Patch test for plate bending

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

Model:

Thickness, t = 0.001.

Material:

Linear elastic, Young's modulus = 1.0 × 10⁶, Poisson's ratio = 0.25.

Boundary conditions:

(applied to all exterior nodes)

$u_{x} = u_{y} = $ 0, $u_{z} = $ 10⁻³( $x^{2} + x y + y^{2}$ )/2, $θ_{x} = $ 10⁻³( $y + x$ /2), $θ_{y} = $ −10⁻³( $x + y$ /2).

Reference solution

Stress: $σ_{x} = σ_{y} = \pm$ 0.6667, $σ_{x y} = \pm$ 0.20.

Results and discussion

All elements yield exact solutions except S8R. S8R will pass the patch test if the element shapes are rhombic, but they fail the test for general quadrilaterals.

Input files

esf3sxp3.inp: S3/S3R elements.
ese4sxp3.inp: S4 elements.
esf4sxp3.inp: S4R elements.
es54sxp3.inp: S4R5 elements.
es68sxp3.inp: S8R elements.
es58sxp3.inp: S8R5 elements.
es59sxp3.inp: S9R5 elements.
es63sxp3.inp: STRI3 elements.
es56sxp3.inp: STRI65 elements.