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Analytical Solution for a Pressurized Thick-Walled Spherical Shell Based on a Simplified Strain Gradient Elasticity TheoryDepartment of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA The problem of a pressurized thick-walled spherical shell is analytically solved using a simplified strain gradient elasticity theory. The closed-form solution derived contains a material length scale parameter and can account for microstructural effects, which qualitatively differs from Lamé’s solution in classical elasticity. When the strain gradient effect (a measure of the underlying material microstructure) is not considered, the newly derived strain gradient elasticity solution reduces to Lamé’s classical elasticity solution. To illustrate the new solution, a sample problem with specified geometrical parameters, pressure values and material properties is solved. The numerical results reveal that the magnitudes of both the radial and tangential stress components in the shell wall given by the current strain gradient solution are smaller than those given by Lamé’s solution. Also, it is quantitatively shown that microstructural effects can be large and Lamé’s solution may not be accurate for materials exhibiting significant microstructure dependence.
Key Words: Strain gradient theory • elasticity • Lamé’s solution • thick-walled spherical shell • microstructural effect • length scale • pressure vessel
This version was published on November
1, 2009 Mathematics and Mechanics of Solids, Vol. 14, No. 8,
747-758 (2009) |
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