4.10.6 3DNLG-6: Buckling of a flat plate when subjected to in-plane shear

Product: ABAQUS/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:

along all edges. 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

where

= 1.0,

= 0.2897,

= –0.0706,

= –0.0691,

= 0.0384, and

= 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 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

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.