A two dimensional deformation due to internal heat source in a thermoelastic solid with microtemperatures under the dependence of modulus of elasticity and thermal conductivity on reference temperature has been studied. A mechanical force of constant magnitude is applied at the free surface of thermoelastic half space. The normal modes technique has been applied to obtain the exact expressions ...

In this paper, the dynamic characteristics of clamped-clamped silicon microbeam subjected to electrostatic excitation and mechanical shock is investigated. The Euler-Bernoulli beam model based on the modified couple stress theory with von Kármán geometric non-linearity is utilized in theoretical formulation. Afterwards, squeeze-film damping effects of microstructures for small amplitude vibrati...

in classical mechanics, considering hook’s law stress is a linear function of strain. while in strain gradient theory stress is a function of strain and strain differentials. in this paper, novel formulation relating stress and strain and also new boundary conditions are derived based on minimum potential energy principle. in strain gradient theory a length coefficient parameter is defined. thi...

The modeling of the elastic properties of granular or nanoscale systems requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which a microscopic justification of elasticity exists are (nearly) uniformly strained lattices. A microscopic theory of elasticity, as well as simulations, reveal that sta...

Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the a...

Uniform finite facets are frequently observed at grain boundaries (GBs) and are usually attributed to equilibrium stabilization by GB stress. We report calculations for an aluminum twin GB using density functional theory, the embedded-atom method, and continuum elasticity theory. These methods show that GB stress is much too small to stabilize finite facets, suggesting that the usual explanatio...

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...

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...