Cylindrical elements

Elements tested

CCL9
CCL9H
CCL18
CCL18H
CCL12
CCL12H

CCL24
CCL24R
CCL24H
CCL24RH

Features tested

Elements are tested for concentrated and distributed load cases. Different types of analyses (linear and nonlinear) are studied. Both elastic and hyperelastic material models are used.

Problem description

Mesh:

The mesh presented above is used for elements with a rectangular cross-section. For elements with a triangular cross-section, two elements are used for each element represented above. The axis of symmetry is the z-axis.

Material:

Linear elasticity: Linear elastic, Young's modulus = 30 × 10⁶, Poisson's ratio = 0.3. Hyperelasticity: Hyperelastic, polynomial strain energy potential, N=2, $C_{10}$ = 1 × 10⁵, $C_{01}$ = 0.5 × 10⁵, $C_{20}$ = 0.5 × 10⁵, $C_{11}$ = 0.8 × 10⁵, $C_{02}$ = 0.75 × 10⁵, $D_{1}$ = 1 × 10⁻⁷, $D_{2}$ = 1 × 10⁻⁷.

Boundary conditions:

CASE 1

Segment AD is fixed. Axisymmetric boundary conditions are enforced.

CASE 2

Segment AD is fixed. Axisymmetric boundary conditions are enforced.

CASE 3

CCL12 and CCL9: Segment AD is fixed. Axisymmetric boundary conditions are enforced.CCL24 and CCL18: Segment AB is fixed. Axisymmetric boundary conditions are enforced.

CASE 4

Segment AB is fixed.

Loading:

CASE 1: concentrated load caseCASE 2: distributed load caseCASE 3: distributed surface load caseCASE 4: concentrated load case(See previous figures)

Results and discussion

The results are compared to the results obtained using axisymmetric elements. CCL9 elements are compared to CAX3 (and CGAX3, when appropriate), CCL12 elements are compared to CAX4 (and CGAX4, when appropriate), CCL18 elements are compared to CAX6 (and CGAX6, when appropriate), and CCL24 are compared to CAX8 (and CGAX8, when appropriate). Cylindrical elements and axisymmetric elements yield the same results with differences less than 2%.

