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.

This page discusses:

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:

Uz=0 along all edges. Ux=Uy=θz=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⁢f⁢(x,y)f⁢(L/2,L/2),

where f⁢(x,y)=Σm Σn am⁢n sin(m⁢π⁢x)L sin (n⁢π⁢x)L, a11 = 1.0, a22 = 0.2897, a13 = −0.0706, a31 = −0.0691, a33 = 0.0384, and a42 = 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.