Constant curvature test for shells

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Elements tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/Standard

Elements tested

S3R

S4R

S4R5

S8R

S8R5

S9R5

STRI3

STRI65

Problem description

Material:

Linear elastic, Young's modulus = 1 × 10³, Poisson's ratio = 0.3.

Boundary conditions:

$u_{z} = 0$ at nodes A, B, and D, $u_{x} = u_{y} = 0$ at all nodes along the perimeter.

Loading:

$F_{z} = $ −2.0 at node C, $M_{x} = $ 20.0 at nodes A and B, $M_{x} = $ −20.0 at nodes C and D, $M_{y} = $ 10.0 at nodes B and C, $M_{y} = $ −10.0 at nodes A and D.

Reference solution

Displacements: $u_{z}^{C} = $ −12.48.

Results and discussion


Element type	$u_{z}^{C}$
S3/S3R	−12.51
S4R	−12.54
S4	−12.54
S4R5	−12.496
S8R*	−12.555
S8R5	−12.527
S9R5	−12.527
STRI3	−12.480
STRI65	−12.545

*A refined mesh consisting of two elements is used for the S8R model since hourglassing occurs in a one-element mesh.

Input files

esf3sxs9.inp: S3/S3R elements.
ese4sxs9.inp: S4 elements.
esf4sxs9.inp: S4R elements.
es54sxs9.inp: S4R5 elements.
es68sxs9.inp: S8R elements.
es58sxs9.inp: S8R5 elements.
es59sxs9.inp: S9R5 elements.
es63sxs9.inp: STRI3 elements.
es56sxs9.inp: STRI65 elements.