Classical Continuum Mechanics
暫譯: 經典連續介質力學
Surana, Karan S.
- 出版商: CRC
- 出版日期: 2024-12-19
- 售價: $2,380
- 貴賓價: 9.5 折 $2,261
- 語言: 英文
- 頁數: 510
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0367615215
- ISBN-13: 9780367615215
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商品描述
This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua.
Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics.
This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.
商品描述(中文翻譯)
這本書提供了物理和數學的基礎，以及對固體和流體連續體變形的數學描述和本構理論的完整推導，涵蓋可壓縮和不可壓縮的情況，並清楚區分拉格朗日（Lagrangian）和歐拉（Eulerian）描述，以及共變（co-variant）和反變（contra-variant）基底。使用曲線坐標系介紹共變和反變張量及張量微積分，然後專門針對笛卡爾坐標系進行說明。書中呈現了伽利略（Galilean）和非伽利略坐標變換，並用於建立客觀張量和客觀速率。使用傳統方法以及非伽利略變換推導了對流時間導數，並在固體連續體的有限變形以及流體連續體的情況下說明了其重要性。
本構理論是基於熵不等式和表示定理推導而來。將固體和流體連續體的總變形分解為體積變形和扭曲變形，對於提供一個健全、通用且嚴謹的框架以推導本構理論至關重要。能量方法和虛功原理被證明是變分法的一個小而獨立的子集。數學模型的微分形式和變分法排除了能量方法和虛功原理。本書的內容從非常基本的概念開始發展，逐步進展到高級主題。
這本書包含與數學概念和理論相關的核心科學知識，旨在為研究生準備基礎和基本的工程及科學研究。書中提供了詳細且一致的推導，清晰易懂，非常適合自學。
作者簡介
Karan S. Surana attended undergraduate school at Birla Institute of Technology and Science (BITS), Pilani, India and received a B.E. in mechanical engineering in 1965. He then attended the University of Wisconsin, Madison where he obtained M.S. and Ph.D. in mechanical engineering in 1967 and 1970. He joined The University of Kansas, Department of Mechanical Engineering faculty where he is currently serving as Deane E. Ackers University Distinguished Professor of Mechanical Engineering. His areas of interest and expertise are computational mathematics, computational mechanics, and continuum mechanics. He is the author of over 350 research reports, conference papers, and journal papers.
作者簡介(中文翻譯)
Karan S. Surana 於1965年在印度比爾拉科技與科學學院（Birla Institute of Technology and Science, BITS）畢業，獲得機械工程學士學位。隨後，他前往威斯康辛大學麥迪遜分校（University of Wisconsin, Madison），於1967年和1970年分別獲得機械工程碩士和博士學位。他加入堪薩斯大學（The University of Kansas）機械工程系，目前擔任德恩·艾克斯（Deane E. Ackers）機械工程大學傑出教授。他的研究興趣和專長包括計算數學、計算力學和連續介質力學。他已發表超過350篇研究報告、會議論文和期刊論文。
