(\mathrm{Pa})\) \({\sigma }_{\mathrm{zz}}(\mathrm{Pa})\)

1.63 x 106 1.65 x 106 5.51 x 106

Field \(\mathrm{Up}+\mathrm{Ug}\)

Point \(E\)

\(u(m)\)

\(v(m)\)

—7.46 x 10—6 10—21

Point \(F\)

\(u(m)\)

\(v(m)\)

—7.44 x 10—6 10—21

Point \(B\)

\({\sigma }_{\mathrm{xx}}(\mathrm{Pa})\)

\({\sigma }_{\mathrm{yy}}(\mathrm{Pa})\) \({\sigma }_{\mathrm{zz}}(\mathrm{Pa})\)

1.56 x 106 1.57 x 106 5.25 x 106

5.4. notes#

  • There are no reference values for this modeling. The results are to be compared with those of the AXIS_FOURIER \((A,B,D)\) models.

  • At point \(B\) (located in the plane of symmetry), we have: \({\sigma }_{\mathrm{rr}}={\sigma }_{\mathrm{xx}}\), \({\sigma }_{\theta \theta }={\sigma }_{\mathrm{yy}}\)