Static and Dynamic Analysis of Functionally Graded Skew Plates Gulshan Taj 1 and Anupam Chakrabarti 2 Abstract: The static and dynamic analysis of functionally graded material (FGM) skew plates under mechanical load is studied. The FEM formulation based on a third-order shear deformation (TOSD) theory that does not require any shear correction factor is used in the analysis. The C 1 continuity requirement of the higher-order theory has been overcome in this study by adopting a C 0 continuous isoparametric Lagrangian element with seven degrees of freedom at each node. The Mori-Tanaka homogenization scheme is used to estimate the effective properties of the constituents, and it is assumed that mechanical properties vary according to a power-law distribution of the volume fraction of the constituents. The efficiency of the present model has been validated by comparing the results obtained with those available in the literature. The effects of skew angle, boundary conditions, volume-fraction exponent, loading conditions, aspect ratio, thickness ratio, and other parameters on deflection, natural frequency, and critical buckling load of functionally graded skew plates are reported for the first time based on TOSD that can serve as the benchmark for future research. DOI: 10.1061/(ASCE)EM.1943-7889.0000523. © 2013 American Society of Civil Engineers. CE Database subject headings: Finite element method; Vibration; Buckling; Plates; Skewness; Comparative studies. Author keywords: Functionally graded material skew plates; Vibration; Buckling. Introduction Functionally graded materials (FGMs) are a new class of com- posite materials that were developed in the Sendai area of Japan to address the problem of thermal shock observed in aerospace, nuclear, and other automotive industries. In FGMs, mechanical properties vary smoothly and continuously from one interface to the other (Fukui 1991). Typical FGMs have a ceramic component on one side of the structure that resists high temperatures, whereas the metal component on the other side prevents fracture due to thermal stresses. The mechanical properties are considered to be functions of position along the direction of the plate to achieve a desirable benefit of the material. Given their wide applications in aerospace and other engineering systems, it is necessary to un- derstand the static and dynamic characteristics of FGM skew plates under mechanical loads. A significant number of investigations based on first- and third- order shear deformation theories have been carried out to understand the static and dynamic behaviors of FGM plates (Praveen and Reddy 1998; Reddy 2000). Talha and Singh (2010) employed an iso- parametric Lagrangian finite element (FE) model with 13 degrees of freedom (DOFs) per node to study the static response and free vibration of FGM plates based on higher-order shear deformation theory. Wu and Li (2010) used a Reissner mixed variational theorem based on third-order shear deformation (TOSD) theory to study the static behavior of multilayered functionally graded plates under mechanical loads. Higher-order shear and normal deformable plate theory and a meshless local Petrov-Galerkin method were employed to analyze the static and dynamic deformations of FGM plates (Qian et al. 2004; Gilhooley et al. 2007). Lu et al. (2009) provided an semianalytical three-dimensional (3D) elasticity solution for ortho- tropic multidirectional functionally graded plates using the differential- quadrature method. Lee et al. (2009) and Woo and Meguid (2001) have conducted thermoelastic analysis of FGM plates subjected to in-plane loads and temperature fields. Abrate (2006) carried out extensive study on static, free-vibration, and buckling analyses of functionally graded plates, and he reported that natural frequencies of FGM plates are always proportional to those of homogeneous plates. Different plate theories have been employed to understand the bucking behavior of functionally graded plates under different types of loading conditions (Samsam Shariat et al. 2005; Samsam Shariat and Eslami 2007; Mahdavian 2009; Bodaghi and Saidi 2010; Ganapathi et al. 2006; Chun-Sheng Chen 2009). An ex- tensive amount of research also has been done based on meshless methods to study the vibration behavior of functionally graded plates (Zhao et al. 2009; Ferreira et al. 2006). Matsunaga (2008) presented the two-dimensional (2D) higher-order theory for free- vibration and buckling analysis of functionally graded plates. An analytical solution for free vibration of FGM plates based on higher-order shear deformation theory was proposed by Suresh Kumar et al. (2011). Uymaz and Aydogdu (2007) carried out vibra- tion analysis of FGM plates and used Chebyshev polynomials to ex- press displacement fields along with the Ritz method. Ebrahimi and Rastgo (2008) studied the free-vibration behavior of functionally graded circular plates integrated with piezoelectric material based on classical plate theory. Hosseini-Hashemi et al. (2011) presented the closed-form procedure based on the Reissner-Mindlin plate theory for free-vibration analysis of thick functionally graded rectangular plates. 1 Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India (corresponding author). E-mail: gulshantaj19@yahoo.co.in 2 Assistant Professor, Dept. of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India. E-mail: anupam1965@ yahoo.co.uk Note. This manuscript was submitted on February 13, 2012; approved on August 3, 2012; published online on August 15, 2012. Discussion period open until December 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the Journal of Engineering Mechanics, Vol. 139, No. 7, July 1, 2013. ©ASCE, ISSN 0733-9399/2013/ 7-848–857/$25.00. 848 / JOURNAL OF ENGINEERING MECHANICS © ASCE / JULY 2013 J. Eng. Mech. 2013.139:848-857. Downloaded from ascelibrary.org by INDIAN INST OF TECHNOLOGY - ROORKEE on 07/28/13. Copyright ASCE. For personal use only; all rights reserved.