4.10.2 3DNLG-2: Elastic large deflection response of a pear-shaped cylinder under end shortening

Product: ABAQUS/Standard  

Elements tested

S3R    S4    S4R    S4R5    S8R    S8R5    S9R5   

STRI3    STRI65   

SC6R    SC8R   

Problem description

Model:

A quarter model is used because of symmetry.

Material:

Young's modulus = 1.0 × 107, Poisson's ratio = 0.3.

Boundary conditions:

Symmetry on plane x = 0 (). Symmetry on plane z = 0 (). Simply supported on plane z = = 0.4 ().

Loading:

Uniform end shortening. A displacement of –0.0016 is applied incrementally using the RIKS algorithm to all nodes lying on one end of the cylinder with the plane z = 0.4.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-2 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 collapse load is defined as the loading point in the deformation path at which further deformation occurs without an increase in the applied load. The path after this point is termed the postbuckling path. The postbuckling path shows a decrease in the load with further deformation; the postbuckled structure can attain equilibrium only at a load level lower than the buckling load once it has buckled.

Collapse Loads
Element
S3R2708–0.03168
S4R2626–0.03124
S42619–0.03116
S4R52604–0.03127
S8R2490–0.03072
S8R52472–0.03063
S9R52474–0.03034
STRI32596–0.03096
STRI652460–0.03051
SC6R2653–0.03166
SC8R2601–0.03155

Response predicted by ABAQUS (element S8R5)

Input files

n3g2x58x_s3r.inp

S3R elements.

n3g2x58x_s4.inp

S4 elements.

n3g2x58x_s4r.inp

S4R elements.

n3g2x58x_s4r5.inp

S4R5 elements.

n3g2x58x_s8r.inp

S8R elements.

n3g2x58x_s8r5.inp

S8R5 elements.

n3g2x58x_s9r5.inp

S9R5 elements.

n3g2x58x_stri3.inp

STRI3 elements.

n3g2x58x_stri65.inp

STRI65 elements.

nlg2_std_sc6r.inp

SC6R elements.

nlg2_std_sc8r.inp

SC8R elements.