Unified Functional Approach to the Solution of Formally Adjoint Problems of Continuum Mechanics.

摘要

After showing that the exact solutions of the subject problems constitute the unique element common to two dual linear manifolds parallel to two orthogonal subspaces of a suitably defined Hilbert space, dual and reciprocal variational principles are formulated, bounds for the exact solutions are derived and error estimates for approximate solutions are obtained. It is furthermore shown that such known theorems as Castigliano, Clapeyron, Pasternak theorems hold for all linear formally adjoint problems irrespective of the particular field of continuum mechanics they belong to. (Author)