Tensors

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This course discusses the mathematical quantities called tensors and, their properties. Tensors and vector fields are discussed as well.
This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

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This course starts with a discussion on the motion of continuum bodies — how to describe and analyze the motion. The lectures cover the study of kinematics of motion divided into four subcategories: Motion and Deformation, Lagrangian description, Eulerian description, and Material Derivatives. From basic representation, all the subcategories will be discussed in this course. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we discuss how to mathematically describe the distortion that solids and fluids undergo. We cover important topics such as (i) deformation of curves, surfaces and volumes; (ii) measures of strain; (iii) polar decomposition and (iv) rate of deformation. On completing this course, we will have a better understanding of the kinematics that underlies continuum mechanics. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, balance laws will be discussed, including the balance of mass, momentum, and energy. The balance of mass can be associated with diffusion. The balance of linear momentum is associated with Newton’s laws of motion, and the balance of angular momentum is associated with Euler’s equation. The balance of energy gives rise to the heat equation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, balance laws will be discussed, including the balance of mass, momentum, and energy. The balance of mass can be associated with diffusion. The balance of linear momentum is associated with Newton’s laws of motion, and the balance of angular momentum is associated with Euler’s equation. The balance of energy gives rise to the heat equation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, we discuss how to mathematically describe the distortion that solids and fluids undergo. We cover important topics such as (i) deformation of curves, surfaces and volumes; (ii) measures of strain; (iii) polar decomposition and (iv) rate of deformation. On completing this course, we will have a better understanding of the kinematics that underlies continuum mechanics. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.

In this course, balance laws will be discussed, including the balance of mass, momentum, and energy. The balance of mass can be associated with diffusion. The balance of linear momentum is associated with Newton’s laws of motion, and the balance of angular momentum is associated with Euler’s equation. The balance of energy gives rise to the heat equation. This course was created for Ansys Innovation Courses by Professor Krishna Garikipati and Dr. Gregory Teichert, University of Michigan, in partnership with Ansys.