Part 1. Three-dimensional theory 3 Outline 3 1.1. Notation, definitions, and some basic formulas 3 1.2. Equations of equilibrium 5 1.3. Constitutive equations of elastic materials 8 1.4. The equations of nonlinear and linearized three-dimensional elasticity 11 1.5. A fundamental lemma of J.L. Lions 13 1.6. Existence theory in linearized three-dimensional elasticity 14 1.7. Existence theory in n...

In this paper, a size-dependent formulation for the Bernoulli-Euler beam is developed based on a new model of couple stress theory presented by Hadjesfandiari and Dargush. The constitutive equation obtained in this new model, consists of only one length scale parameter that is capable of capturing the micro-structural size effect in predicting the mechanical behavior of the structure. Having on...

The present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is ...

This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal elasticity theory. The nano-beam is sandwiched with two piezoelectric layers through it’s upper and lower sides. The electromechanical coupled equations governing the problem are derived based nonlocal theory considering to Euler-Bernoulli beam assumptions and based on the nonlocal piezoelectricity acco...

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal fo...

Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classic...

This paper studies the dynamic behavior of price elasticity and its effects on the overall profit. Although price elasticity has a significant effect on sales, its dynamics have not been examined so far in pricing models. In this paper, a simple pricing model is suggested in which, price elasticity is considered dynamic. The suggested pricing model is concerned with a monopolist that its object...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

A well known result from the non-linear theory of elasticity applied to spherical shells is that classical Mooney-Rivlin constitutive law may give either a monotonic or non-monotonic pressure-inflation response for finite deformation. Specifically, this determined by two factors: relative shell thickness, and $I_{1}$ $I_{2}$ contribution in M-R law. Here we consider how residual stress field af...

The present paper deals with the dynamic behavior of nano-column subjected to follower force using the nonlocal elasticity theory. The nonlocal elasticity theory is used to analyze the mechanical behavior of nanoscale materials. The used method of solution is the Differential Quadrature Method (DQM). It is shown that the nonlocal effect plays an important role in the vibrational behavior of nan...