Patch Test A - GCMLab/GCMLab-FEM GitHub Wiki

This patch test applies constant tensile stress to a domain.

Geometry and Mesh

Nine Q4 elements used.

Material properties

Parameter Symbol Value
Young's Modulus E 2540 kPa
Poisson's Ratio nu 0.3
Applied Traction t 3.495 kPa

Plane stress conditions applied

Applied loads

N/A

Boundary conditions

Displacement prescribed on all degrees of freedom based on nodal position (x, y).

Horizontal displacement: (1 - nu)* t / E * x

Vertical displacement: (1 - nu)* t / E * y

Solution

The displacements are prescribed so as to establish tensile stress t in both directions of the domain. The total horizontal reaction force is 8.0385 N/m. The total vertical reaction force is 5.06775 N/m. The stress components are in the x- and y-directions are 3.495 kPa and there is no shear stress.

Node x (m) y (m) Force X (N) Force Y (N)
1 0 0 -1.33975 -1.26694
2 1.45 0 1.33975 -1.26694
3 1.45 2.3 1.33975 1.26694
4 0 2.3 -1.33975 1.26694
5 0.725 0 0 -2.53388
6 1.45 0.7667 2.6795 0
7 1.45 1.5333 2.6795 0
8 0.725 2.3 0 2.53388
9 0 1.5333 -2.6795 0
10 0 0.7667 -2.6795 0
11 0.7866 1.1018 0 0
12 0.4513 1.6262 0 0
13 0.8677 0.5081 0 0
14 1.0304 1.6240 0 0
15 0.5993 0.4069 0 0
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