This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies whic...

A general approach to the dimensional reduction of non-linear finite element models of solid dynamics is presented. For the Newmark implicit time-discretization, the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments. To deal with this, it is shown how the problem can be formulated in an approximation (Ritz) basis of much ...

The conventional method to evaluate earthquake induced permanent deformations of slopes is the one proposed by Newmark. In this paper, permanent displacement of slopes is studied using a combination of distinct element and finite difference methods and the results of these numerical evaluations are compared with those of the Newmark's approach. Several parameters involved, including peak ground...

Abstract. In this paper we consider the transmission problem of a material composed of three components; one of them is a Kelvin–Voigt viscoelastic material, the second is an elastic material (no dissipation), and the third is an elastic material inserted with a frictional damping mechanism. The main result of this paper is that the rate of decay will depend on the position of each component. W...

Continued fraction absorbing boundary conditions (CFABCs) are new arbitrarily high-order local absorbing boundary conditions that are highly effective in simulating wave propagation in unbounded domains. The current versions of CFABCs are developed for the non-dispersive acoustic wave equation with convex polygonal computational domains. In this paper, the CFABCs are modified through augmentati...

A mode III crack problem in a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ` and `′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived ass...

The main characteristics of the numerical methods for dynamic response analysis of single degree of freedom (SDOF) system in both frequency-domain and time-domain are briefly reviewed in this paper. Based on the uniform recursive formula, four methods (Central difference method, Newmark’s method, Ztransform method and Duhamel’s step integral method) are systematically studied. The advantages, d...

Generalized-α time integration methods were originally designed for large scale problems in structural mechanics [1] but may be used as well for constrained systems of moderate dimension that are typical of multibody dynamics [2]. For more than a decade, the method has been used successfully in industrial simulation software that is based on a finite element approach in multibody dynamics [3]. ...

This practice and experience paper describes a robust C++ implementation of several nonlinear solid 3D deformable object strategies commonly employed in computer graphics, named the Vega FEM simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint-Venant Kirchhoff FEM model, mass-spring system, and invertible FEM models: neo-Hookean, Saint-Venant Kirchh...

In this paper, the development of a large-displacement large-strain 3-D finite element model of the vocal fold is reported. A fold is discretized into 720 8-node brick elements with a total of 1001 nodes and 3003 displacement degrees of freedom. The structure has realistic dimensions and geometry. The model includes geometric and material nonlinearities. The geometric nonlinearity appears in th...