Closed-Form Formulation for Bending Analysis of Functionally Graded Thick Plates

Journal of Solid Mechanics

مقاله 3، دوره 15، شماره 2، شهریور 2023، صفحه 160-173   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2023.1973962.1758

نویسندگان

M Shaban^{* 1}؛ M. J Khoshgoftar²

¹Mechanical Engineering Department, Bu-Ali Sina University, Hamadan, Iran

²Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran

چکیده

Due to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thick functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closed-form is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic thick plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for thick FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories.

کلیدواژه‌ها

Functionally graded material؛ Bending analysis؛ Elasticity approach؛ Thick plate؛ Exact solution

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