4.10.5 3DNLG-5: Large deflection of a curved elastic cantilever under transverse end load

Product: ABAQUS/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 ( = 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 3-D 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 ()
B31(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

LoadTip Displacement ()
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

LoadTip Displacement ()
B31(H)B32(H)B33(H)
300.040.4340.4740.50
450.048.6748.7048.73
600.053.5853.6053.63
3000.068.5568.4668.52

Response predicted by ABAQUS (element B31)

Input files

n3g5x32x_b31.inp

B31 elements.

n3g5x32x_b31h.inp

B31H elements.

n3g5x32x_b32.inp

B32 elements.

n3g5x32x_b32h.inp

B32H elements.

n3g5x32x_b33.inp

B33 elements.

n3g5x32x_b33h.inp

B33H elements.