4.10.7 3DNLG-7: Elastic large deflection response of a hinged spherical shell under pressure loading

Product: ABAQUS/Standard

Elements tested

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

Material:

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

Boundary conditions:

Simply supported along all edges ().

Loading:

Evenly distributed follower pressure load normal to shell surface. = 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 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

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	at center	Pressure	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