Physical Components of Tensors
暫譯: 張量的物理組成
Altman, Wolf, Oliveira, Antonio Marmo De
- 出版商: CRC
- 出版日期: 2024-12-31
- 售價: $2,870
- 貴賓價: 9.5 折 $2,727
- 語言: 英文
- 頁數: 236
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1138826421
- ISBN-13: 9781138826427
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商品描述
Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory of physical and anholonomic components of tensors and applies the theory of dimensional analysis to tensors and (anholonomic) connections. This theory shows the relationship and compatibility among several existing definitions of physical components of tensors when referred to nonorthogonal coordinates. The book assumes a basic knowledge of linear algebra and elementary calculus, but revisits these subjects and introduces the mathematical backgrounds for the theory in the first three chapters. In addition, all field equations are also given in physical components as well.
Comprised of five chapters, this noteworthy text:
- Deals with the basic concepts of linear algebra, introducing the vector spaces and the further structures imposed on them by the notions of inner products, norms, and metrics
- Focuses on the main algebraic operations for vectors and tensors and also on the notions of duality, tensor products, and component representation of tensors
- Presents the classical tensor calculus that functions as the advanced prerequisite for the development of subsequent chapters
- Provides the theory of physical and anholonomic components of tensors by associating them to the spaces of linear transformations and of tensor products and advances two applications of this theory
Physical Components of Tensors
商品描述(中文翻譯)
《張量的物理組成》闡述了張量微積分的重要方面，並突顯其最實用的特徵，提供了一個權威且完整的張量微積分解釋，該解釋基於向量空間基底的變換，而非坐標的變換。這本書是為了研究彈性和殼理論的研究生、教授和研究人員而撰寫，重點關注張量的物理和非完整組成部分，並將其應用於理論中。它建立了張量的物理和非完整組成部分的理論，並將維度分析的理論應用於張量和（非完整）連接。這一理論顯示了在非正交坐標系下，幾個現有的物理組成部分定義之間的關係和相容性。本書假設讀者具備線性代數和初等微積分的基本知識，但在前三章中重新探討這些主題並介紹理論的數學背景。此外，所有場方程也以物理組成部分的形式給出。
本書由五章組成，這本值得注意的文本：
- 處理線性代數的基本概念，介紹向量空間及其內積、範數和度量所施加的進一步結構
- 專注於向量和張量的主要代數運算，以及對偶性、張量積和張量的組成表示的概念
- 呈現作為後續章節發展的進階前提的經典張量微積分
- 通過將張量的物理和非完整組成部分與線性變換和張量積的空間關聯，提供張量的物理和非完整組成部分的理論，並推進該理論的兩個應用
《張量的物理組成》包含了張量微積分的全面說明，是關心固體和結構力學的研究生或工程師的重要參考書。
作者簡介
Wolf Altman obtained his Ph.D. from Stanford University in 1966. His dissertation was published in the Journal of IABSE and became a classic. Professor Altman is an engineering educator and researcher with experience as a consultant in structural mechanics in general and in the City Hall of Sao Caetano do Sul. His research endeavors, which include over 60 articles in international journals, have been mainly on weak variational formulations, including the effects of conservative and nonconservative loads on beams, plates and shells, and on physical and nonholonomic components of tensors with application to the theory of elasticity and shells.
Antonio Marmo De Oliveira
作者簡介(中文翻譯)
沃夫·阿特曼於1966年在史丹佛大學獲得博士學位。他的論文發表在IABSE期刊上，並成為經典。阿特曼教授是一位工程教育者和研究者，擁有結構力學方面的顧問經驗，特別是在聖卡塔諾市市政府。他的研究工作包括在國際期刊上發表的60多篇文章，主要集中在弱變分形式上，包括保守和非保守載荷對樑、板和殼的影響，以及與彈性理論和殼體應用相關的張量的物理和非完整組件。
安東尼奧·馬爾莫·德·奧利維拉
