Search

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]

A virtual element framework for nonlinear elastodynamics is outlined within this work. The virtual element method (VEM) can be considered as an extension of the classical finite element method. While the finite element method (FEM) is restricted to the usage of regular shaped elements, VEM allows to use non‐convex shaped elements for the spatial discretization [1]. It has been applied to various engineering problems in elasticity and other areas, such as plasticity or fracture mechanics as outlined in [3, 4]. This work deals with the extension of VEM to dynamic problems. Low‐order ansatz functions in two and three dimensions, with elements being arbitrary shaped, are used in this contribution. The formulations considered in this framework are based on minimization of energy, where a pseudo potential is used for the dynamic behavior. While the stiffness‐matrix needs a suitable stabilization, the mass‐matrix can be calculated fully through the projection part. For the implicit time integration, Newmark‐Method is used. To show the performance of the method, various numerical examples in 2D and 3D are presented. [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]

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]

In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media. [ABSTRACT FROM AUTHOR]

In this article, we study the class of linear elastodynamic problems with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this article is the 'goal-oriented' proper orthogonal decomposition (POD)-Greedy sampling strategy within the RB approximation context. The proposed sampling strategy looks for the parameter points such that the output error approximation will be minimized by Greedy iterations. In estimating such output error approximation, the standard POD-Greedy algorithm is invoked to provide enriched RB approximations for the FE outputs. We propose a so-called 'cross-validation' process to choose adaptively the dimension of the enriched RB space corresponding with the dimension of the RB space under consideration. Numerical results show that the new goal-oriented POD-Greedy sampling procedure with the cross-validation process improves significantly the space-time output computations in comparison with the ones computed by the standard POD-Greedy algorithm. The method is thus ideally suited for repeated, rapid, and reliable evaluations of input-output relationships in the space-time setting. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 575-608, 2015 [ABSTRACT FROM AUTHOR]

Numerically stable and accurate time integration methods are important in structural dynamics. We propose such a method based on a mixed variational formulation of the underlying semi‐discrete equations of motion. The newly developed scheme relies on a specific combination of the so‐called continuous Galerkin (cG(k)) method and the discontinuous Galerkin (dG(k)) method. We refer to [2] for an introduction of the original cG(k) and dG(k) methods for ODEs (see also [1]). The mixed approach relies on polynomial approximations of degree k on the level of each time finite element. In particular we make use of hierarchical interpolation polynomials. The present approach is closely related to Hellinger‐Reissner type mixed variational formulations for elastodynamics. The mixed method yields implicit time‐stepping schemes with order of accuracy equal to 2k for the displacements and velocities. In addition to that, the method is capable of conserving the energy in the case of conservative mechanical systems. Numerical examples are presented which highlight the numerical properties of the newly proposed mixed approach. [ABSTRACT FROM AUTHOR]

It is well‐known that the classical Cauchy‐Boltzmann continuum, in spite of its simplicity, has its limitations, e.g. on the simulation of strain localization phenomena or size effects. For a remedy, one may resort to the so‐called generalized continuum theories, see e.g. [2] and references therein. Amongst others, we consider a class of higher order continua, namely the micromorphic continua, where the kinematics are enriched by means of a microstructure undergoing an affine micro deformation. As a drawback, the enriched kinematics lead to additional constitutive equations, increasing the number of material parameters, and therefore making the parameter identification procedure more involved. Here, the parameter identification is viewed as an inverse problem minimizing a least‐square function, see also [3] for a micropolar continuum. For simplicity, we restrict ourselves to a small strain theory. The increasing number of the degrees of freedom and the material parameters clearly motivates an application of adaptive methods. For an application on the direct micromorphic problems, we refer to [5]. Here for the inverse micromorphic problems, we follow the general ansatz by [1] for goal‐oriented error estimation and adaptivity, with which we control the spatial discretization errors of the finite element method. For illustration, numerical examples are presented. [ABSTRACT FROM AUTHOR]

In the framework of solving elastodynamic problems using a least-squares mixed finite element method (LSFEM) the implementation of a stress-velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first-order div - grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L2-norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two-dimensional problem. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]