Introduction to Continuum Mechanics (MAGIC090)
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This course is part of the MAGIC core.
The theory of continuous media is the common denominator of several physical theories concerned with the global (macroscopic) behaviour of substances under the influence of external agents. Two main examples of such theories are fluid mechanics and elasticity theory. The main feature which distinguishes continuum mechanics from other physical theories like, for example, quantum mechanics, is that all the fine microscopic details are disregarded; in particular, it is assumed that the highly discontinuous structure of matter can be replaced by a smoothed hypothetical body. Quantities such as density, displacement and velocity (the so-called field variables) are taken to be continuous functions of position and their values are calculated via axiomatic rules. In this course we develop the general mathematical apparatus required for the analysis of the deformation of solids and the flow of fluids. An understanding of continuum mechanics is of paramount importance in many applications, including meteorology, seismology, chemical engineering, biomechanics, civil engineering, aircraft design, etc.
Spring 2021 (Monday, January 25 to Friday, March 19; Monday, April 26 to Friday, May 7)
Vector Calculus, Linear Algebra, Newtonian Dynamics
1. Vectors and tensors. 2. Kinematics (the geometry of deformation and strain). 3. Balance Laws (mechanical stress, Cauchy's equation of motion) 4. Constitutive behaviour (objectivity, elastic materials, hyperelasticity, incompressibility) 5. Linear elasticity and boundary-value problems.
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