The modeling of the elastic properties of disordered or nanoscale solids 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 microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first...

In this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). The small scale effect is taken into consideration based on nonlocal elasticity theory of E...

We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This obtained from simplification exact solution to continuum elasticity problem takes familiar form Hertz’ law, with difference being orientation-dependence material-specific modulus. rema...

In this study, the numerical solution of Fredholm integro–differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution u x ð Þ is represented in the form of series in the space W 2 2 ½a; bŠ. In the mean time, the n-term approxima te solution u n ðxÞ is o...

In this paper we established a Carleman estimate for the elasticity system with the residual stresses. As an application of this estimate we obtain exact controllability results for the same system with locally distributed control.

Abstract The present paper is devoted to the construction and comparative study of upwind methods as applied to the system of one-dimensional nonlinear elasticity equations. We derive a simple approach for building up exact solutions to the Riemann problem and construct a suite of test problems to assess numerical methods. Then we carry out the implementation and a systematic comparative study ...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...