In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cros...

Three-dimensional (3D) cell cultures represent fundamental tools for the comprehension of cellular phenomena both in normal and in pathological conditions. In particular, mechanical and chemical stimuli play a relevant role on cell fate, cancer onset and malignant evolution. Here, we use mechanically-tuned alginate hydrogels to study the role of substrate elasticity on breast adenocarcinoma cel...

We revisit the asymptotic convergence properties – with respect to the thickness parameter – of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model ...

In this paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of icosahedral quasicrystals are determined. They are connected with 20 independent third-order elastic constants. By means of non-linear elasticity, phason stra...

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

Two bonding models i.e cumullenic and acetylenic models have been proposed to account for thebonding patterns in linear carbon clusters while the bonding patterns in cyclic and 3D geometrieS of theseclusters have remained ambiguous.This work presents the bonding patterns in various C4 and C5 pure clusters at MP2/aug-cc-pVTZ level oftheory. This subject is studied in the light of modern bonding ...

In this article free vibration of a Timoshenko nanobeam with variable cross-section is investigated using nonlocal elasticity theory within the scope of continuum mechanics. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width through the beam length with constant thickness. Analytical solution is achiev...

In this paper we study Steklov eigenvalues for the Lam\'e operator which arise in theory of linear elasticity. eigenproblem spectral parameter appears a Robin boundary condition, linking traction and displacement. To establish existence countable spectrum problem, present an extension Korn's inequality. We also show that proposed conforming Galerkin scheme provides convergent approximations to ...