Time-dependent and Vibration Problems

✍ Scribed by S. Kobayashi (auth.), Dr. Carlos A. Brebbia (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1985
• Tongue: English
• Leaves: 272
• Series: Topics in Boundary Element Research 2
• Edition: 1
• Category: Library

✦ Synopsis

This series has been developed in response to the interest shown in boundary ele­ ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im­ portant topic it is time to produce a work of a more permanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto­ dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the effectiveness of the technique for engineering. Chapter 2 examines some of the various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for­ mulation is compared with the displacement-potential case. The special character­ istics of the elastodynamics fundamental solutions are discussed in detail and a criti­ cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problem and the suggestions for further work make an important contribu­ tion to the development of the method.

✦ Table of Contents

Front Matter....Pages I-XIV
Fundamentals of Boundary Integral Equation Methods in Elastodynamics....Pages 1-54
Elastic Potentials in BIE Formulations....Pages 55-62
Time Dependent Non-Linear Potential Problems....Pages 63-86
Further Developments on the Solution of the Transient Scalar Wave Equation....Pages 87-123
Transient Elastodynamics....Pages 124-155
Propagation of Surface Waves....Pages 156-190
Boundary Integral Formulation of Mass Matrices for Dynamic Analysis....Pages 191-208
Boundary Element Method for Laminar Viscous Flow and Convective Diffusion Problems....Pages 209-229
Asymptotic Accuracy and Convergence for Point Collocation Methods....Pages 230-257
Back Matter....Pages 259-262

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering;Mechanics