Unified Functional Approach to the Solution of Formally Adjoint Problems of Continuum Mechanics.
Abstract
The report presents and discusses a unified functional approach for the solution of problems of continuum mechanics which are governed by formally adjoint linear differentail operators. It is first shown 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. Subsequently dual and reciprocal variational principles are formulated, bounds for the exact solutions are derived and error estimates for approximate solutions are obtained. The analysis is carried out and the results established for a formally adjoint linear differential operator of arbitrary even order. More detailed presentation and further elaboration of the more relevant aspects of the general theory are given in an Appendix in connection with the particular case of a second order operator. The unified theory presented has many practical and important implications both from a general and a computational point of view. For instance, it allows, one to establish that such known theorems of structural mechanics as Betti, Castigliano, Clapeyron, Pasternak theorems hold for all linear formally adjoint problems irrespective of the particular field of continuum mechanics they belong to. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1972
- Accession Number
- AD0766949
Entities
People
- Luigi G. Napolitano
Organizations
- University of Naples Federico II