10.57647/jsm.2026.1801.01

Stress Analysis for FGM Sphere in the Couple Stress Elasticity

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  • Foad Saadi1,
  • Mohsen Jabbari*2,
  • Mehdi Yarmohammad Tooski,
  1. Islamic Azad University South Tehran Branch
  2. IT Department, South Tehran Branch,Islamic Azad University, Tehran, Iran

Received: 2025-12-18

Revised: 2026-02-26

Accepted: 2026-03-20

Published in Issue 2026-03-31

Copyright (c) 2026 Foad Saadi, Mohsen Jabbari, Mehdi Yarmohammad Tooski (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Saadi, F., Jabbari, M., & Yarmohammad Tooski, M. (2026). Stress Analysis for FGM Sphere in the Couple Stress Elasticity. Journal of Solid Mechanics, 18(1). https://doi.org/10.57647/jsm.2026.1801.01
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Abstract

This study develops an analytical framework based on Modified Couple Stress Theory (MCST) to investigate the stress response of functionally graded hollow spheres. The governing equations, which consider both material gradation and microstructural length-scale parameters, are solved with high accuracy using the Generalized Differential Quadrature (GDQ) method. The proposed framework exhibits numerical stability and strong convergence, and shows excellent agreement with benchmark analytical solutions reported in the literature, with a deviation of less than 3%. For a microstructural length-scale parameter of 0.1 μm, the results are in close agreement with classical elasticity predictions, with a deviation of less than 2%, confirming the robustness and reliability of the formulation in a multiscale context. Furthermore, increasing the material gradient index increases the sensitivity of the stress to the length-scale parameter, highlighting the coupling between material composition and microstructural effects. This integrated MCST-GDQ approach provides a solid and efficient foundation for further research on microstructured materials, smart composites, and multiscale mechanical systems.

Keywords

  • Functionally graded materials (FGM),
  • Couple stress theory,
  • Modified Couple Stress Theory (MCST),
  • Hollow sphere,
  • Generalized Differential Quadrature (GDQ),
  • Microstructural Length Scale
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