Quasi-static and dynamic response of functionally graded viscoelastic plates

Free vibration analysis of viscoelastic plates with simultaneous calculation of natural frequency and viscous damping

SummaryBased on the one‐dimensional differential matrix derived from the Lagrange series expansion, the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials. In this paper, the formulation of the Lagrange finite block method with boundary type in the strong form is presented and applied to non‐conforming contact problems for the functionally graded materials subjected to either static or dynamic loads. The first order partial differential matrices are only needed both in the governing equations and in the Neumann boundary condition. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate of global system to the normalized coordinate with eight seeds. Time dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin's inversion method is applied to determine all the physical values in the time domain. Conforming and non‐conforming contacts are investigated by using the iterative algorithm with full load technique. Illustrative numerical examples are given and comparisons have been made with analytical solutions. Copyright © 2015 John Wiley & Sons, Ltd.

On stability and convergence of semi-Lagrangian methods for the first-order time-dependent nonlinear partial differential equations in 1D

Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders

By using a non-linear 3-D elastic waves real-time expert system, the new theory of “ Non-linear Real-Time Expert Seismology ” is investigated, for the exploration of the on-shore and off-shore petroleum and gas reserves all over the world. Such a highly innovative and groundbreaking technology is working under Real Time Logic for searching the on-shore and off-shore hydrocarbon reserves developed on the continental crust and in deeper water ranging from 300 to 3000 m, or even deeper. Consequently, this real-time expert system, will be the best device for the exploration of the continental margin areas (shelf, slope and rise) and the very deep waters, as well. The proposed modern technology can be used at any depth of seas and oceans all over the world and for any depth in the subsurface of existing oil reserves. Beyond the above, the various mechanical properties of rock regulating the wave propagation phenomenon appear as spatially varying coefficients in a system of time-dependent hyperbolic partial differential equations. The propagation of the seismic waves through the earth subsurface is described by the wave equation, which is then reduced to a Helmholz differential equation. Furthermore, the Helmholtz differential equation is numerically evaluated by using the Singular Integral Operators Method (S.I.O.M.). Several properties are further analyzed and investigated for the wave equation. Finally, an application is proposed for the determination of the seismic field radiated from a pulsating sphere into an infinite homogeneous medium. Thus, by using the S.I.O.M., then the acoustic pressure radiated from the above pulsating sphere is determined. Key word s : Non-linear real-time expert seismology; Singular integral operators method (S.I.O.M.); Time-dependent hyperbolic partial differential equations; Oil and gas reserves; Petroleum reservoir engineering; Helmholtz differential equation; Real-time expert system; Wave equation

In this manuscript, we investigate the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with fractional Brownian motion and memory in Hilbert space. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate our results.

The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations

Adherence boundary conditions for time dependent partial differential equations, via Chorin algorithm, can be reduced to a parabolic problem with Robin–Fourier boundary conditions in the three-dimensional context. In the spirit of panel methods, one establishes an integral formulation whose key point is the estimation of the potential density, introducing a kind of panel method for tangential kinematic boundary conditions. This paper discusses explicit estimations of this density in the general case of an arbitrarily shaped three-dimensional body, which leads to a fast numerical scheme. An error analysis is also provided, involving body smoothness, the Hölder exponent of the density, and whether the body presents torsion or not.

In this article we propose a general procedure that allows us to determine both the number and type of boundary conditions for time dependent partial differential equations. With those, well-posedness can be proven for a general initial-boundary value problem. The procedure is exemplified on the linearized Navier--Stokes equations in two and three space dimensions on a general domain.

Model order reduction for a linearized robust PDE constrained optimization.

Time dependent partial differential equations are often solved using algorithms which parallelize the solution process in the spatial domain. However, as the number of processors increases, the parallel efficiency is limited by the increasing communication/computation ratio. Recently, several researchers have proposed algorithms incorporating time domain parallelism in order to increase efficiency. In this paper we discuss a class of such algorithms and analyze it rigorously.

Non-isothermal flow of a Johnson–Segalman liquid in a lubricated pipe with wall slip

Mean field games with congestion

A residual based error estimate for Leja interpolation of matrix functions

Wong–Zakai approximation for the stochastic Landau–Lifshitz–Gilbert equations