A general analytical solution of stresses around circular holes in functionally graded plates under various in-plane loading conditions

• Published in: Acta mechanica 2023-02, Vol.234 (2), p.671-691
• Main Authors: Khechai, Abdelhak, Belarbi, Mohamed-Ouejdi, Bouaziz, Ahmed, Rekbi, Fares Mohammed Laid
• Format: Article
• Language: English
• Subjects: Classical and Continuum Physics; Complex variables; Composite materials; Control; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Exact solutions; Finite element method; Functionally gradient materials; Heat and Mass Transfer; Laminated materials; Laminates; Load; Lumping; Material properties; Mechanical properties; Original Paper; Plates; Resultants; Solid Mechanics; Stress concentration; Stress distribution; Theoretical and Applied Mechanics; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-022-03413-1

In the present work, for the first time, a general analytical solution is developed and applied for functionally graded (FG) composite laminated plates with circular cutouts under various in-plane loading conditions. The stress resultants are expressed in a simple and elegant form. Firstly, the extension is achieved by first introducing arbitrarily oriented uniaxial, biaxial, and shear loading conditions into Greszczuk’s solution. Then, the expressions of effective moduli of unsymmetrical laminated plates, obtained by the layer lumping method, are introduced in the present solution. The FG plate can be discretized into a large number of skinny orthotropic layers such that a continuous gradation of their mechanical properties can be obtained. The material properties of the FG plate are graded continuously through the thickness direction according to a power-law function. The robustness and accuracy of the proposed analytical solution are ascertained by comparing its results with analytical findings using the complex variable method and those predicted by the finite element method (FEM). This comparison demonstrates a good level of agreement between these results. Results also show the validity of the proposed solution for both symmetric and non-symmetric FG-laminated plates. Moreover, a comprehensive parametric study is examined and discussed in detail to show the effects of various parameters such as gradation of the material properties and applied loading on the orientation of material axes and the stress distribution around the cutout. The present analytical findings can serve as a benchmark for future research on the modeling of multilayered perforated FG plates.