THE METHOD OF HOMOGENEOUS SOLUTIONS AND BIORTHOGONAL EXPANSIONS IN THE PLANE PROBLEM OF THE THEORY OF ELASTICITY FOR AN ORTHOTROPIC BODY

In connection with the solution of boundary-value problems of the theo ry of elasticity for-an orthotropic strip the problem of expanding two different limiting functions in series in terms of the characteristic elements of the generalized eigenvalue problem is considered. A syste m of functions biorthogonal to the system of characteristic elements i s constructed. The double completeness of characteristic elements is p roved. It is shown that the biorthogonality condition is equivalent to a generalized orthogonality relation of Papkovich type. The form of s ystems of biorthogonal functions is established. For expansions of a s pecial form the biorthogonal systems are identical with the systems of characteristic elements. Biorthogonal systems of functions are constr ucted corresponding to expansions of a general form. Using the biortho gonal systems obtained, explicit expressions for the expansion coeffic ients are found. An example demonstrating the existence of a non-trivi al double null expansion is given. (C) 1996 Elsevier Science Ltd.