Input files

ecc9gfs1a.inp: CCL9 elements, load and boundary conditions of Case 1, perturbation step, elastic material.
ecc9gfs1b.inp: CCL9 elements, load and boundary conditions of Case 1, general step, elastic material.
ecc9gfs1c.inp: CCL9 elements, load and boundary conditions of Case 1, assumed nonlinear geometry, elastic material.
ecc9ghs1d.inp: CCL9H elements, load and boundary conditions of Case 1, assumed nonlinear geometry, hyperelastic material.
ecc9gfs2a.inp: CCL9 elements, load and boundary conditions of Case 2, perturbation step, elastic material.
ecc9gfs2b.inp: CCL9 elements, load and boundary conditions of Case 2, general step, elastic material.
ecc9gfs2c.inp: CCL9 elements, load and boundary conditions of Case 2, assumed nonlinear geometry, elastic material.
ecc9ghs2d.inp: CCL9H elements, load and boundary conditions of Case 2, assumed nonlinear geometry, hyperelastic material.
ecc9gfs3a.inp: CCL9 elements, load and boundary conditions of Case 3, perturbation step, elastic material.
ecc9gfs3b.inp: CCL9 elements, load and boundary conditions of Case 3, general step, elastic material.
ecc9gfs3c.inp: CCL9 elements, load and boundary conditions of Case 3, assumed nonlinear geometry, elastic material.
ecc9ghs3d.inp: CCL9H elements, load and boundary conditions of Case 3, assumed nonlinear geometry, hyperelastic material.
ecc9gfs4a.inp: CCL9 elements, load and boundary conditions of Case 4, perturbation step, elastic material.
ecc9gfs4b.inp: CCL9 elements, load and boundary conditions of Case 4, general step, elastic material.
ecc9gfs4c.inp: CCL9 elements, load and boundary conditions of Case 4, assumed nonlinear geometry, elastic material.
ecc9ghs4d.inp: CCL9H elements, load and boundary conditions of Case 4, assumed nonlinear geometry, hyperelastic material.
ecccgfs1a.inp: CCL12 elements, load and boundary conditions of Case 1, perturbation step with LOAD CASE, elastic material.
ecccgfs1b.inp: CCL12 elements, load and boundary conditions of Case 1, general step, elastic material.
ecccgfs1c.inp: CCL12 elements, load and boundary conditions of Case 1, assumed nonlinear geometry, elastic material.
ecccghs1d.inp: CCL12H elements, load and boundary conditions of Case 1, assumed nonlinear geometry, hyperelastic material.
ecccgfs2a.inp: CCL12 elements, load and boundary conditions of Case 2, perturbation step, elastic material.
ecccgfs2b.inp: CCL12 elements, load and boundary conditions of Case 2, general step, elastic material.
ecccgfs2c.inp: CCL12 elements, load and boundary conditions of Case 2, assumed nonlinear geometry, additional linear perturbation step with LOAD CASE, elastic material.
ecccghs2d.inp: CCL12H elements, load and boundary conditions of Case 2, assumed nonlinear geometry, hyperelastic material.
ecccgfs3a.inp: CCL12 elements, load and boundary conditions of Case 3, perturbation step, elastic material.
ecccgfs3b.inp: CCL12 elements, load and boundary conditions of Case 3, general step, elastic material.
ecccgfs3c.inp: CCL12 elements, load and boundary conditions of Case 3, assumed nonlinear geometry, elastic material.
ecccghs3d.inp: CCL12H elements, load and boundary conditions of Case 3, assumed nonlinear geometry, hyperelastic material.
ecccgfs4a.inp: CCL12 elements, load and boundary conditions of Case 4, perturbation step, elastic material.
ecccgfs4b.inp: CCL12 elements, load and boundary conditions of Case 4, general step, elastic material.
ecccgfs4c.inp: CCL12 elements, load and boundary conditions of Case 4, assumed nonlinear geometry, elastic material.
ecccghs4d.inp: CCL12H elements, load and boundary conditions of Case 4, assumed nonlinear geometry, hyperelastic material.
eccigfs1a.inp: CCL18 elements, load and boundary conditions of Case 1, perturbation step, elastic material.
eccigfs1b.inp: CCL18 elements, load and boundary conditions of Case 1, general step, elastic material.
eccigfs1c.inp: CCL18 elements, load and boundary conditions of Case 1, assumed nonlinear geometry, elastic material.
eccighs1d.inp: CCL18H elements, load and boundary conditions of Case 1, assumed nonlinear geometry, hyperelastic material.
eccigfs2a.inp: CCL18 elements, load and boundary conditions of Case 2, perturbation step, elastic material.
eccigfs2b.inp: CCL18 elements, load and boundary conditions of Case 2, general step, elastic material.
eccigfs2c.inp: CCL18 elements, load and boundary conditions of Case 2, assumed nonlinear geometry, elastic material.
eccighs2d.inp: CCL18H elements, load and boundary conditions of Case 2, assumed nonlinear geometry, hyperelastic material.
