Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which ...

We find Feynman–Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

Abstract We develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action Feynman–Kac operator associated diffusion and first passage probabilities are obtained using matrix exponentials. show how compute exponentials efficiently prove that carefully designed scheme achieves second-order con...

The paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials, i.e., materials for which the yield limits soften as a function of the total strain. Both plasticity and damage models are considered. It is verified analytically in a simple way that the nonlocal integral-type model with de...

On the local systems hamiltonian in the weakly nonlocal Poisson brackets. Abstract We consider nonlocal field-theoretical Poisson brackets containing the operator of integration in the nonlocal part. The main attention is given to the nonlocal brackets of Hydrodynamic Type for which we introduce the Physical and Canonical forms. We use the Canonical form of these brackets for the investigation ...