Geometrically non linear analysis of functionally graded material plates using higher order theory

Abstract

The analysis of functionally graded material (FGM) plates with material variation parameter (n), boundary conditions, aspect ratios and side to thickness ratios are investigated using higher order displacement model. The derivation of equations of motion for higher order displacement model is obtained using principle of virtual work. The nonlinear simultaneous equations are obtained by Navier's method considering certain parameters, loads and boundary conditions. The nonlinear algebraic equations are solved using Newton Raphson iterative method. The numerical results are obtained for various boundary conditions, material variation parameter, aspect ratio, side to thickness ratio and compared with the available solutions. The effect of shear deformation and nonlinearity response of functionally graded material plate is studied.

Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution

“…Suresh [24], studied the non-linear bending of FGPs with an HSDT. However, both of the free traction condition, and the consistency of transverse shear strain energy on the displacement field were not satisfied.…”

Comparison of nonlinear Von Karman and Cosserat theories in very large deformation of skew plates

“…Derived equations have been solved by various numerical and analytical methods. Kumar et al (2011) and Shi (2007) worked on bending analysis of plates using higher order shear deformation plate theory (HSDT) and nonlinear Von Karman theory analytically. Tahouneh and Naei (2016a, b) investigated the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations.…”

Modelling of FGM plate

“…where h is the plate thickness, the subscripts 1 and 2 indicate the top z = h/2 and bottom z = −h/2 surfaces, E -Young's modulus, ν -Poisson's ratio, ρ is mass density, n -material parameter (Reddy, 2000;Efraim, 2011;Kim and Reddy, 2013;Kumar et al, 2011). Mokhtar et al (2009) use the following definition of the function p(z)…”