TENSOR ANALYSIS FOR ENGINEERS Third Edition
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.
TABLE OF CONTENTS
1. Introduction. 2. Coordinate Systems Definition. 3. Basic Vectors and Scale Factors.
4. Contravariant Components and Transformations. 5. Covariant Components and Transformations.
6. Physical Components and Transformations. 7. Tensors – Mixed and Metric. 8. Metric Tensor Operation on Tensor Indices. 9. Dot and Cross Products of Tensors 10. Gradient Vector Operator-Christoffel Symbols.
11. Derivative Forms-Curl, Divergence, Laplacian. 12. Cartesian Tensor Transformation-Rotations.
13. Coordinate Independent Governing Equations. 14. Collection of Relations for Selected Coordinate Systems. 15. Rigid Body Rotation: Euler Angles, Quaternions, And Rotation Matrix. 16. Mechanical Stress Transformation. 17. The Worked Examples. 18. Exercises. References. Index.
ABOUT THE AUTHOR
Mehrzad Tabatabaian holds a PhD from McGill University and is currently Chair of the BCIT School of Energy Research Committee. He has published several papers for scientific journals and conferences, and he has written textbooks on multiphysics and turbulent flow modelling, thermodynamics, and direct energy conversion. He holds several registered patents in the energy field and currently teaches courses in renewable energy and thermal engineering.