Plate with hole (symmetry planes via normal constraints)

Stress concentration factor (Kirsch problem) for a tensioned plate with a central hole, solved on a quarter-symmetry model using surface normal constraints (n·u = 0) vs full model.

Tolerance:

5%

Problem statement

Geometry

Square plate 200 × 200 × 5 mm with circular hole of radius R = 20 mm. Quarter model: 100 × 100 × 5 mm domain.

Material

Structural steel: E = 200 GPa, ν = 0.3.

Boundary conditions

Normal constraint (n·u = 0) on symmetry planes x = 0 and y = 0; uniform tension σ0 = 100 MPa on outer edge x = 100 mm; z = 0 clamped to prevent rigid drift.

Measured quantity

Peak von Mises stress σ_max at the hole edge (r = R). Quarter-symmetry model yields 325.06 MPa vs full plate 320.62 MPa (deviation 1.38%). Normal constraint on planar symmetry faces matches global axis fixations to exact machine precision (Δu = 0.00%).

Results comparison

Updated: 2026-08-06 · WebCAE solver