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In recent years, there has been increasing attention on the development of non-destructive evaluation (NDE) methods using guided waves for long-length materials such as thin plates and pipes. The guided waves are capable of long-distance propagation in thin plates and pipes, and they exhibit properties such as multimodality and dispersion. These characteristics of the guided waves make inspection using guided waves challenging. In this study, we apply a 2-D elastodynamic time-reversal method to detect surface breaking cracks of a thin plate where guided waves are present. The finite element method (FEM) is used to calculate the scattered waves from surface breaking cracks and their corresponding time-reversal waves. We also employ topological sensitivity as an assessment index for detecting surface breaking cracks using the time-reversal method. As numerical examples, we demonstrate guided wave propagation, scattering, and the time-reversal wave propagation obtained by using the FEM. Finally, we present the results of surface breaking crack detection in a thin plate and discuss the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. This introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark- β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility. [ABSTRACT FROM AUTHOR]

An alternative approach to local transmitting boundaries for wave propagation problems in unbounded media is the application of the Perfectly Matched Layers (PML) around the finite region of interest. The PML model consists of absorbing layers that absorb almost perfectly propagating waves of all non-tangential angels-of-incident and all non-zero frequencies. This paper presents and verifies the concept of FE/PML methodology on the basis of two different formulations for the PML model in the context of time harmonic wave propagation analysis. A finite element numerical scheme is developed in which both PML formulations are successfully implemented as a macro-finite element in a commercial FEM program. Moreover, the parameters that influence the performance of the FE/PML method are extensively discussed and recommendations are given for the proper selection. Classical soil-structure interaction problems of surface or embedded rigid footing on homogeneous or heterogeneous half-plane containing layers and tunnels are investigated and the high accuracy and the easy implementation of FE/PML computational tool is demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: A hybrid model for evaluation of the seismic response of a complex poroelastic soil region containing an underground structure is developed. The model is based on an efficient computational technique unifying the benefits of both boundary element method (BEM) and finite element method (FEM). The mechanical model takes the whole seismic wave path from the seismic source, through the heterogeneous geological saturated deposits, till the local site with underground structure into consideration. The seismic load comprises time‐harmonic or transient P‐ and SV‐wave, thus covering the plane strain case. A viscoelastic isomorphism to Biot's equations of dynamic poroelasticity presented by Bardet's model is used. The direct BEM is applied for the unbounded part of the geological region, while the FEM is used for the local finite geological profile containing an underground structure. The BEM model is inserted as a macro finite element in commercial program ABAQUS used for solution of the entire problem. The simulation results reveal that the seismic response is sensitive to the site conditions such as the existence of surface relief and layers, to soil inhomogeneity and poroelasticity, and most importantly to the soil‐underground structure interaction. [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]

A new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain. Our method is based on equal-order interpolation discrete spaces for both the velocity (or displacement) and stress (or strain) tensor variables. The mixed form is derived using either the velocity/stress or velocity/strain pair of unknowns, the latter being instrumental in extensions of the method to nonlinear mechanics. The proposed approach works equally well on hexahedral or tetrahedral grids and, for this reason, it is suitable for time-domain engineering applications in complex geometry. The peculiarity of the proposed approach is the use of the rate form of the stress update equation, which yields a set of governing equations with the structure of a non-dissipative space/time Friedrichs’ system. We complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity (or displacement). Weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes, because they do not require dedicated data structures for the imposition of the boundary degrees of freedom, but, rather, they utilize the structure of the variational formulation. We also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi-domain simulations of heterogeneous media. A complete analysis including stability and convergence proofs is included, in the case of a space–time variational approach. A series of computational tests are used to demonstrate and verify the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers elastic wave propagation in seven-wire parallel strands. Under a transverse distributed force, the stress state of seven-wire strands is derived from the Hertzian theory, which is regarded as the prestress state for the dynamic analysis. According to the wave finite element method, the elastodynamic equation with prestress is discretized corresponding to harmonic wave motion. Firstly, the results are verified by the semi-analysis finite element method. Then, dispersion properties in seven-wire parallel strands are computed and compared to those of double cylindrical rods. Besides, the results from parallel strands and helical strands indicate that wave propagation in the former is significantly different from that in the latter. For the deep understanding of wave characteristics, the displacement vectors are used to identify the propagating modes. It is found that there is only one torsional-like mode which rotates with a twist center in the whole region. Meanwhile, it is found that the variation of prestress has large influence on the torsional-like mode for low frequencies, but little on propagating modes for high frequencies. In addition, there appears the notch frequency and the effect of prestress on it is discussed in detail. The notch frequency decreases with the rising of the prestress in a certain range. [ABSTRACT FROM AUTHOR]

The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems. [ABSTRACT FROM AUTHOR]

Error estimates for the space-semidiscrete finite element approximation of solutions to initial boundary value problems for linear, second-order hyperbolic systems in bounded polygons [ABSTRACT FROM AUTHOR]

This paper presents the investigation of guided wave propagation in prestressed double-cylinder structure. Based on Hertzian contact theory, the interaction between two rods is treated as a plane strain problem and the stress state in the waveguide under the static load is obtained. The stress state is considered as a prestressed configuration for elastic wave propagation analysis in double cylindrical rods. The elastodynamic equation of the prestressed structure is established with the updated Lagrangian formulation and the wave finite element (WFE) method. Firstly, the equation is verified by the application on an aluminum rod compared with the Euler–Bernoulli beam theory. Then, dispersion curves for single rod and double cylindrical rods without prestress are computed. Besides, at the dimensionless frequency 0.25 the propagating modes in double cylindrical rods are identified with mode shapes and displacement vectors. The guided waves in double rods consist of the modes different from single rod. Particularly, there exist two kinds of torsional-like modes, one of which has a twist center and the other has two. The latter changes obviously with the increase of prestress in the waveguide. At low frequencies, torsional-like modes are very sensitive to the variation of prestress; in addition, the prestress configuration has little influence on propagating modes at mid-frequencies but some at high frequencies. [ABSTRACT FROM AUTHOR]

