Z. S. Chen

A Galerkin-type BE-FE formulation for elasto-acoustic coupling

The interactions between the vibrations of an elastic structure and the sound field in the surrounding fluid are taken into account by coupling a symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering with a standard finite element formulation for the dynamic behavior of elastic structures.

A Symmetric Galerkin Formulation of the Boundary Element Method for Acoustic Radiation and Scattering

A symmetric Galerkin formulation of the Boundary Element Method for acoustic radiation and scattering is presented. The basic integral equations for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral equations a Galerkin-type numerical solution scheme is proposed. The evaluation of the weakly-singular and the hypersingular integrals, occurring in this formulation, is addressed briefly. An improved CHIEF-method is employed in order to prevent the singularity of the coefficient matrix of the algebraic system of equations at so-called irregular frequencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional closed part of a structure, is described. The numerical study contains comparisons of analytical solutions for simple academic examples with the numerical results. In addition, a comparison of measured and computed results is presented for a structure, consisting of both a three-dimensional closed part and a thin-walled part.

A 3D BOUNDARY ELEMENT METHOD FOR DETERMINATION OF ACOUSTIC EIGENFREQUENCIES CONSIDERING ADMITTANCE BOUNDARY CONDITIONS

A 3D boundary element method for the determination of the acoustic eigenfrequencies of car compartments, characterized by a unified treatment of Robin, Dirichlet, and Neumann boundary conditions, is presented. The drawback of frequency-dependent matrices of the eigenvalue problem is overcome by means of the Particular Integral Method. Thus, the standard numerical algorithms for the extraction of eigenvalues can be applied. The numerical study contains both a comparison of numerical results with analytical solutions of a simple problem with different types of boundary conditions and a comparison of numerical results of a large-scale problem with respective numerical results, computed on the basis of the finite element method. In addition, for the latter example, different numerical algorithms for the eigenvalue extraction are examined.

Coupling of FE- and BE-Discretizations for 3D-Stress Analysis of Tunnels in Layered Anisotropic Rock

After introducing the method developed for the coupling of finite element (FE) and boundary element (BE) discretizations of subregions of solids, comments on the inadmissibility of symmetrizing the resulting coupling stiffness matrix and on the solution of the edge problem within the framework of the BEM are made. Somigliana’s identity is used to obtain BE discretizations of subregions of solids. It contains results from the fundamental solution for a transversely isotropic material. After describing the mode of consideration of layers of rock in the context of the BEM, selected results from 3D stress analysis of a stretch of a tunnel in layered, anisotropic rock are presented, considering sequences of driving and securing of the tunnel. Finally, the BEM is applied to obtain a 3D solution of the problem of lowering the ground water table by means of compressed air which plays an important role as a dewatering measure in modern tunnelling.

A Galerkin–type BE–formulation for Acoustic Radiation and Scattering of Structures with Arbitrary Shape

This chapter deals with a Galerkin–type boundary element formulation for acoustic radiation and scattering of structures with arbitrary shape. The integral equations for radiation and scattering of sound are derived for three dimensional closed structures, thin–walled open structures and for combinations of both. For the numerical solution of these integral equations a Galerkin–type numerical solution scheme is described and programming aspects related to the evaluation of the hyper–singular integrals, determination of the number of unknowns at a particular nodal point and prevention of the singularity of the coefficient matrix at so–called irregular frequencies are addressed. Finally, the proposed method is applied to the numerical solution of some benchmark problems for acoustic radiation and scattering.

On a Combined Stability and Contact Problem Concerning Multi-Lamellae Compression Flanges of I-Beams

Loss of stability of multi-lamellae compression flanges of steel I-beams is characterized by joint buckling of the lamellae. This fact is ignored in engineering practice. Instead of it, the assumption of independent buckling of the individual lamellae is made. The smallest of the so-obtained buckling stresses is considered to be relevant for determination of the safety against buckling under service loads. The purpose of this paper is to present a method of solution of the combined stability and contact problem resulting from consideration of joint buckling of the lamellae.