Size dependent nano-spherical pressure vessels based on strain gradient theory

Document Type : Research Paper


1 Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

2 Department of Electrical Engineering, Islamic Azad University, Tehran, Iran

3 Department of Mechanical Engineering, University of Guilan, Rasht, Iran


This study investigates the effect of size scale material parameters on stress distribution and radial displacement of nanosphere based on strain gradient theory. This model is more capable of studying mechanical behavior than classical elasticity theory as the size scale effect of the nanosphere is also considered. Minimum total potential energy is used to derive governing differential equation of nanosphere under internal hydrostatic pressure. Using the efficient numerical generalized differential quadrature (GDQ) method, the governing equation and corresponding boundary conditions are solved. The classical elasticity equation is obtained by setting the value of size scale material parameters to zero. With the comparison of these theories, the importance of the size scale material parameters is achieved. It is found that the radial displacement of nanosphere predicted by strain gradient theory is less than those predicted by classical elasticity theory but comparing the distribution of stress components along radius is more complex. The effect of the size of the nanosphere on the radial stress components is also studied. With an increasing outer radius of the nanosphere, the mechanical behavior predicted by strain gradient theory tends toward those in classical elasticity theory.


Volume 52, Issue 2
June 2021
Pages 307-319
  • Receive Date: 24 April 2021
  • Revise Date: 31 May 2021
  • Accept Date: 31 May 2021