Physical Components of Tensors (Applied and Computational Mechanics)

Book Details

• Publisher: CRC Press

• Author: Wolf Altman

• Language: English

• Edition: 1

• ISBN: 9781482263824

• Pages: 200

• Cover: Hardcover

• Dimensions: 9.4 x 6.3 x 0.7 inches

About The Book

Physical Components of Tensors by Wolf Altman is a definitive guide to tensor calculus, focusing on its practical and physical aspects. Written for graduate students, professors, and researchers in the fields of elasticity and shell theories, this text offers an authoritative and complete explanation of tensor calculus based on transformations of vector space bases rather than coordinate transformations. This approach provides a clearer understanding of the physical components of tensors, especially in nonorthogonal coordinates.

The book presents a theory of physical and anholonomic components of tensors, offering insightful applications to theories of elasticity and structural mechanics. Altman also introduces dimensional analysis in relation to tensors and (anholonomic) connections, establishing the relationship and compatibility among several existing definitions of physical components of tensors.

Divided into five comprehensive chapters, the text covers:

• Basic concepts of linear algebra, including vector spaces, inner products, norms, and metrics.

• Algebraic operations for vectors and tensors, along with duality, tensor products, and component representation.

• Classical tensor calculus, a prerequisite for the development of more advanced topics.

• The theory of physical and anholonomic components of tensors, with applications in the spaces of linear transformations and tensor products.

This book assumes a foundational knowledge of linear algebra and calculus but revisits and introduces these concepts in the early chapters to ensure clarity. With its emphasis on physical components and real-world applications, Physical Components of Tensors is an essential reference for those studying solid and structural mechanics, particularly in the context of elasticity and shell theories.