3DNLG-1: Elastic large deflection response of a Z-shaped cantilever under an end load

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

  • B31
  • B31H
  • B32
  • B32H
  • B33
  • B33H
  • CSS8
  • S4
  • S4R
  • SC6R
  • SC8R

Problem description



Model:

Uniform thickness (t = 1.7).

Material:

Linear elastic, Young's modulus = 2.0 × 105, Poisson's ratio = 0.3.

Boundary conditions:

All degrees of freedom restrained at built-in end.

Loading:

Concentrated end load (P = 4000).

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-1 from NAFEMS Publication R0024 “A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3D Beams and Shells (SUMMARY).”

The published results for this problem were obtained with Abaqus. Thus, a comparison of Abaqus and NAFEMS results is not an independent verification of Abaqus. The NAFEMS study includes results from other sources for comparison that may provide a basis for verification of this problem.

Results and discussion

Displacements converge faster than stresses. Even though the displacements seem to have converged, the lower-order elements need more refined meshes (compared to the higher-order elements) before the stresses are observed to converge. Stresses are most accurate at the integration points within the element. When stress values are extrapolated from the integration points to the nodes and then averaged, the stress values calculated may not capture the peak values if a stress gradient is present. Since the higher-order elements (B32, B32H, B33, and B33H) use linear extrapolation within an element, a stress gradient in an element may be captured adequately when extrapolating stresses to the nodes. However, constant extrapolation is used for linear elements (B31, B31H, S4, S4R, and SC8R), which results in slow convergence of nodal stress values. Higher mesh refinement near stress gradients is needed for such elements.

Tip Displacement
Element Type Number of Elements Applied Load
104.5 1263.0 4000.0
B31 72 80.42 133.1 143.5
B31H 72 80.42 133.1 143.5  
B32 9 80.42 133.1 143.4
B32H 9 80.42 133.1 143.4
B33 9 80.42 133.1 143.4
B33H 9 80.42 133.1 143.4
S4 1 × 72 80.42 133.1 143.5
S4R 1 × 72 80.42 133.1 143.5
SC6R 2 × 72 × 1 80.61 133.1 143.5
SC8R 1 × 72 × 1 80.61 133.1 143.5
CSS8 1 × 72 × 1 80.46 133.1 143.5
Moment at A
Element Type Number of Elements Applied Load
104.5 1263.0 4000.0
B31 72 −8333 −5508 9926
B31H 72 −8333 −5508 9925
B32 9 −8308 −4962 10747
B32H 9 −8308 −4961 10746
B33 9 −8316 −4982 10659
B33H 9 −8317 −4979 10661
S4 1 × 72 −8334 −5506 9940
S4R 1 × 72 −8334 −5506 9940
SC6R 2 × 72 × 1 –8358 –5608 9720
SC8R 1 × 72 × 1 –8324 –5466 9832

Response predicted by Abaqus (element B32)