Tensor Mechanics

Course guarantor:

Milan Jirásek

Lecturer:

Milan Jirásek

Tutor:

Milan Jirásek

Supervisor:

Department of Mechanics

Synopsis:

This course covers the fundamentals of tensor algebra and calculus and demonstrates the power of tensor notation applied to formulation and solution of engineering problems. Selected examples cover solid and fluid mechanics, as well as heat and mass transport problems. The first part of the course is devoted to the definition of tensors, understood as linear mappings, to algebraic operations with tensors, to tensor fields and their differentiation, and to transformations between volume and surface integrals based on the Green and Gauss theorems. In the second part, it is shown how these mathematical tools enable an elegant description and analysis of various physical problems, with focus on applications in civil and structural engineering.

The classes combine lectures and seminars, with emphasis on problems assigned as homework, which form the basis of presentations and discussions in class. The objective is not only to transfer specific knowledge, but also to develop the students‘ aptitude for independent thinking and critical analysis. At the same time, mastering of tensorial notation by the students will greatly facilitate their future reading of modern scientific literature in many fields of research.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

•Lecture notes prepared by the instructor

•M. Itskov: Tensor Algebra and Tensor Analysis for Engineers, Springer 2013

•D. A. Danielson: Vectors and Tensors in Engineering and Physics, 2nd ed., Westview Press 2003

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: