4.2.5 LE5: Z-section cantilever

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

S3 S3R S4R S4R5 S4RS S4RSW S8R S8R5 S9R5 STRI3 STRI65

B31OS B32OS

Problem description

Model:

Z-section cantilever under torsional loading.

Material:

Linear elastic, Young's modulus = 210 GPa, Poisson's ratio = 0.3, density = 7800 kg/m³.

Boundary conditions:

All displacements are zero along the edge at 0.

Loading:

Torque of 1.2 MN-m applied at 10. The torque is applied by two uniformly distributed edge shears of 0.6 MN at each flange when shell elements are used. In the explicit dynamic analysis the loading rate is applied such that a quasi-static solution is obtained.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test LE5 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Axial stress, –108 MPa at midsurface, point A.

Results and discussion

The results are shown in Table 4.2.5–1 and Table 4.2.5–2. The values enclosed in parentheses are percentage differences with respect to the reference solution. Slow convergence toward the target solution is seen as the mesh is refined.

Table 4.2.5–1 ABAQUS/Standard analysis.

Element	, Coarse Mesh	, Refined Mesh
S3/S3R	–24.266 MPa (–78%)	–92.166 MPa (–15%)
S4	–110.36 MPa (2.2%)	–110.38 MPa (2.2%)
S4R	–50.480 MPa (–53%)	–96.732 MPa (–10%)
S4R5	–50.116 MPa (–54%)	–96.378 MPa (–11%)
S8R	–109.85 MPa (1.7%)	—
S8R5	–109.72 MPa (1.6%)	—
S9R5	–109.72 MPa (1.6%)	—
STRI3	–30.389 MPa (–72%)	–94.532 MPa (–12%)
STRI65	–107.32 MPa (–0.63%)	—
B31OS	–108.09 MPa (0.08%)	—
B32OS	–107.34 MPa (–0.61%)	—