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FSI-RMEAcad. year: 2012/2013
The course deals with the following topics: Definition of variational problems, demonstration of the equivalence of the integration of a differential equation and seeking the minimum of a suitable functional. Weak solution. Functionals and operators in the Hilbert space. Variational principles of the linear elasticity. Hashin-Shtrikman variational principles in the mechanics of composite materials. Methods of weighted residuals and direct variational methods. Method of boundary integral equations in the linear elasticity. Fundamental solution. Numerical methods for the solutions of boundary integral equations. Physical and mathematical aspects of the stability problems. Stability of elastic systems, energy criterion of stability, bifurcation and limit points. Nonlinear systems and stability criterion. Thermodynamic approach to stability. Percolation theory.
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branch M-IMB , 1 year of study, summer semester, compulsory
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