3DNLG-5: Large deflection of a curved elastic cantilever under transverse 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

Problem description



Material:

Young's modulus = 1.0 × 107, Poisson's ratio = 0.0.

Boundary conditions:

All degrees of freedom restrained at A.

Loading:

Concentrated load at B (Pz = 3000).

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-5 from NAFEMS Publication R0024 “A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3D Beams and Shells (SUMMARY).”

The published results of 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

All elements are tested with meshes using the same nodal spacing.

The results vary slightly between different element types. The maximum difference in the reported displacement components is 1.3%. The hybrid element results are identical to their non-hybrid counterparts to the precision reported here. The tip displacement components are compared in the tables below.

LoadTip Displacement (Ux)
PzB31(H)B32(H)B33(H)
300.0 −7.097 −7.173 −7.188
450.0 −10.82 −10.92 −10.93
600.0 −13.62 −13.73 −13.74
3000.0 −24.99 −25.06 −25.04
Load Tip Displacement (Uy)
Pz B31(H) B32(H) B33(H)
300.0 −12.13 −12.17 −12.19
450.0 −18.70 −18.74 −18.76
600.0 −23.78 −23.81 −23.85
3000.0 −47.70 −47.70 −47.78
Load Tip Displacement (Uz)
Pz B31(H) B32(H) B33(H)
300.0 40.43 40.47 40.50
450.0 48.67 48.70 48.73
600.0 53.58 53.60 53.63
3000.0 68.55 68.46 68.52

Response predicted by Abaqus (element B31)