Kitahara M. Boundary Integral Equation Methods in Eigenvalue Problems of Elastodynamics and Thin Plates

Elsevier Science Publishers B.V., 1985, 281 pages, ISBN 0-444-42447-4The boundary integral equation (BIE) method, or alternatively the boundary element method, has attracted considerable attention in recent years and is now well established in many engineering fields such as potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, steady-state and transient elastodynamics. Now the method is being developed in the field of inelastic materials, large deformations and other non-linear problems. In my opinion, the BIE method is most suited for the analysis of wave propagation problems which have semi-infinite or infinite extent and will be advantageously used as a tool in the earthquake-resistant design of an underground structure. These developments of BIE methods are summarized in a bibliography in the Introduction section.This book is devoted to the application of BIE methods to eigenvalue problems of elastodynamics and thin plates, and is not intended to be an exhaustive treatise. The many important topics mentioned above are omitted because they have already been extensively discussed in other books and developing series. One important feature of this book is to clarify the structure of boundary integral
equations for elastodynamics and to show their mutual relationship by considering the eigenvalues of boundary integral equations. In this process, a pitfall of the boundary integral equation approach to the exterior elastodynamic problems is pointed out, together with its remedy. Of course, many important numerical results on eigenvalues, eigendensities and eigenmodes are demonstrated in order
to show the feasibility and the versatility of the BIE method for this class of eigenvalue problem. This work is divided into two parts. Eigenvalue problems of elastodynamics are investigated in Part I, while eigenvalue problems of thin plates, including the buckling problem of a plate, are investigated in Part II.