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

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:

Elements tested
Problem description
Reference solution
Results and discussion
Response predicted by Abaqus (element S8R5)
Input files

ProductsAbaqus/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 ( $U_{x} = θ_{y} = θ_{z} = 0$ ). Symmetry on plane z = 0 ( $U_{z} = θ_{x} = θ_{y} = 0$ ). Simply supported on plane z = $L / 2$ = 0.4 ( $U_{x} = U_{y} = 0$ ).

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 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 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	$P_{m a x}$	$U_{2}$
S3R	2708	−0.03168
S4R	2626	−0.03124
S4	2619	−0.03116
S4R5	2604	−0.03127
S8R	2490	−0.03072
S8R5	2472	−0.03063
S9R5	2474	−0.03034
STRI3	2596	−0.03096
STRI65	2460	−0.03051
SC6R	2653	–0.03166
SC8R	2601	–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.