H. Antes

A boundary element procedure for transient wave propagations in two-dimensional isotropic elastic media

Abstract An integral formulation of the elastodynamic equations is presented and discretized to develope a numerical solution procedure. Constant space and linear time dependent interpolation functions are implemented. The expression obtained, the boundary element equations can be solved using a time-stepping scheme. An example is given for comparison with known solutions.

Efficient 3D modelling of vibration isolation by open trenches

Abstract Several vibration isolation methods are investigated using the 3D direct boundary element method. The results of the present numerical simulation are initially compared to an analytical and other numerical solutions. After this validation of the programme, a source isolation example from literature is investigated. A comparison between numerical results and measured data is finally presented for the case of vibration isolation by an open trench, that was constructed for full-scale testing. The influence of different parameters on the amplitude reduction, due to the presence of a trench, is studied.

Time domain boundary element method approaches in elastodynamics: a comparative study

Abstract Boundary Element Method formulations of elastodynamic problems under plane strain/plane stress conditions are presented. The formulations are performed in the time domain allowing consideration of loads with transient time variation. The advantages, efficiency and accuracy of the methods are depicted through comparative studies of a representative soil-structure interaction problem.

Fundamental solutions of products of Helmholtz and polyharmonic operators

Abstract Many problems in engineering lead to linear systems of partial differential equations. In certain cases the determinant of the system of partial differential operators reduces to a product of Helmholtz, metaharmonic (modified Helmholtz), or polyharmonic operators. Fundamental solutions of these systems are available in the mathematics literature. However, their existence is not necessarily well known to the engineering and boundary element community. This research note lists some of these solutions to facilitate their use.

Dynamic response analysis of rigid foundations and of elastic structures by Boundary Element procedures

Boundary element procedures are employed in the frequency as well as in the time domain to determine the dynamic response of rigid foundations and of flexible elastic structures when placed on or embedded in an elastic soil medium under plane strain conditions. Parametric studies examining the damping effect dependence on the soil medium and on the embedment depth are presented.

Transient elastodynamics around cracks including contact and friction

In this paper, some numerical investigations of fast transient elastodynamic problems are presented, which consider especially the interaction of elastic waves with cracks, including contact and friction. For this purpose, a boundary element formulation in the time domain is coupled with contact mechanics models previously proposed and tested by the authors in the framework of elastostatic contact problems. In the numerical examples, qualitative and quantitative effects of the interaction between elastic waves and non-classical, unilateral cracks are briefly discussed.

Flaw identification in elastomechanics: BEM simulation with local and genetic optimization

Single and multiple flaw identification problems are considered. Static and steady-state dynamic analysis of structures with flaw(s) is performed by the boundary element method. Inverse problems are formulated as output (i.e. measurement) error minimization problems and they are solved by numerical optimization techniques. As it is shown in this paper by means of numerical experiments, for elastostatic cases, an appropriate modelling of the structural analysis problem, a good choice of the error measure, and the use of established numerical optimization software are usually sufficient for the solution of the problem. Even multiple flaw identification is possible. Elastodynamic loadings lead to nonconvex problems which are solved here by means of global, genetic optimization algorithms.

Neural crack identification in steady state elastodynamics

An inverse crack identification problem with harmonic excitation in linear elastodynamics is treated here by means of back-propagation neural network methods and boundary element techniques. The problem concerns the determination of the existence and the characteristics of a hidden crack within an elastic structure by means of measurements of the structural response on the accessible boundary for given external time-periodic loadings. The direct problem is solved by a boundary element formulation in the frequency domain which leads to a system of linear equations with frequency-dependent matrices. Thus, for a given frequency, certain similarities with linear elastostatics exist. Feed-forward multilayer neural networks trained by back-propagation are used to learn the (inverse) input-output relation of the structural system. Then, the inverse problem is solved by a simple application of the neural network recalling (production) ability.

Noise radiation from moving surfaces

In the present work, the development of a 3-D boundary element method (BEM) for determining the radiation, the reflexion and the diffraction of the sound field around several independently moving bodies with vibrating and, hence, sound producing surfaces is described. Starting from the differential equation for linear acoustics, the so-called general Kirchhoff formula can be derived. This integral equation is the basis for the numerical approximation by the BEM. For the investigation of the sound field of independently moving bodies, an evaluation in the time domain is inevitable. The singular integrals, which arise in the direct BEM, require a careful evaluation. The numerical effort for the calculation and solution of the arising systems of equations can be reduced considerably by restricting the movement of the sound sources to uniform translation with constant velocity. The stability and accuracy of the method is investigated using some simple examples. A comparison with an analytical solution shows that the application of the presented method is possible even at high subsonic speeds (see, Baaran, Schallfeldanalyse bei sich bewegenden schallerzeugenden Korpern. Braunschweiger Schriften zur Mechanik 38-1999, Mechanik-Zentrum der TU Braunschweig 1999). Here, the performance of the algorithm is demonstrated by the computation of two realistic examples.

Dynamic interaction effects in underground traffic systems

Abstract Dynamic interaction effects in tunnel systems subjected to above and below ground traffic loads are studied numerically under conditions of plane strain. Linear elastic or viscoelastic material behavior for both the structure and the soil is assumed. Two numerical schemes are employed in the computations for comparison purposes. The first works in the time domain and combines the finite element method for the structure with the boundary element method for the soil, while the second works in the frequency domain and uses the boundary element method for both the structure and the soil. The dynamic behaviour of a typical tunnel system is studied in detail for a variety of dynamic and geometric parameters in order to assess their effects on the system.