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The numerical solution of the elastodynamic problem with kinematic boundary conditions is considered using mixed finite elements for the space discretization and a staggered leap-frog scheme for the discretization in time. The stability of the numerical scheme is shown under the usual CFL condition. Using the general form of Robin-type boundary conditions some cases of debonding and the resulting acoustic emission are studied. The methodology presented finds applications to geophysics such as in seismic waves simulation with dynamic rupture and energy release. In this paper, we focus on problems of fracture occurring at the interface of composite materials. Our goal is to study both the mechanism of crack initiation and propagation, as well as the acoustic emission of the released structure-borne energy which may be used in structural health monitoring and prognosis applications. [ABSTRACT FROM AUTHOR]

Within the framework of linear two-dimensional elastodynamics, stress wave intensity attenuators are studied under material and boundary condition discontinuities collectively. The influence of various parameters on the efficiency of stress wave attenuators is investigated thoroughly and a comprehensive understanding of the response is developed under dynamic loadings for a wide range of frequencies. In particular, the effect of in-plane and out-of-plane dimensions, incident wave frequencies (wavelength), rigidity of the host structure, and impedance mismatch between different layers have been examined. The dependence of stress wave attenuator efficiency and robustness are found to be a complex function of all relevant parameters, and performance is observed to vary significantly for various combinations. To illustrate the significance of combined effects of various parameters on the potential efficiency of the stress wave intensity attenuators, an optimization problem is solved. An optimal material set-up of a 12-layered structure, subjected to transient loadings with varying durations and wide range of frequency contents, is presented. A coupled genetic algorithm-finite element methodology is developed specifically for the optimal design of layered structures. This methodology is highly suitable for investigating the solution space that is too large to be explored by an exhaustive parametric study. The results of the optimal designs evidently show that the efficiency of the stress wave attenuators depends significantly on the duration of transient loading, and high efficiency can be attained for short durations. [ABSTRACT FROM AUTHOR]

In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort. [ABSTRACT FROM AUTHOR]

We evaluated the performance of the classical and spectral finite element method in the simulation of elastodynamic problems. We used as a quality measure their ability to capture the actual dispersive behavior of the material. Four different materials are studied: a homogeneous non-dispersive material, a bilayer material, and composite materials consisting of an aluminum matrix and brass inclusions or voids. To obtain the dispersion properties, spatial periodicity is assumed so the analysis is conducted using Floquet-Bloch principles. The effects in the dispersion properties of the lumping process for the mass matrices resulting from the classical finite element method are also investigated, since that is a common practice when the problem is solved with explicit time marching schemes. At high frequencies the predictions with the spectral technique exactly match the analytical dispersion curves, while the classical method does not. This occurs even at the same computational demands. At low frequencies however, the results from both the classical (consistent or mass-lumped) and spectral finite element coincide with the analytically determined curves. [ABSTRACT FROM AUTHOR]