Abstract We provide a fully nonlinear port‐Hamiltonian formulation for discrete elastodynamical systems as well structure‐preserving time discretization. The governing equations are obtained in variational manner and represent index‐1 differential algebraic equations. Performing an index reduction, one obtains the state space model, which features strains independent next to position velocity. ...

The problem of two cracks emanating from the same origin and propagating asymmetrically at different velocities in an elastic and isotropic solid is treated in this paper. An unbounded and otherwise undisturbed medium and a constant anti-plane loading at infinity were assumed. Techniques of self-similar elastodynamics were utilized in conjunction with analytic-function theory. Since a closed-fo...

In this paper, a mathematical model of rotor-bearing system is presented. The includes modal elastodynamics flexible rotor as well the in-plane radial dynamics bearing with outer race. Elastodynamics shaft utilises solution based on Green's function to provide computationally efficient approach. race modelled using Timoshenko beam theory. also detailed lubricated contact mechanics balls-to-race...

Friction loss in an internal combustion engine largely depends on elastohydrodynamic lubrication. The piston compression ring is a contributor to such parasitic losses the subsystem. complex elastodynamics of are responsible for transient and regime-altering film that affects lubrication liner contact conjunction. current paper will discuss radial, lateral deformation, axial twist, its effect p...

Molecular dynamics (MD) and experiments indicate that the high-speed dislocations dominate plasticity properties of crystal materials under high strain rate. New physical features arise accompanied with increase in dislocation speed, such as “Lorentz contraction” effect moving screw dislocation, anomalous nucleation, annihilation interaction. The static description is no longer applicable. elas...

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton’...

Abstract. We present an automated multilevel substructuring (AMLS) method for eigenvalue computations in linear elastodynamics in a variational and algebraic setting. AMLS first recursively partitions the domain of the PDE into a hierarchy of subdomains. Then AMLS recursively generates a subspace for approximating the eigenvectors associated with the smallest eigenvalues by computing partial ei...

Non-symmetric matrices may arise in the discretization of self-adjoint problems when a Petrov–Galerkin, collocation, or finite-volume method is employed. While these methods have been widely applied, this paper it shown that use non-symmetric incompatable with conservation energy elastodynamics. First, consistency between continuous forms momentum equation and examined. It linear equivalent to ...

We present a multiscale model for numerical simulation of dynamics of crystalline solids. The method couples nonlinear elastodynamics as the continuum description and molecular dynamics as another component at the atomic scale. The governing equations on the macroscale are solved by the discontinuous Galerkin method, which is built up with an appropriate local curl-free space to produce a coher...