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January 2020

Advanced continuum mechanics with applications to finite elasicity

Listed as Applied Mathematics Topic C in the Course Planner.

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This course is designed to enable students to access modern advanced continuum theory, including; tensors; two-point tensor fields; stress and strain tensors; invariant constitutive theory; strain-energy functions; stress-strain relations for perfectly elastic materials and the variational calculus. These notions will be illustrated with a number of special problems and applications in Finite Elasticity, including the importance of the assumption of material incompressibility. The subject will be developed from the perspective of energy minimization for hyperelastic materials, and will involve several lectures on the variational calculus. The special problems in finite elasticity will include; simple extension; simple shear; straightening and stretching of a sector of a hollow cylinder; torsion of a solid cylinder; compression of a half-cylindrical cross-section; inflation of cylindrical tubes and hollow spheres, and with particular reference to the neo-Hookean, Mooney and Varga strain-energy functions. General familiarity with these topics will enable the student to access the advanced constitutive theory that is applicable to a wide range of modern fluid and solid materials, and a basic knowledge of tensor calculus will enable the student to readily understand general relativity and other cosmological theories.



Topics: An introduction to mathematical epidemiology Discrete-time and continuous-time discrete-state stochastic infection models Numerical methods for studying stochastic infection models: EXPOKIT, transforms and their inversion Methods for simulating stochastic infection models: classical (Gillespie) algorithm, more efficient exact and approximate algorithms Methods for parameterising stochastic infection models: frequentist approaches, Bayesian approaches, approximate Bayesian computation Optimal observation of stochastic infection models


Graduate attributes

    Linkage future

    This course is not recorded as prequisite for other courses.

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