We consider the numerical solution of nonlocal constrained value problems associated with linear nonlocal diffusion and nonlocal peridynamic models. Two classes of discretization methods are presented, including standard finite element methods and quadrature based finite difference methods. We discuss the applicability of these approaches to nonlocal problems having various singular kernels and...

We consider the Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension. Due to Cattaneo’s law, replacing Fourier’s law for heat conduction, the system is hyperbolic. We first investigate the local well-posedness as a strictly hyperbolic system, and then discuss the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness. For the g...

This paper investigates the natural frequency, steady-state resonance and stability for the transverse vibrations of a nanobeam subjected to a variable initial axial force, including axial tension and axial compression, based on nonlocal elasticity theory. It is reported that the nonlocal nanoscale has significant effects on vibration behavior, which results in a new effective nonlocal bending ...

We prove global existence for a simplified model of one-dimensional thermoelasticity. The governing equations satisfy the balance of momentum and a modified energy balance. The application we wish to study by investigating this model are shapememory alloys. They are a prominent example of solids undergoing structural phase transitions. A characteristic feature of these materials is that several...

We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...

We present local density approximation augmented by the Hubbard-type correction calculations of high-temperature elastic properties of bridgmanite with composition (Mg(1−x)Fe x )SiO3 for 0≤×≤0.125. Results of elastic moduli and acoustic velocities for the Mg end-member (x=0) agree very well with the latest high-pressure and high-temperature experimental measurements. In the iron-bearing system,...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

in this article, an analytical solution is developed to study the free vibration analysis offunctionally graded rectangular nanoplates. the governing equations of motion are derived basedon second order shear deformation theory using nonlocal elasticity theory. it is assumed that thematerial properties of nanoplate vary through the thickness according to the power lawdistribution. our numerical...