Multiscale Methods in Quantum Mechanics, Philippe Blanchard; Gianfausto Dell`Antonio

Автор: Pavliotis
Название: Multiscale Methods
ISBN: 0387738282 ISBN-13(EAN): 9780387738284
Издательство: Springer
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Описание: The book is meant to be an introduction, aimed primarily towards graduate students. Part I of the book (theoretical foundations) and Part III of the book (proving theorems concerning simplified versions of the models that are studied in Part II) are necessarily terse and present the wide range of applications of the ideas, and illustrate their unity. The subject matter in these set of notes has, for the most part, been known for several decades. However, the particular presentation of the material here is particularly suited to the pedagogical goal of communicating the subject area to the wide range of mathematicians, scientists and engineers who are currently engaged in the use of these tools to tackle the enormous range of applications that require them.Extensions and generalizations of the results presented in these notes, as well as references to the literature, are given in the Discussion and Bibliography section, at the end of each chapter. With the exception of Chapter 1, all chapters are supplemented with exercises.

Автор: Rene de Borst; Ekkehard Ramm
Название: Multiscale Methods in Computational Mechanics
ISBN: 9400733860 ISBN-13(EAN): 9789400733862
Издательство: Springer
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Описание: This work gives a modern, up-to-date account of recent developments in computational multiscale mechanics. Both upscaling and concurrent computing methodologies are addressed for a range of application areas in computational solid and fluid mechanics.

Автор: Xia Liang
Название: Multiscale Structural Topology Optimization
ISBN: 1785481002 ISBN-13(EAN): 9781785481000
Издательство: Elsevier Science
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Описание: Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. . Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. . This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain.