AA-SB-001: Analysis And Design Of Composite And Metallic Flight Vehicle Structures

Third Edition

12.3.1. Formulas for Stress and Deformations Due to Pressure Between Elastic Bodies

Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

12.3.1.1. Sphere on Sphere

Figure 12.3.1‑1: Sphere on Sphere Contact

 Shape of Contact Area:

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-001 Contact Stresses – Sphere on a Sphere      

12.3.1.2. Sphere in Spherical Socket

Figure 12.3.1‑2: Sphere in Spherical Socket Contact

Shape of Contact Area:

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-002 Contact Stresses – Sphere in a Spherical Socket    

12.3.1.3. Sphere on a Flat Panel

Figure 12.3.1‑3: Sphere on Flat Panel Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

Distribution of normal pressure in the contact area as a function of distance (r’) from the center of the circle:

Figure 12.3.1‑4: Sphere on Flat Panel Contact – Bearing Stress Distribution

Figure 12.3.1‑4: Sphere on Flat Panel Contact – Bearing Stress Distribution

Depth of Indentation:

A spreadsheet for this method is available at the link below:

AA-SM-008-003 Contact Stresses – Sphere on a Flat Plate  

12.3.1.4. Cylinder on a Cylinder with Axes Parallel

Figure 12.3.1‑5: Cylinder on Cylinder Axes Parallel Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-004 Contact Stresses – Cylinder on a Cylinder – Parallel

12.3.1.5. Cylinder in a Cylindrical Groove

Figure 12.3.1‑6: Cylinder in Cylindrical Groove Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-005 Contact Stresses – Cylinder in a Cylindrical Groove  

12.3.1.6. Cylinder on a Flat Panel

Figure 12.3.1‑7: Cylinder on Flat Panel Contact

 Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-006 Contact Stresses – Cylinder on a Flat Plate

12.3.1.7. Cylinder on a Cylinder with Axes Perpendicular

Figure 12.3.1‑8: Cylinder on Cylinder Axes Perpendicular Contact

Shape of Contact Area:

The contact area between the two cylinders is derived using the following 3 parameters: K1, K2 and K3.

Figure 12.3.1‑9: Contact Regions Parameters

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-007 Contact Stresses – Cylinder on a Cylinder -Perpendicular

12.3.1.8. Rigid Knife Edge on a Panel

Figure 12.3.1‑10: Rigid Knife Edge on a Panel Contact

Maximum Bearing Compression Stress, at any point Q:

A spreadsheet for this method is available at the link below:

AA-SM-008-008 Contact Stresses – Rigid Knife Edge on Plate

12.3.1.9. Rigid Cone on a Panel

Figure 12.3.1‑11: Rigid Cone on a Panel Contact

Maximum Deflection:

Depth of the Contact Region:

Radius of the Contact Region:

Distribution of normal pressure in the contact area as a function of distance (r’) from the center of the circle:

Figure 12.3.1‑12: Rigid Cone on a Panel – Bearing Stress Distribution

The pressure distribution has a singularity at the center of the contact region.

A spreadsheet for this method is available at the link below:

AA-SM-008-009 Contact Stresses – Rigid Cone on Plate

12.3.1. Formulas for Stress and Deformations Due to Pressure Between Elastic Bodies

Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

12.3.1.1. Sphere on Sphere

Figure 12.3.1‑1: Sphere on Sphere Contact

 Shape of Contact Area:

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-001 Contact Stresses – Sphere on a Sphere      

12.3.1.2. Sphere in Spherical Socket

Figure 12.3.1‑2: Sphere in Spherical Socket Contact

Shape of Contact Area:

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-002 Contact Stresses – Sphere in a Spherical Socket    

12.3.1.3. Sphere on a Flat Panel

Figure 12.3.1‑3: Sphere on Flat Panel Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

Distribution of normal pressure in the contact area as a function of distance (r’) from the center of the circle:

Figure 12.3.1‑4: Sphere on Flat Panel Contact – Bearing Stress Distribution

Figure 12.3.1‑4: Sphere on Flat Panel Contact – Bearing Stress Distribution

Depth of Indentation:

A spreadsheet for this method is available at the link below:

AA-SM-008-003 Contact Stresses – Sphere on a Flat Plate  

12.3.1.4. Cylinder on a Cylinder with Axes Parallel

Figure 12.3.1‑5: Cylinder on Cylinder Axes Parallel Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-004 Contact Stresses – Cylinder on a Cylinder – Parallel

12.3.1.5. Cylinder in a Cylindrical Groove

Figure 12.3.1‑6: Cylinder in Cylindrical Groove Contact

Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-005 Contact Stresses – Cylinder in a Cylindrical Groove  

12.3.1.6. Cylinder on a Flat Panel

Figure 12.3.1‑7: Cylinder on Flat Panel Contact

 Shape of Contact Area:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-006 Contact Stresses – Cylinder on a Flat Plate

12.3.1.7. Cylinder on a Cylinder with Axes Perpendicular

Figure 12.3.1‑8: Cylinder on Cylinder Axes Perpendicular Contact

Shape of Contact Area:

The contact area between the two cylinders is derived using the following 3 parameters: K1, K2 and K3.

Figure 12.3.1‑9: Contact Regions Parameters

Deflection:

Maximum Bearing Compression Stress:

A spreadsheet for this method is available at the link below:

AA-SM-008-007 Contact Stresses – Cylinder on a Cylinder -Perpendicular

12.3.1.8. Rigid Knife Edge on a Panel

Figure 12.3.1‑10: Rigid Knife Edge on a Panel Contact

Maximum Bearing Compression Stress, at any point Q:

A spreadsheet for this method is available at the link below:

AA-SM-008-008 Contact Stresses – Rigid Knife Edge on Plate

12.3.1.9. Rigid Cone on a Panel

Figure 12.3.1‑11: Rigid Cone on a Panel Contact

Maximum Deflection:

Depth of the Contact Region:

Radius of the Contact Region:

Distribution of normal pressure in the contact area as a function of distance (r’) from the center of the circle:

Figure 12.3.1‑12: Rigid Cone on a Panel – Bearing Stress Distribution

The pressure distribution has a singularity at the center of the contact region.

A spreadsheet for this method is available at the link below:

AA-SM-008-009 Contact Stresses – Rigid Cone on Plate