This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler–Bernoulli beam resting on fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, parameter considering elastic stress gradient field material length scale strain field. Additionally, von Karman strain–displacement relation is used describe geometrical ...

The paper deals with the problem of nonlocal generalization of constitutive models such as microplane model M4 for concrete, in which the yield limits, called stress–strain boundaries, are softening functions of the total strain. Such constitutive models call for a different nonlocal generalization than those for continuum damage mechanics, in which the total strain is reversible, or for plasti...

We prove Dirichlet’s principle for a nonlocal p-Laplacian system which arises in the nonlocal setting of peridynamics when p = 2. This nonlinear model includes boundary conditions imposed on a nonzero volume collar surrounding the domain. Our analysis uses nonlocal versions of integration by parts techniques that resemble the classical Green and Gauss identities. The nonlocal energy functional ...

In the present work, thermo-electro vibration of the piezoelectric nanoplates resting on the elastic foundations using nonlocal elasticity theory are considered. In-plane and transverse displacements of the nanoplate have been approximated by six different modified shear deformation plate theories considering transverse shear deformation effects and rotary inertia. Moreover, two new distributio...

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei (Comm Pure Appl Math 62(4):501–564, 2009) for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier– Stoke...

In this paper, a scalar peridynamic model is analyzed. The study extends earlier works in the literature on nonlocal diffusion and nonlocal peridynamic models to include a sign changing kernel. We prove the well-posedness of both variational problems with volume constraints and time-dependent equations with or without damping. The analysis is based on some nonlocal Poincaré type inequalities an...

In this work we model and numerically analyse, the dynamics of a single species food-limited model with delay, we focus in the asymptotic behavior. We use the sub and supersolutions method to provide some numerical simulations of the asymptotic behavior for several cases, autonomous, periodic, almost periodic concluding with a model that incoporates nonlocal delays as well as a continuous delay...

Multianticipative driving behavior, where a vehicle reacts to many vehicles in front, has been extensively studied and modeled using a car-following (i.e., microscopic) approach. A lot of effort has been undertaken to model such multianticipative driving behavior using a macroscopic approach, which is useful for real-time prediction and control applications due to its fast computational demand....

The scale effect of carbon nanotubes (CNTs) in the macro CNT-reinforced composites (CNTRCs) is analyzed, and free vibration characteristics a composite beam resting on viscoelastic foundation were studied. By combining nonlocal theory with Eshelby–Mori–Tanaka (EMT) method, EMT constitutive equation considering CNTs CNTRCs proposed. Based Timoshenko theory, governing equations corresponding boun...

We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the out...