Plate with hole#

This example demonstrates a stress concentration analysis on a flat plate with a central circular hole using PyMechanical-MCP. It is a classic benchmark for validating stress concentration factors against the theoretical value of approximately 3x.

Engineering objective#

Compute the stress concentration factor for a 200 millimeter x 100 millimeter x 5 millimeter rectangular plate with a 30 millimeter-diameter central hole under uniaxial tension. Compare the maximum principal stress near the hole to the nominal far-field stress and confirm Kt is approximately equal to 3.

Geometry#

  • File: plate.step

  • Plate dimensions: 200 millimeters x 100 millimeters x 5 millimeters (with a diameter central hole of 30 millimeters)

Setup requirements#

Setting

Value

Material

Structural steel (default)

Mesh

Element size is 2 millimeters (fine mesh to resolve stress concentration)

Fixed support

Left end face (YZ face at X = -100 millimeters)

Tensile force

10,000 newton in +X direction on right end face (YZ face at X = +100 millimeters)

Tool workflow#

  1. Connect to or launch Mechanical using connect_to_mechanical or launch_mechanical.

  2. Upload the plate.step file using upload_file.

  3. Assign structural steel as the material to the plate body using run_python_script.

  4. Generate a two-millimeter element size mesh for fine resolution near the hole using run_python_script.

  5. Apply a fixed support on the left end face using run_python_script.

  6. Apply a 10,000 newton tensile force in +X on the right end face using run_python_script.

  7. Run the solver using solve_analysis.

  8. Add total deformation, equivalent stress, and normal stress X results using run_python_script.

  9. Capture a screenshot of the equivalent stress contour using screenshot.

Expected outcome#

  • Stress concentration factor of approximately 3x at the hole edges (top and bottom)

  • Classic butterfly stress pattern: high stress (red) at the hole edges tapering to nominal (blue/green)

  • Maximum stress approximately three times the applied nominal stress

Theory#

For a plate with a central circular hole under uniaxial tension, Kt is approximately 3.0 when the hole diameter is small relative to the plate width. For this geometry (d/W = 30/100 = 0.3), Kt is approximately 3.0.

Prompt example#

Perform a static structural analysis on a plate with a central circular hole.
Upload the geometry file plate.step.

- Material: Structural Steel (default)
- Mesh: element size 2 mm (fine mesh to capture stress concentration around hole)
- Fixed support on left end face (YZ face at X = -100 mm)
- Tensile force of 10,000 N in +X on right end face (YZ face at X = +100 mm)
- Results: Total Deformation, Equivalent (von Mises) Stress, Normal Stress X
- Take a screenshot of the von Mises stress result