Modeling of Functionally Graded Material Shells

¹ Hassan II University of Casablanca, Laboratoire d’Ingénierie et Matériaux LIMAT, B.P 7955 Sidi Othman, Casablanca, Morocco
² Central Casablanca, Centre de Recherche Systèmes Complexes et interactions, Ville Verte, Bouskoura, 27182, Morocco
³ Ningxia University, School of Mathematics and Statistics, Yinchuan 750021, China
⁴ Hassan First University of Settat, Ecole Nationale des Sciences Appliqueès, LAMSAD Laboratory, Berrechid 26100, Morocco

^* Corresponding author: khalile.siham@gmail.com

Abstract

In this research, we propose an algorithm to study the buckling of thin Functionally Graded Material (FGM) shells, utilizing a novel implementation of the asymptotic numerical method (ANM). Our approach integrates a three-step process: representation of variables and loading conditions through a truncated Taylor series, discretization using the finite element method (FEM), and advancement via a continuation method. This method is particularly effective for tracking the solution curve through systematic matrix inversion and tolerance adjustments. By applying this robust algorithm within the framework of Kirchhoff-Love theory, we analyze how the properties of FGM shells vary smoothly from metal at the base to ceramic at the surface, crucial for applications in aeronautics and civil engineering where stability under load is paramount. The results are validated against the Abaqus industrial code, demonstrating the accuracy of our model. Furthermore, we detail the impact of the volume fraction index on the load-displacement behavior and structural deformations, providing valuable insights for enhancing the design and safety of these critical structures.