4.6.2 NL2: Axisymmetric thick cylinder

Product: ABAQUS/Standard  

Elements tested

CAX8R    CCL24R   

Problem description

Material:

Linear elastic, Young's modulus = 207 GPa, Poisson's ratio = 0.3, yield stress = 207.9 MPa.

Boundary conditions:

= 0 for all nodes.

Loading:

An initial internal pressure of 80 MPa is increased in steps of 20 MPa to 160 MPa.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test NL2 from NAFEMS Publication NNB, Rev. 1, “NAFEMS Non-Linear Benchmarks,” October 1989.

The target radial stress and the target circumferential (hoop) stress are given by and , respectively.

r (mm)Internal pressure (MPa)
80100120140160
104.2–71.55124.9–89.74149.9–110.1130.0–130.1110.0–150.189.92
115.8–52.89106.2–66.65133.7–84.87154.7–104.9135.2–124.9115.2
124.2–42.4698.50–53.47120.6–68.32154.1–87.92151.9–107.9132.1
135.8–31.1984.52–39.27106.4–50.17136.0–66.66172.3–86.61153.3
146.3–23.1676.49–29.1696.32–37.26123.1–49.51163.5–68.61170.9
163.7–13.1466.48–16.5583.71–21.15107.0–28.10142.1–41.94195.9
176.3–7.64360.98–9.62476.78–12.3098.10–16.34130.4–24.55195.9
193.7–1.76955.10–2.22769.38–2.84688.65–3.781117.8–5.682177.0

Results and discussion

All results agree exactly with the reference solution, except for the result of at a load of 80 MPa and a distance of 124.2 mm. The value obtained here for both element types is 95.8 MPa, a difference of –2.74%.

Input files

nnl2xr8x.inp

CAX8R elements.

nnl2xrccl24.inp

CCL24R elements.