β Scribed by Christian Constanda, Dale Doty, William Hamill (auth.)
No coin nor oath required. For personal study only.
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analyticallyβby means of direct and indirect boundary integral equation methods (BIEMs)βand numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy.
The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.
Front Matter....Pages i-xii
The Mathematical Model....Pages 1-8
The Layer Potentials....Pages 9-24
Existence of Solutions....Pages 25-33
Software Development....Pages 35-91
Computational Examples....Pages 93-228
Back Matter....Pages 229-232
Integral Equations; Partial Differential Equations; Functions of a Complex Variable
π SIMILAR VOLUMES
<p><p>Elliptic partial differential equations are important for approaching many problems in mathematical physics, and boundary integral methods play a significant role in their solution. This monograph investigates the latter as they arise in the theory characterizing stationary vibrations of thin
<p><p>Elliptic partial differential equations are important for approaching many problems in mathematical physics, and boundary integral methods play a significant role in their solution. This monograph investigates the latter as they arise in the theory characterizing stationary vibrations of thin