This article focuses on studying the nonlinear vibration of functionally graded (FG) curved nanobeams resting Pasternak-Winkler elastic foundation based nonlocal strain gradient theory along with first-order shear deformation beam (FSDBT) considering von-Kármán hypothesis. The Hamilton principle is applied to extract three motion equations and Galerkin method (GM) utilized spatially reduce diff...

We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. first prove global existence of evolution variational inequality solution with general initial data using gradient flow structure. Then monotone data, we subdifferential associated convex functional is indeed single-valued, which gives higher regularities solution. Particularly, regula...

The expressions for the free energy in two recent formulations of strain gradient plasticity are extended to include the locked-in strain energy around statistically stored dislocations. This is accomplished by using the strain dependent factor h(ep), which represents the fraction of the rate of plastic work converted into heat in accordance with the latent heat measurements from classical meta...

In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories render displacement, slope and curvature as degrees of freedom for an Euler-Bernoulli beam. A generalize scheme is presented herein to implementation the mult...

Calibration of scanners and cameras usually involves measuring the point spread function (PSF). When edge data is used to measure the PSF, the differentiation step amplifies the noise. A parametric fit of the functional form of the edge spread function (ESF) directly to the measured edge data is proposed to eliminate this. Experiments used to test this method show that the Cauchy functional for...

It is well known that glassy polymer nanocomposites (PNC) exhibit heterogeneous mechanical properties, with a distinct polymer/nanoparticle (NP) interfacial region. The interphase rigidity in particular can significantly influence the overall response of PNCs. Continuum theories typically describe behavior such to depend only on deformation and, thus, they discard strong internal gradients with...