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In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed. [ABSTRACT FROM PUBLISHER]

In this work, the influence of uniaxial and biaxial nonuniform edge loads on buckling characteristics of composite laminates with and without cutout is investigated by using a finite element method. Furthermore, this investigation addresses the effects of different degree of edge restraints on buckling analysis. Regarding this, a nine node heterosis plate element has been adapted by employing the effects of shear deformation and rotary inertia. The influence of different parameters, such as ply-orientations, nonuniform edge loads, boundary conditions, and cutout sizes, has been considered and studied in detail. It is clearly illustrated that cutout sizes under different loading conditions have remarkable effects on buckling behavior of composite laminates. [ABSTRACT FROM AUTHOR]

A size-dependent finite element (FE) formulation including surface free energy effect is developed in this article to study the post-buckling behavior of nanofilms under the action of thermal loads. The Gurtin-Murdoch surface elasticity theory is utilized to consider the surface effects. Moreover, the principle of virtual work is used so as to derive the equilibrium equations. The proposed FE formulation is based on the first-order shear deformation theory (FSDT). The von Kármán nonlinear relations are also employed to take the geometric nonlinearity into account. After deriving the FE equations, the resulting set of parameterized non-linear equations is solved using the pseudo arc-length continuation algorithm, and bifurcation diagrams of nanofilms are obtained. Selected numerical results are presented for the influences of surface stress on the thermal post-buckling characteristics of nanofilms subject to different types of boundary conditions. [ABSTRACT FROM PUBLISHER]

Where deflections of thick plates are concerned, sufficient studies have been performed on circular and rectangular plates using first-order shear deformation theory (FSDT). Less attention, however, has been placed on the use of higher-order theories and plates of other shapes. This article proposes a deflection model for a simply supported and under uniformly loaded equilateral triangular plate that fulfils the third-order shear deformation theory (TSDT). Comparison of maximum plate deflections using this exact TSDT model with the FSDT and the simplified TSDT models reveals that the former exhibits better correlation agreement with the exact TSDT. Using the plate deflection from the exact TSDT, a refined shear correction factor, which is a function of Poisson's ratio, relative thickness, and location on plate, is extracted for the FSDT model. Results suggest that the usual shear correction model of 5/6 in Mindlin plates is highly accurate when dealing with moderately thick triangular plates made from negative Poisson's ratio materials, while the prescription of the refined shear correction factor obtained herein is advised for very thick triangular plates made from large Poisson's ratio materials. The results avail an FSDT deflection model for very thick triangular plates with the accuracy of exact TSDT. [ABSTRACT FROM PUBLISHER]

Shear band formation and evolution is a predominant mechanism of deformation patterning in granular materials. Independent rotations of separate particles can affect the pattern formation by adding the effect of rotational degrees of freedom to the mechanism of instability. We conducted 2D physical modelling where the particles are represented by smooth steel discs. We use the digital image correlation in order to recover both displacement and independent rotation fields in the model. We performed model calibration and determine the values of mechanical parameters needed for a DEM numerical modelling. Both mono- and polydisperse particle assemblies are used. During the loading, the deformation pattern undergoes stages of shear band formation followed by its dissolution due to recompaction and particle rearrangement with the subsequent formation of multiple shear bands merging into a single one and the final dissolution. We show that while the average (over the assembly) values of the angles of disc rotations are insignificantly different from zero, the particle rotations exhibit clustering at the mesoscale (sizes larger than the particles but smaller than the whole assembly): monodisperse assemblies produce vertical columns of particles rotating the same direction; polydisperse assemblies 2D form clusters of particles with alternating rotations. Thus, particle rotations produce a structure on their own, a structure different form the ones formed by particle displacements and force chains. This can give a rise to moment chains. These emerging mesoscopic structures – not observable at the macroscale – indicate hidden aspects of ‘Cosserat behaviour’ of the particles. [ABSTRACT FROM PUBLISHER]