Author: Leonid P. Lebedev Publisher: Springer Science & Business Media ISBN: 0387227253 Category : Mathematics Languages : en Pages : 245
Book Description
This book covers functional analysis and its applications to continuum mechanics.; The mathematical material is treated in a non-abstract manner and is fully illuminated by the underlying mechanical ideas.; The presentation is concise but complete, and is intended for specialists in continuum mechanics who wish to understand the mathematical underpinnings of the discipline.; Graduate students and researchers in mathematics, physics, and engineering will find this book useful.; Exercises and examples are included throughout with detailed solutions provided in the appendix.
Author: Christian Bucher Publisher: CRC Press ISBN: 0203876539 Category : Mathematics Languages : en Pages : 248
Book Description
Proper treatment of structural behavior under severe loading - such as the performance of a high-rise building during an earthquake - relies heavily on the use of probability-based analysis and decision-making tools. Proper application of these tools is significantly enhanced by a thorough understanding of the underlying theoretical and computation
Author: Wilhelm Flügge Publisher: Springer Science & Business Media ISBN: 3642883826 Category : Science Languages : en Pages : 215
Book Description
Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Author: Donald Adam DaDeppo Publisher: ISBN: 9780138597948 Category : Structural analysis (Engineering). Languages : en Pages : 0
Book Description
For a modern two-semester course in Structural Mechanics and Analysis. Designed to better prepare students for advanced studies in structural mechanics, this text focuses on the fundamental principles of mechanics and the basic assumptions that are the heart of the linear theory of structures. It explores the important classical methods for the analysis of statically determinate and statically indeterminate structures, and presents a uniquely different mode of reasoning and derivation of the virtual work method for calculating small displacements of structures.
Author: Petre Teodorescu Publisher: John Wiley & Sons ISBN: 1118614623 Category : Computers Languages : en Pages : 458
Book Description
A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.
Author: Qing-Ming Tan Publisher: Springer Science & Business Media ISBN: 3642192343 Category : Technology & Engineering Languages : en Pages : 199
Book Description
Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author’s research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.
Author: M. Francaviglia Publisher: Elsevier ISBN: 0444597379 Category : Science Languages : en Pages : 572
Book Description
Providing a logically balanced and authoritative account of the different branches and problems of mathematical physics that Lagrange studied and developed, this volume presents up-to-date developments in differential goemetry, dynamical systems, the calculus of variations, and celestial and analytical mechanics.
Author: Leonid P. Lebedev Publisher: Springer Science & Business Media ISBN: 0306483971 Category : Mathematics Languages : en Pages : 259
Book Description
This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.
Author: J.F. Doyle Publisher: Springer Science & Business Media ISBN: 9780792312086 Category : Science Languages : en Pages : 464
Book Description
This book is concerned with the static and dynamic analysis of structures. Specifi cally, it uses the stiffness formulated matrix methods for use on computers to tackle some of the fundamental problems facing engineers in structural mechanics. This is done by covering the Mechanics of Structures, its rephrasing in terms of the Matrix Methods, and then their Computational implementation, all within a cohesivesetting. Although this book is designed primarily as a text for use at the upper-undergraduate and beginning graduate level, many practicing structural engineers will find it useful as a reference and self-study guide. Several dozen books on structural mechanics and as many on matrix methods are currently available. A natural question to ask is why another text? An odd devel opment has occurred in engineering in recent years that can serve as a backdrop to why this book was written. With the widespread availability and use of comput ers, today's engineers have on their desk tops an analysis capability undreamt of by previous generations. However, the ever increasing quality and range of capabilities of commercially available software packages has divided the engineering profession into two groups: a small group of specialist program writers that know the ins and outs of the coding, algorithms, and solution strategies; and a much larger group of practicing engineers who use the programs. It is possible for this latter group to use this enormous power without really knowing anything of its source.
Author: Leonid P. Lebedev
Author: Yoshikazu Giga
Author: Christian Bucher
Author: Wilhelm Flügge
Author: Donald Adam DaDeppo
Author: Petre Teodorescu
Author: Qing-Ming Tan
Author: M. Francaviglia
Author: Leonid P. Lebedev
Author: J.F. Doyle