1.5.6 Patch test for plate bending

Product: ABAQUS/Standard

Elements tested

S3 S3R S4 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)

0, 10^–3()/2, 10^–3(/2), –10^–3(/2).

Reference solution

Stress: 0.6667, 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

S3/S3R elements.

S4 elements.

S4R elements.

S4R5 elements.

S8R elements.

S8R5 elements.

S9R5 elements.

STRI3 elements.

STRI65 elements.