Integral Methods in Science and Engineering

by Schiavone, Peter; Constanda, Christian; Mioduchowski, A.; Scjoavpne, C.

• ISBN13: 9780817642136
• ISBN10: 0817642137
• Format: Hardcover
• Copyright: 2002-02-01
• Publisher: Birkhauser

Summary

This book is an outgrowth of the sixth international conference on integral methods in science and engineering. The chapters focus on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. Integral Methods in Science and Engineering describes the construction and application of various analytic and numerical integration techniques. Problem solving in areas such as solid mechanics, fluid dynamics, thermoelasticity, plates and shells, liquid crystals, diffusion and diffraction theory, Hamiltonian systems, resonance, nonlinear waves, plasma, flight dynamics, and structural networks are presented in an accessible manner. The book offers a vehicle for the quick dissemination of new results in these domains, and will help create an ideal environment for investigative interdisciplinary study among a variety of research areas. Topics:* Offers an illustration by prominent researchers of efficient methods of solution with numerical results and rigorous analytic methods* Presents applications of integral methods to a wide variety of mathematical and physical problems* Provides new results in the study of various physical and mechanical models* A clear, concise focus on a class of methodologies rather than a specific field of study This book is a practical resource for a broad audience of professionals, researchers, and practitioners in applied mathematics, mechanical engineering, and theoretical physics, who are interested in current research in ordinary and partial differential equations, integral equations, numerical analysis, mechanics of solids, fluid mechanics, and mathematical physics. Graduate students will find this a helpful guide to the wide range of applications that integral methods have in science and engineering.

Table of Contents

Preface
Contributors
Use of Elastodynamic Reciprocity Theorems for Field Calculations	p. 1
Linear Solvers for the Galerkin Boundary Element Method	p. 15
Reciprocity of Hopf's and Feautrier's Operators in Radiation Transport Theory	p. 21
Spectral Approximation of Weakly Singular Integrable Kernels Using Projections	p. 27
Effect of Imperfect Interface on Thermal Inclusion with an Interior Radial Crack	p. 33
An Integrodifferential Equation of Atomic Diffusion	p. 39
Nonradiating Dislocations in Uniform Supersonic Motion in Anisotropic Linear Elastic Solids	p. 45
On the Use of the Conjugate Gradient Method for the Numerical Solution of First-Kind Integral Equations in Two Variables	p. 51
On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables	p. 57
An Initial-Boundary Value Problem for Thermoelastic Plates	p. 63
A Global Existence Result for Functional Differential Equations with Causal Operators	p. 69
Direct Stiffness-Modification Route to Linear Consistency Between Incompatible Finite Element Meshes	p. 75
Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method	p. 81
Seminal Ideas in Integral Methods	p. 87
Mixed Boundary Value Problem with Two Displacement Boundaries for Thin Plate Bending	p. 99
Use of Cross-Referencing for Solving the Parameter Choice Problem in Generalized CLS	p. 105
Numerical Technique for Solving an Ordinary Differential Equation by Picard's Method	p. 111
On a Class of Boundary Conditions Splitting Coupled Thermoelasticity Problems	p. 117
Recent Mathematical Developments for Functionally Graded Linearly Elastic Materials	p. 123
Ground Vibration Dynamics During Pile Hammering	p. 131
Connection Between Liquid Crystal Theory and Plate Theory	p. 137
Product Integration Quadratures for the Radiative Transfer Problem with Hopf's Kernel	p. 143
A Numerical Scheme for Determining Diffraction Coefficients in Anisotropic Materials	p. 149
Effect of Imperfect Inclusion/Matrix Interaction Between a Circular Inclusion and a Radial Matrix Crack	p. 155
Neutral Equations with Causal Operators	p. 161
Computation of Free-Surface Flows Under the Influence of Pressure Distribution	p. 167
Solution of Eigenvalue Problems for Rectangular Plates by Differential Transformation	p. 173
Free Vibrations of Structural Hyperbolic Paraboloid Networks	p. 179
Sharp Invertibility Results for Layer Potentials in 2D	p. 185
An Enhanced Theory of Bending of Plates	p. 191
Comparison of Zonal, Spectral Solutions for Compressible Boundary Layer and Navier-Stokes Equations	p. 197
Hybrid Laplace and Poisson Solvers I: Dirichlet Boundary Conditions	p. 203
Estimation of Boundary Conditions for Different Experimental Data Using the LTS[subscript N] Method and Tikhonov Regularization	p. 209
Analytical-Numerical Treatment of the One-Phase Stefan Problem with Constant Applied Heat Flux	p. 215
Integral Equations Arising in Boundary Value Problems at Resonance	p. 221
Thermal Stress Analysis of an Elliptic Inclusion with Imperfect Interface Embedded in an Infinite Elastic Medium	p. 227
Three-Dimensional Elasticity Solutions for Anisotropic and Inhomogeneous Plates and Shells	p. 233
A Circular Inclusion with Homogeneous Interface	p. 245
Multiwavelets for Geometrically Complicated Domains and Their Application to Boundary Element Methods	p. 251
Mathematical Investigation of Contact Problems with Friction in Fracture Dynamics	p. 257
Index	p. 263
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