A. Arbind

MODIFIED COUPLE STRESS-BASED THIRD-ORDER THEORY FOR NONLINEAR ANALYSIS OF FUNCTIONALLY GRADED BEAMS

A microstructure-dependent nonlinear third-order beam theory which accounts for through-thickness power-law variation of a two-constituent material is developed using Hamiltons principle. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Karman nonlinear strains. The modified couple stress theory contains a material length scale parameter that can capture the size effect in a functionally graded material beam. The influence of the material length scale parameter on linear bending is investigated. The finite element models are also developed to determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on linear and nonlinear response.

On Gradient Elasticity and Discrete Peridynamics with Applications to Beams and Plates

In this paper two different nonlinear elasticity theories that account for (a) geometric nonlinearityand (b) microstructure-dependent size effects are revisited to establish the connection betweenthe two theories. The first theory is based on modified couple stress theory of Yang et al. [1]and the second one is based on Srinivasa–Reddy gradient elasticity theory [2]. The modified couplestress theory includes a material length scale parameter that can capture the size effect in a material.The gradient elasticity theory was developed for finitely deforming hyperelastic cosserat continuum,and it is a generalization of small deformation couple stress theories. The Srinivasa–Reddy theorycontains, as a special case, the first one. These two theories are used to derive the governing equationsof beams and plates. In addition, a discrete peridynamics idea as an alternative to the conventionalperidynamics is also presented.

Nonlinear Analysis of Plates with Rotation Gradient–Dependent Potential Energy for Constrained Microrotation

AbstractIn this study, the weak-form finite-element model has been developed for bending of plates considering the rotation gradient–dependent potential energy along with the conventional strain en...