CONSTRUCTIVE SOLUTION OF PROBLEMS IN MECHANICS OF CONTINUA

It is well known the importance of the effective solution, both analytically or numerically, of problems in mechanics. In this work we extend the multiple orthogonal sequence method to the energetic space of an abstract linear monotone operator. The method leads to an abstract eigenvalue problem that it produces orthonormal bases in some nested Hilbert spaces, that they are suitable to develop abstract Fourier or Galerkin-projection methods. Some examples are given and the constructive solution of the dynamical problem in linear elasticity is shown.