# Continuum Mechanics

**Institution**: DICAR (UNIPV)

**Term**: 1^{st} Semester – Academic Year 2017-2018

**Instructor**: Sauro Manenti (sauro.manenti@unipv.it)

**CFU**: 6

**SSD**: ICAR/01

**Duration**: 01-10-2017 – 31-10-2017

**Schedule**:

**Office hours**: Wed 4–5 PM (to be confirmed via email)

**OBJECTIVES**

The course aims at providing the fundamental theoretical concepts and mathematical tools for the analysis of relevant problems in the hydraulic engineering field.

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**DESCRIPTION**

Review of mathematical foundations: vector and tensor algebra, coordinate systems, Stokes theorem and Gauss theorem.

Analysis of stress: the continuum concept, Cauchy stress principle, stress tensor, principal stress, Mohr circles, deviator and spherical stress tensor.

Deformation and strain: Lagrangian and Eulerian description, small deformation theory, strain tensor, principal strains, spherical and deviator strain tensor, plane strain, compatibility equations, velocity gradient tensor, rate of deformation tensor, vorticity tensor.

Fundamental laws of continuum mechanics: mass conservation – continuity equation, Reynolds transport theorem, linear momentum conservation, angular momentum conservation, energy conservation.

Constitutive equations: Newtonian fluid.

Navier-Stokes equations: perfect fluid, Euler and Bernoulli equations, Kelvin theorem.

**REQUIREMENTS**

Basics of vector and tensor algebra. Foundations of mathematical physics.

**REFERENCES**

- Prager “Introduction to mechanics of continua” Ginn and Co. 1961
- Aris “Vectors, tensors, and the basic equations of fluid mechanics” Dover pub.
- C. Chou & N.J. Pagano “Elasticity, tensor, dyadic, and engineering approaches” Dover pub.
- Course notes will be provided during the course.

**ASSESSMENT**

The final examination will consist of an essay on a course’s topic to be selected and discussed orally by the student.