3DNLG-7: Elastic large deflection response of a hinged spherical shell under pressure loading

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

  • CSS8
  • S3
  • S3R
  • S4
  • S4R
  • S4R5
  • S8R
  • S8R5
  • S9R5
  • STRI3
  • STRI65
  • SC6R
  • SC8R

Problem description



Model:

The shell midsurface is defined in terms of global Cartesian coordinates, where

z=2.0285×10-4 {x(L-x) + y(L-y)}.

Material:

Young's modulus = 69, Poisson's ratio = 0.3.

Boundary conditions:

Simply supported along all edges (Ux=Uy=Uz=0).

Loading:

Evenly distributed follower pressure load normal to shell surface. pm⁢a⁢x = 0.1.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-7 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

In the following table, limit points 1 and 2 correspond to the peak and local minimum, respectively, of the load-displacement curve. All the meshes share the same nodal spacing.

Element Limit point 1 Limit point 2
  Pressure Uz at center Pressure Uz at center
S3/S3R 0.06639 78.15 0.03300 220.9
S4 0.06581 78.84 0.03133 223.5
S4R 0.06581 78.98 0.03134 223.5
S4R5 0.06281 79.62 0.02956 224.4
S8R 0.06263 79.14 0.02849 223.6
S8R5 0.06261 79.21 0.02882 223.7
S9R5 0.06261 79.08 0.02883 223.4
STRI3 0.06397 78.61 0.03175 221.9
STRI65 0.06244 79.26 0.02886 224.0
SC6R 0.06749 81.0 0.03388 217.1
SC8R 0.06679 81.9 0.03213 217.6
CSS8 0.06619 83.9 0.03278 221.1

Response predicted by Abaqus

Similar load-displacement curves are obtained for all test cases. The response predicted using S8R5 elements is shown below.