Tensor Analysis For Engineers

Tensor Analysis for Engineers

Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists with the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. It includes expanded content on the application of mechanical stress transformation. The geometry is limited to the Euclidean space/geometry, where the Pythagorean Theorem applies, with well-defined Cartesian coordinate systems as the reference. Quantities defined in curvilinear coordinate systems, like cylindrical, spherical, parabolic, etc. are discussed and several examples and coordinates sketches with related calculations are presented. In addition, the book has several worked-out examples for helping the readers with mastering the topics provided in the prior sections. FEATURES: Expanded content on the application of mechanical stress transformation Covers rigid body rotation and Cartesian tensors by including Euler angles and quaternion methods Uses easy to understand mathematical concepts through numerous figures, solved examples, and exercises Lists gradient-like operators for major systems of coordinates and rotation matrices for proper Euler and Tait-Bryan angles

Tensor Algebra and Tensor Analysis for Engineers

This second edition is completed by a number of additional examples and exercises. In response of comments and questions of students using this book, solutions of many exercises have been improved for a better understanding. Some changes and enhancements are concerned with the treatment of sk- symmetric and rotation tensors in the ?rst chapter. Besides, the text and formulae have thoroughly been reexamined and improved where necessary. Aachen, January 2009 Mikhail Itskov Preface to the First Edition Like many other textbooks the present one is based on a lecture course given by the author for master students of the RWTH Aachen University. In spite of a somewhat di?cult matter those students were able to endure and, as far as I know, are still ?ne. I wish the same for the reader of the book. Although the present book can be referred to as a textbook one ?nds only little plain text inside. I tried to explain the matter in a brief way, nevert- lessgoinginto detailwherenecessary.Ialsoavoidedtediousintroductions and lengthy remarks about the signi?cance of one topic or another. A reader - terested in tensor algebra and tensor analysis but preferring, however, words instead of equations can close this book immediately after having read the preface.

Tensor Analysis for Engineers