in this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. the timoshenko beam theory is applied instead of the classical euler-bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. t...

We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly represent many commonly engineered shapes, suc...

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...

It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to infinitely many axioms, and countable model the Löwenheim–Skolem theorem. This paper presents axioms one accept get rid of these features. For matter, some twenty are formulated in non-classical first-orde...

Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links. Herein, we consider an incompressible and flat elastomer film of an axisymmetric shape confined between two large hard co-planar substrates, with the axis of t...

Composite material properties are dependent on their microstructure. To adequately model these microstructural effects, a formulation of elasticity that accounts for effects must be considered. Size-dependent behaviour is an inherent property such materials, resulting in need non-classical continuum theories adequate characterization. A three-dimensional exponentially graded composite with deve...

In this paper, it is tried to find an approximate single layer equivalent for multi-layer graphene sheets based on third order non-local elasticity theory. The plates are embedded in two parameter Winkler-Pasternak elastic foundation, and also the thermal effects are considered. A uniform transverse load is imposed on the plates. Applying the non-local theory of Eringen based on third order she...

In classical elasticity theory the stress-field of a dislocation is characterized by $1/r$-type singularity. When such considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces order parameter, resulting in non-physical (and discretization-dependent) predictions interaction between dislocations and phase-, twin- or gra...

The Thermodynamics of linear irreversible processes is presented from a unified viewpoint. This provides a new and synthetic approach to the linear mechanics of deformation of solids, which includes as particular cases the classical theory of Elasticity, Thermoelasticity and Viscoelasticity. The first two sections constitute an introduction to the general concepts and principles of linear Therm...