The present work is an extension of the previous one [1] which dealt with error analysis of a finite volume scheme of first order (both in time and space) for second order hyperbolic equations on general nonconforming multidimensional spatial meshes introduced recently in [4]. The aim of this contribution is to get some second–order time accurate schemes for a finite volume method for second or...

A general approach to the dimension reduction of non-linear finite element models of solid dynamics is presented. It is shown how for the Newmark implicit discretization in time the computationally most expensive phase in the equilibrium iteration, namely the solution of the system of linear equations for displacement increments, can be formulated in an approximation basis of much reduced dimen...

The paper deals with a numerical analusis for the seismic response of reinforced concrete structures containing cable elements. The cable behaviour is considered as nonconvex and nonmonotone one and is described by generalized subdifferential relations including loosening, elastoplastic fracturing etc. effects. The problem is treated incrementally by double discretization: in space by finite el...

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with ...

This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the...

Abstract In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set equations motion approximations are transformed into their corresponding equivalents. dynamic system is then represented by one algebraic equation only. This projected coupled pair equations, which so...

In this paper, we numerically study porosity problems with three different dissipation mechanisms. The root behavior is analyzed for each case. Then, by using the finite element method and Newmark-β scheme, fully discrete approximations are introduced some numerical results described to show energy evolution depending on viscosity coefficient.