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An analytical method for nonlinear thermo-mechanical buckling evaluation of functionally graded circular microplates
[Méthode analytique pour l’évaluation du flambement thermo-mécanique non linéaire des microplaques circulaires à gradient de propriétés]
Duc Nguyen Minh1 orcid ; Thom Do Van1 orcid ; Minh Phung Van1 orcid 
1Department of Solid Mechanics, Faculty of Mechanical Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet Street, Nghia Do Ward, Hanoi, 100000, Vietnam
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 293-312

This paper analytically investigates the nonlinear static buckling behavior of functionally graded (FG) circular microplates by integrating Kirchhoff plate theory, von Kármán geometric nonlinearity, and the modified couple stress theory to account for size-dependent effects. The microplate is concurrently exposed to a uniform pressure and a uniformly increasing through-thickness thermal load. A method based on displacement is used, where the expected movement and bending of the plate are described using polynomial functions that fit the fixed edges of the plate. This choice reduces computational cost while maintaining sufficient accuracy in predicting the nonlinear structural response. By using the Ritz energy method, we can derive straightforward formulas for the critical thermal buckling load and how the load relates to deflection after buckling for the FG circular microplate. The numerical results show that changes in the volume fraction index, material length-scale parameter, and shape features are very important in determining how strong the FGM structure is against buckling and how it behaves after buckling. The results give important insights and serve as a helpful guide for designing microscale functionally graded structures that experience both heat and mechanical stress.

Cet article étudie analytiquement le comportement de flambement statique non linéaire des microplaques circulaires à gradient de propriétés (FG) en intégrant la théorie des plaques de Kirchhoff, la non-linéarité géométrique de von Kármán et la théorie modifiée des couples de contraintes afin de prendre en compte les effets dépendants de la taille. La microplaque est simultanément soumise à une pression uniforme et à une charge thermique uniformément croissante à travers son épaisseur. Une méthode basée sur les déplacements est utilisée, dans laquelle les déformations et la flexion attendues de la plaque sont décrites à l’aide de fonctions polynomiales satisfaisant les conditions d’encastrement des bords. Ce choix permet de réduire le coût de calcul tout en conservant une précision suffisante pour prévoir la réponse structurelle non linéaire. En utilisant la méthode énergétique de Ritz, il est possible de dériver des expressions simples de la charge critique de flambement thermique ainsi que la relation entre la charge et la déflexion après flambement pour la microplaque circulaire FG. Les résultats numériques montrent que les variations de l’indice de fraction volumique, du paramètre de longueur caractéristique du matériau et des paramètres géométriques influencent fortement la résistance au flambement de la structure FGM ainsi que son comportement post-flambement. Ces résultats fournissent des informations importantes et constituent un guide utile pour la conception de structures microscopiques à gradient de propriétés soumises à des sollicitations thermo-mécaniques.

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DOI : 10.5802/crmeca.353
Keywords: FGM circular microplate, Nonlinear thermal buckling, Von Kármán nonlinearity, Modified couple stress theory, Size-dependent effect, Post-buckling behavior
Mots-clés : Microplaque circulaire FGM, Flambement thermique non linéaire, Non-linéarité de von Kármán, Théorie modifiée des contraintes de couple, Effet d’échelle, Comportement post-flambement

Duc Nguyen Minh  1   ; Thom Do Van  1   ; Minh Phung Van  1

1 Department of Solid Mechanics, Faculty of Mechanical Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet Street, Nghia Do Ward, Hanoi, 100000, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Duc Nguyen Minh; Thom Do Van; Minh Phung Van. An analytical method for nonlinear thermo-mechanical buckling evaluation of functionally graded circular microplates. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 293-312. doi: 10.5802/crmeca.353
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     publisher = {Acad\'emie des sciences, Paris},
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