For the first time, we have obtained accurate numerical solutions for wave propagation in inhomogeneous materials under impact loading. We have extended the earlier developed numerical approach for elastodynamics problems in homogeneous materials to inhomogeneous materials. The approach includes the two-stage time-integration technique with the quantification and the filtering of spurious oscillations, the special design of non-uniform meshes as well as includes the standard finite elements and the elements with reduced dispersion. Similar to wave propagation in homogeneous materials in the 1-D case, we have obtained very accurate results for composite and functionally graded materials using the linear elements with lumped mass matrix and the explicit central difference method. We have also shown that specific non-uniform meshes yield much more accurate results compared to uniform meshes. We have also shown the efficiency of the finite elements with reduced dispersion compared with the standard finite elements. [ABSTRACT FROM AUTHOR]

Abstract: For the first time, accurate numerical solutions to impact problems have been obtained with the standard, spectral, and isogeometric high-order finite elements. Spurious high-frequency oscillations appearing in numerical results are quantified and filtered out by the two-stage time-integration approach. We also use the 1-D impact problem with a simple analytical solution for the comparison of accuracy of the different space-discretization techniques used for transient acoustics and elastodynamics problems. The numerical results show the computational efficiency of the linear finite elements with reduced dispersion compared with other space-discretization techniques used for elastodynamics with implicit and explicit time-integration methods. We also show that for all space-discretization methods considered (except the linear finite elements with the lumped mass matrix), very small time increments which are much smaller than stability limit should be used in basic computations at large observation times. We should note that the size of time increments used at the filtering stage and calculated according to the special formulas defines the range of actual frequencies and can be used as a quantitative measure for the comparison and prediction of the accuracy of different space-discretization techniques. We also show that the new findings are valid in the multidimensional case. [Copyright &y& Elsevier]

For considering elastic seismic wave propagation in large domains, efficient absorbing boundary conditions are required with numerical modelling in finite domains. Since their introduction by Bérenger, the perfectly matched layers (PML) has become the state-of-the art method because of its efficiency and ease of implementation. However, for anisotropic media, theoretical analysis and numerical experiments show that the PML method is amplifying, that is it exhibits numerical instabilities. Numerical experiments can also exhibit numerical instabilities of the PML when dealing with long time simulations even for isotropic media, especially for finite element methods in unstructured grids. Recently, a new method, called SMART layers approach, has been proposed. This method is shown to be stable even for anisotropic media. The drawback is that the SMART layers are not perfectly matched. We have implemented this new approach in a discontinuous Galerkin method and we illustrate that this method does not exhibit numerical instabilities while PML do for an isotropic elastodynamic simulation. We show that this approach is also competitive with respect to the PML method in terms of efficiency and computational cost. [ABSTRACT FROM AUTHOR]

In this paper, a novel numerical methodology to deal with longitudinally invariant soil–structure interaction problems is proposed. The methodology uses the finite element method to model the structure and the singular boundary method to model the wave propagation in the soil, both formulated in the wavenumber–frequency domain. The versatility presented by the finite element method combined with the simplicity and computational efficiency of the singular boundary method results in a friendly, robust and accurate novel methodology to address the soil–structure interaction problems. The accuracy of the proposed method is assessed by comparing it against 2.5D FEM–MFS and 2.5D FEM–BEM approaches for two cases: a thin cylindrical shell and a star-like beam structure, both embedded in a full-space medium. Moreover, the computational efficiency of the proposed method is evaluated against 2.5D FEM–MFS and 2.5D FEM–BEM methods. In the final step, the applicability of the proposed method is studied through an example of a railway tunnel embedded in a layered half-space. The results presented in this work exhibit the advantages of the novel approach in modelling simplicity, numerical efficiency and robustness with respect to previous methodologies. • A novel methodology for 2.5D soil–structure interaction problems is developed. • As a novelty, a 2.5D SBM approach is used to model the soil. • A 2.5D FEM approach is used to model the structure. • This coupled 2.5D FEM–SBM is simpler and more efficient than previous approaches. • Its application for railway-induced vibration assessment is presented. [ABSTRACT FROM AUTHOR]

• A methodology to deal with soil-structure interaction problems is developed. • A 2.5D FEM-BEM approach is used to model the structure and the surrounding soil. • A 2.5D MFS approach is used to model the wave propagation through the soil. • Accuracy and efficiency of the method are checked against a 2.5D FEM-BEM approach. • A control technique is presented that minimises the MFS error. This paper is concerned with a new prediction methodology for longitudinally invariant soil-structure interaction problems in elastodynamics. The method uses the finite-element method to model the structure, the boundary-element method to model the local soil surrounding the structure and the method of fundamental solutions to model the wave propagation through the soil, all of them formulated in the two-and-a-half dimensional domain. The proposed method firstly obtains the displacement field on the soil-structure interaction boundary making use of a two-and-a-half dimensional coupled finite element–boundary element method. The method of fundamental solutions is used then as a post-processing tool to compute the response of the soil, increasing the computational efficiency of the overall methodology with respect to a methodology that considers the boundary element method as a model of the wave propagation through the soil. The accuracy of the methodology is verified for four calculation examples: a solid cylinder and a circular thin shell embedded in a homogeneous full-space and also in a homogeneous half-space. This verification is performed comparing the results with available analytical or semi-analytical solutions and a conventional two-and-a-half dimensional coupled finite element–boundary element method. Furthermore, a control methodology to increase the robustness of the method is presented. [ABSTRACT FROM AUTHOR]