NL4: Snap-back under displacement control

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

T2D2

Problem description



Model:

AE = 5.0 × 107, L = 2500, αL = 25, K1 = 1.5, K2 = AE/L(1 + α​2)1/2 = 19999.0, K3 = 0.25, K4 = 1.0

Boundary conditions:

uy=​ 0 at node 1 and node 11, ux=0 at node 9.

Loading:

A load is applied to node 11 in the x-direction.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test NL4 from NAFEMS Publication NNB, Rev. 1, “NAFEMS Non-Linear Benchmarks,” October 1989.

Pu​1u​2v
649.9 0.0904 650 5.241
1300 0.2328 1300 13.26
1949 0.5149 1950 27.08
2599 1.334 2600 56.50
3243 7.089 3250 162.6
−1099 4999 3900 41.95

Results and discussion

The RIKS algorithm was used for this problem. In this case it is not possible to obtain the solution at particular force values. The results below were obtained from the Abaqus results by linear interpolation between the two nearest increments. Therefore, there is some error associated with this interpolation procedure. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Pu​1u​2v
649.9 0.0906 (+0.22%) 650 (0.0%) 5.254 (+0.25%)
1300 0.2333 (+0.21%) 1300 (0.0%) 13.29 (+0.23%)
1949 0.5152 (+0.06%) 1949 (−0.05%) 27.08 (0.0%)
2599 1.337 (+0.22%) 2600 (0.0%) 56.57 (+0.12%)
3243 7.241 (+2.14%) 3250 (0.0%) 163.9 (+0.08%)
−1099 4999 (0.0%) 3900 (0.0%) 43.49 (+3.67%)