3DNLG-6: Buckling of a flat plate when subjected to in-plane shear

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

The following topics are discussed:

Elements tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/Standard

Elements tested

S3
S3R
S4
S4R
S4R5
S8R
S8R5
S9R5

STRI3
STRI65

SC6R
SC8R

Problem description

Material:

Young's modulus = 6.4 × 10⁶, Poisson's ratio = 0.3.

Boundary conditions:

$U_{z} = 0$ along all edges. $U_{x} = U_{y} = θ_{z} = 0$ at center node.

Loading:

Uniform shear load around edges. The RIKS algorithm is used to increment the shear load to a maximum of 2.12 × 10⁸ per edge.

Initial imperfection

The midsurface position of the plate is defined by

z = 0.5 t \frac{f (x, y)}{f (L / 2, L / 2)},

where $f (x, y) = Σ_{m} Σ_{n} a_{m n} \sin \frac{(m π x)}{L} \sin \frac{(n π x)}{L}$ , $a_{11}$ = 1.0, $a_{22}$ = 0.2897, $a_{13}$ = −0.0706, $a_{31}$ = −0.0691, $a_{33}$ = 0.0384, and $a_{42}$ = 0.0032.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-6 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

Very similar load-deflection curves are obtained for all the test cases. The SC6R model shows a slightly stiffer response than the other elements. The response of all elements tested is shown below.

Input files

n3g6xf3x.inp: S3/S3R elements.
n3g6xe4x.inp: S4 elements.
n3g6xf4x.inp: S4R elements.
n3g6x54x.inp: S4R5 elements.
n3g6x68x.inp: S8R elements.
n3g6x58x.inp: S8R5 elements.
n3g6x59x.inp: S9R5 elements.
n3g6x63x.inp: STRI3 elements.
n3g6x56x.inp: STRI65 elements.
nlg6_std_sc6r.inp: SC6R elements.
nlg6_std_sc8r.inp: SC8R elements.