Course Details

Some fundamentals of singular integrals. The definite integral of unbounded functions and the definition in case: as generalized, as main value and finite part. Introduction to the types of integral equations: Fredholm țĮȚ Voltera integral equations of first and second kind. Numerical solution of no singular integral equations: i) the Nystrom method, and II) the technique of boundary method method “BEM”. The Green function, the fundamental solution and the reduction of one- dimensional problems to integral equations.

The potential problem, the fundamental solution of the Laplacian and the development of complete formulation of the potential problem of the isotropic or the non-isotropic medium in two and three dimensions. The numerical solution of the potential problem in two dimensions with the method of boundary elements (BEM) for stable, linear and secondary data. Applications of the BEM method: the Torsion problem, the problem of heat convection.

The development of complete formulation of the linear elastostatik problem in two and three dimensions: The second Betti theorem (reciprocity theorem). The fundamental solution of the problem of linear elasticity of the Navier equation (the Kelvin solution). The Somigliana equation. The mathematical formulation of elastostatik problem with integral equation. The stress problem in interior points. The numerical solution of two-dimensional elastostatik problem with the method of boundary elements (BEM) for stable, linear and secondary data. Applications: Stress concentrationw for plane problems in elasticity.