Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

Abstract

In this paper, a size-dependent microscale plate model is developed to describe the bending, buckling and free vibration behaviors of microplates made of functionally graded materials (FGMs). The size effects are captured based on the modified strain gradient theory (MSGT), and the formulation of the paper is on the basis of Mindlin plate theory. The presented model accommodates the models based upon the classical theory (CT) and the modified couple stress theory (MCST) if all or two scale parameters are set to zero, respectively. By using Hamilton's principle, the governing equations and related boundary conditions are derived. The bending, buckling and free vibration problems are considered and are solved through the generalized differential quadrature (GDQ) method. A detailed parametric and comparative study is conducted to evaluate the effects of length scale parameter, material gradient index and aspect ratio predicted by the CT, MCST and MSGT on the deflection, critical buckling load and first natural frequency of the microplate. The numerical results indicate that the model developed herein is significantly sizedependent when the thickness of the microplate is on the order of the material scale parameters.

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

“…Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al 2014;Kim et al 2008;Hajlaoui et al 2017;Frikha and Dammak 2017;Asemi et al 2014 andAnsari et al 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.…”

A review of continuum mechanics models for size-dependent analysis of beams and plates

“…Ansari et al [364] developed a nonlinear strain gradient FSDT model to examine the postbuckling of FG annular microplates under thermal loading. Ansari et al [365] extended their previous work [363] to study the effect of elevated temperature on the bending, buckling and free vibration responses of FG microplates under various BCs. It is noted that Shenas and Malekzadeh [366] also studied the influence of elevated temperature on the free vibration of FG microplates under various BCs.…”

Nonlinear Dynamics Analysis of FGM Shell Structures with a Higher Order Shear Strain Enhanced Solid-Shell Element

“…In their analysis, the finite element equations based on the First order Shear Deformation Theory (FSDT) and the Plane Stress Assumption (PSA) were formulated. Recently, Ansari et al (2016) developed a nonclassical size-dependent plate model based on the modified strain gradient and the FSDT for the bending, buckling and free vibration analyses of microscale FG plates.…”