The method of homogeneous solutions and biorthogonal expansions in the plane problem of the theory of elasticity for an orthotropic body (Q1361949)

The authors consider the plane problem in the theory of elasticity for a rectangular orthotropic strip with homogeneous boundary conditions on the longitudinal edges. An exact solution of the problem is constructed as an expansion in terms of characteristic elements of a generalized eigenvalue biharmonic problem. Biorthogonal functions for the system of characteristic elements are constructed explicitly, and double completeness of the characteristic elements is proved. The biorthogonality condition is shown to be equivalent to the generalized orthogonality relation of Papkovich type. For expansion of a special form, the biorthogonal system turns out to be identical with the system of characteristic elements. The authors obtain explicit expressions for the coefficients of the expansion, and for illustration apply the results to a semi-infinite strip whose end is subjected to self-balanced normal and shear forces.