We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear rod compressed by axial forces, and a planar circular ring subjected to uniform radial pressure on its outer perimeter. It is demonstrated that while spontaneous twi...

The problem of elastic stability of plates with square, rectangular, and circular holes as well as slotted holes was discussed. The existence of the hole reduces the deformation energy of the plate and it affects the redistribution of stress flow in comparison to a uniform plate which causes a change of the external operation of compressive forces. The distribution of compressive force is defin...

This work discusses the asymptotic behavior of a transmission problem on star-shaped networks of interconnected elastic and thermoelastic rods. Elastic rods are undamped, of conservative nature, while the thermoelastic ones are damped by thermal effects. We analyze the overall decay rate depending of the number of purely elastic components entering on the system and the irrationality properties...

Grain boundaries (GBs) represent one of the most important types of defects in solids and their instability leads to catastrophic failures in materials. Grain boundaries are challenging for theoretical studies because of their distorted atomic structure. Fortunately, quantum-mechanical methods can reliably compute their properties. We calculate and analyze (tensorial) anisotropic elastic proper...

This paper studies dynamic stability of functionally graded beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The Young’s modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing dynamic equation is established. The eff...

In this study, the torsional stability analysis is presented for thin cylindrical with the functionally graded (FG) middle layer resting on the Winker elastic foundation. The mechanical properties of functionally graded material (FGM) are assumed to be graded in the thickness direction according to a simple power law and exponential distributions in terms of volume fractions of the constituents...

In this paper we announce some new mathematical results on the stability of quasistatic paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle.A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously wit...

A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg nu...

In this study, the free vibration analysis of smart vibration control (SVC) systems based on Reddy – Levinson model and modified strain gradient theory is developed. This system consist of a micro beam at middle and two magneto-electro-elastic (MEE) composite micro beams at top and bottom which connected by enclosing elastic medium and simulated by Winkler and Pasternak foundation. The effects ...

A line with bending resilience (Hooke's Law constant b) but invariant length / (elastic line) is confined to a cylindrical surface of radius R. A clamp at its starting point requires its initial direction always to lie along the base circle, but its end point and direction are not constrained. The trajectory in which the elastic line lies for its entire length along the circle is then an equili...