Patch Test C - 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

A uniform traction of t is applied to the right and top edges of the domain through nodal forces. Top edge nodes: 3, 4, 8 Right edge nodes: 2, 3, 6, 7

Boundary conditions

Nodes on the left and bottom edges are restrained. Left edge nodes: 1, 4, 9, 10 Bottom edge nodes: 1, 2, 5

Solution

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) Displacement x (m) Displacement y (m)
1 0 0 -1.33975 -1.26694 0.00000 0.00000
2 1.45 0 1.33975 -1.26694 0.00140 0.00000
3 1.45 2.3 1.33975 1.26694 0.00140 0.00222
4 0 2.3 -1.33975 1.26694 0.00000 0.00222
5 0.725 0 0 -2.53388 0.00070 0.00000
6 1.45 0.7667 2.6795 0 0.00140 0.00074
7 1.45 1.5333 2.6795 0 0.00140 0.00148
8 0.725 2.3 0 2.53388 0.00070 0.00222
9 0 1.5333 -2.6795 0 0.00000 0.00148
10 0 0.7667 -2.6795 0 0.00000 0.00074
11 0.7866 1.1018 0 0 0.00076 0.00106
12 0.4513 1.6262 0 0 0.00043 0.00157
13 0.8677 0.5081 0 0 0.00084 0.00049
14 1.0304 1.6240 0 0 0.00099 0.00156
15 0.5993 0.4069 0 0 0.00058 0.00039
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