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We consider wave propagation problems in 2D unbounded isotropic homogeneous elastic media, with rigid boundary conditions. For their solution, we propose and compare two alternative numerical approaches, both obtained by coupling the differential equation with the associated space-time boundary integral equation. The latter is defined on an artificial boundary, chosen to surround the (bounded) exterior computational domain of interest. The integral equation defines a boundary condition which is non-reflecting for incoming and also for outgoing waves. In both approaches, the differential equations are discretized by applying a finite element method combined with the Crank Nicolson time marching scheme, while the discretization of the integral equation is obtained by coupling a time convolution quadrature with a space collocation boundary element method. The construction of the two approaches is described and discussed. Some numerical tests are also presented. [ABSTRACT FROM AUTHOR]

The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields over large subdomains, and also for its flexibility in terms of spatial discretization, enabling us to define subdomains with arbitrary numbers of boundary elements and hanging nodes. The former, however, is not readily attainable in the cases whose closed-form solution does not exist. Those cases invoke the use of a cascade of expensive computations for the recovery of inner-subdomain solution fields, leaving one of the main assets of the method almost unused. As a remedy, we propose a new solution scheme by which the interior fields of subdomains can be easily recovered so that the full potential of the scaled boundary finite element method can be harvested. No auxiliary variables are introduced to the global algebraic system and the dimensions of the matrices remain constant. Most of the computations are carried out prior to the global algebraic system assembly, and in a completely decoupled manner on the element level, rendering the introduced method to be embarrassingly parallelizable. The inner-subdomain information is not required for the solution process and it can be computed locally for the selected regions and subdomains, also using parallel computing. [ABSTRACT FROM AUTHOR]

3D dynamic interaction of two adjacent elastic foundations embedded in a finite layered soil region rested in a homogeneous elastic isotropic half‐space with a transient dynamic source is studied. The hybrid computational model, the corresponding numerical scheme and the accompanied software are developed, verified and inserted in detail parametric study. The hybrid approach is based on (a) finite element method (FEM) describing the scattered wave field in a finite layered soil profile with two foundations; (b) boundary element method (BEM) considering waves radiating from a dynamic transient source in elastic semi‐infinite range. The aim is to propose an efficient hybrid methodology for evaluation of the dynamic response of a foundation‐soil‐foundation system, taking into account (a) the whole wave path from the dynamic source, through the layered soil region, till the underground structures; (b) the damage state of the geological material. The BEM model is based on the 3D elastodynamic fundamental solution in Fourier domain and it is applied in order to obtain frequency‐dependent stiffness matrix and load vector of the dynamically active semi‐infinite geological zone. Once the BEM model is formulated, it is inserted as a macro‐finite element in the FEM software package ABAQUS. The frequency‐dependent FEM model describing the wave field in finite layered soil profile with two elastic foundations is realized by ABAQUS. Solutions in time domain are obtained through application of the inverse fast Fourier transform. As a final result an efficient hybrid model comprising all in one: dynamic (seismic or other type) source‐homogeneous elastic half‐space‐finite heterogeneous by layers and foundations soil profile, is presented. Parametric study illustrating the sensitivity of the dynamic field to key factors such as the type and properties of the load, the soil layering, the material properties of the far‐ and near‐field soil regions, the damaged state of the geological material and the foundation‐soil‐foundation interaction is shown and discussed. [ABSTRACT FROM AUTHOR]

This paper deals with seismic response evaluation of a finite multilayered geological structure with non-parallel boundaries rested on semi-infinite elastic half-plane subjected to transient seismic wave. The hybrid modelling approach is applied. It is based on the decomposition of the whole domain under consideration into two subregions: a finite-sized near-field zone and the open semi-infinite far-field region. The near-field range is presented by a finite geological profile, which is heterogeneous due to non-parallel layering. The far-field region is semi-infinite elastic isotropic homogeneous medium where the finite layered structure is located. An efficient 2D hybrid computational tool based on the boundary element method (BEM) for the far-field zone and the finite element method (FEM) for the finite layered domain is developed and verified in frequency domain. The BEM model of the seismically active far-field zone is inserted as a macro-finite element (MFE) in the FEM commercial program ANSYS. The hybrid model is of the FEM hosted type, where the boundary element domain (BED) is converted into macro-finite element, the nodal forces along the interface between two zones are expressed through the BED nodal tractions and the entire BEM formulation is converted to FEM-like approach. This hybrid model is applied for modelling of a real geological profile of the main wall of the "Liulyakovitsa" tailing pond, near Panagyurishte town, Bulgaria. Simulation results are given in the form of free surface synthetic seismograms stemming from the real seismic signals recorded at bedrock so as to establish the tailing pond's seismic response. [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]

• 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]

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes. [ABSTRACT FROM AUTHOR]