eccigfs3a.inp: CCL18 elements, load and boundary conditions of Case 3, perturbation step, elastic material.
eccigfs3b.inp: CCL18 elements, load and boundary conditions of Case 3, general step, elastic material.
eccigfs3c.inp: CCL18 elements, load and boundary conditions of Case 3, assumed nonlinear geometry, elastic material.
eccighs3d.inp: CCL18H elements, load and boundary conditions of Case 3, assumed nonlinear geometry, hyperelastic material.
eccigfs4a.inp: CCL18 elements, load and boundary conditions of Case 4, perturbation step, elastic material.
eccigfs4b.inp: CCL18 elements, load and boundary conditions of Case 4, general step, elastic material.
eccigfs4c.inp: CCL18 elements, load and boundary conditions of Case 4, assumed nonlinear geometry, elastic material.
eccighs4d.inp: CCL18H elements, load and boundary conditions of Case 4, assumed nonlinear geometry, hyperelastic material.
eccrgfs1a.inp: CCL24 elements, load and boundary conditions of Case 1, perturbation step, elastic material.
eccrgfs1b.inp: CCL24 elements, load and boundary conditions of Case 1, general step, elastic material.
eccrgfs1c.inp: CCL24 elements, load and boundary conditions of Case 1, assumed nonlinear geometry, elastic material.
eccrghs1d.inp: CCL24H elements, load and boundary conditions of Case 1, assumed nonlinear geometry, hyperelastic material.
eccrgfs2a.inp: CCL24 elements, load and boundary conditions of Case 2, perturbation step, elastic material.
eccrgfs2b.inp: CCL24 elements, load and boundary conditions of Case 2, general step, elastic material.
eccrgfs2c.inp: CCL24 elements, load and boundary conditions of Case 2, assumed nonlinear geometry, elastic material.
eccrghs2d.inp: CCL24H elements, load and boundary conditions of Case 2, assumed nonlinear geometry, hyperelastic material.
eccrgfs3a.inp: CCL24 elements, load and boundary conditions of Case 3, perturbation step, elastic material.
eccrgfs3b.inp: CCL24 elements, load and boundary conditions of Case 3, general step, elastic material.
eccrgfs3c.inp: CCL24 elements, load and boundary conditions of Case 3, assumed nonlinear geometry, elastic material.
eccrghs3d.inp: CCL24H elements, load and boundary conditions of Case 3, assumed nonlinear geometry, hyperelastic material.
eccrgfs4a.inp: CCL24 elements, load and boundary conditions of Case 4, perturbation step, elastic material.
eccrgfs4b.inp: CCL24 elements, load and boundary conditions of Case 4, general step, elastic material.
eccrgfs4c.inp: CCL24 elements, load and boundary conditions of Case 4, assumed nonlinear geometry, elastic material.
eccrghs4d.inp: CCL24H elements, load and boundary conditions of Case 4, assumed nonlinear geometry, hyperelastic material.
eccrgrs1a.inp: CCL24R elements, load and boundary conditions of Case 1, perturbation step, elastic material.
eccrgrs1b.inp: CCL24R elements, load and boundary conditions of Case 1, general step, elastic material.
eccrgrs1c.inp: CCL24R elements, load and boundary conditions of Case 1, assumed nonlinear geometry, elastic material.
eccrgys1d.inp: CCL24RH elements, load and boundary conditions of Case 1, assumed nonlinear geometry, hyperelastic material.
eccrgrs2a.inp: CCL24R elements, load and boundary conditions of Case 2, perturbation step, elastic material.
eccrgrs2b.inp: CCL24R elements, load and boundary conditions of Case 2, general step, elastic material.
eccrgrs2c.inp: CCL24R elements, load and boundary conditions of Case 2, assumed nonlinear geometry, elastic material.
eccrgys2d.inp: CCL24RH elements, load and boundary conditions of Case 2, assumed nonlinear geometry, hyperelastic material.
eccrgrs3a.inp: CCL24R elements, load and boundary conditions of Case 3, perturbation step, elastic material.
eccrgrs3b.inp: CCL24R elements, load and boundary conditions of Case 3, general step, elastic material.
eccrgrs3c.inp: CCL24R elements, load and boundary conditions of Case 3, assumed nonlinear geometry, elastic material.
eccrgys3d.inp: CCL24RH elements, load and boundary conditions of Case 3, assumed nonlinear geometry, hyperelastic material.
eccrgrs4a.inp: CCL24R elements, load and boundary conditions of Case 4, perturbation step, elastic material.
eccrgrs4b.inp: CCL24R elements, load and boundary conditions of Case 4, general step, elastic material.
eccrgrs4c.inp: CCL24R elements, load and boundary conditions of Case 4, assumed nonlinear geometry, elastic material.
eccrgys4d.inp: CCL24RH elements, load and boundary conditions of Case 4, assumed nonlinear geometry, hyperelastic material.