VM289
VM289
Pressurized Spherical Cavity in an Infinite Medium with
Perfectly Matched Layers (PML)
Test Case
A spherical cavity with a radius of 1.0 m is placed in an infinite medium. The spherical cavity is subjected to an internal pressure of 750 Pa. A perfectly matched layer (PML) is used to truncate the infinite boundary. Determine the displacement and stresses with respect to location (from X = 1 m to X = 4 m).
| Material Properties | Geometric Properties | Loading | ||
|---|---|---|---|---|
| Internal radius, a = 1 m | Internal pressure = 750 Pa |
Analysis Assumptions and Modeling Notes
The spherical cavity in the infinite medium and perfectly matched layers are modeled using SOLID186 elements. The PML absorbing condition is defined by setting Keyopt(15) = 1. Only one eighth of the sphere is modeled, using symmetric constraints on the three orthagonal planes. The displacements along the radial direction and the stresses along the radial and tangential directions are then obtained from /POST1 and compared against the analytical solution.
The analytic solution for radial displacement is:
The analytic solution for radial stress is:
The analytic solution for tangential stress is:
where 
is the internal applied pressure, 
is the internal
radius, 
is the rigidity modulus, and 
is the radial
location.
Results Comparison
| Location (m) | Target | Mechanical APDL | Ratio | |
|---|---|---|---|---|
| Radial displacement (m) | 1.0000 | 0.49875 x 10-4 | 0.49852 x 10-4 | 1.000 |
| 1.9474 | 0.13151 x 10-4 | 0.13137 x 10-4 | 0.999 | |
| 3.0526 | 0.53523 x 10-5 | 0.53338 x 10-5 | 0.997 | |
| 3.8421 | 0.33787 x 10-5 | 0.33562 x 10-5 | 0.993 | |
| Radial stress (Pa) | 1.0000 | -750.000 | -736.662 | 0.982 |
| 1.9474 | -101.554 | -101.442 | 0.999 | |
| 3.0526 | -26.366 | -26.589 | 1.008 | |
| 3.8421 | -13.224 | -13.437 | 1.016 | |
| Tangential stress (Pa) | 1.0000 | 375.000 | 368.629 | 0.983 |
| 1.9474 | 50.777 | 50.490 | 0.994 | |
| 3.0526 | 13.183 | 13.060 | 0.990 | |
| 3.8421 | 6.612 | 6.483 | 0.980 |