Description: The concepts of deformation, strain, and stress. Equilibrium equations for a continuum. Elements of the theory of linear elasticity. Classical theories of structural mechanics: The principle of virtual work. Application to truss, beam (Euler-Bernouilli and Timoshenko beams) and plate structures (Kirchhoff and Reissner-Mindlin plates). Solution of fundamental elasticity problems (bending, torsion). Stability and buckling analysis.
Computational Methods in Mechanical Engineering
Description: Weak forms and variational principles. The finite element and finite difference methods: Properties and implementation. Finite element methods for displacement and mixed variational solutions of elasticity problems. Treatment of constraints arising from near incompressibility and bending dominated problems. Finite element methods for nonlinear problems. Material and geometric nonlinearities. Solution techniques for nonlinear equations (Newton-Raphson schemes)
Solids and waves
Description: Principles of wave propagation in solid media. Fundamental principles used to describe linear and nonlinear wave propagation in continuum and discrete media. Recent advancements in the dynamics of periodic media. Basic principles governing the propagation of waves in discrete and continuum solid media used to engineer artificial materials with predefined properties and to design dynamical systems for a variety of engineering applications (e.g., vibration mitigation, sound insulation).