O strukturze rozwiązań w zagadnieniach płyt ortotropowych

Displacement potentials are introduced in the case of rectilinear orthotropy characterized by six independent elastic constants. The potentials are used to solve the static case of an orthotropic plate either arbitrarily loaded on the bounding planes or free from loads. Two independent equations for the displacement components are obtained, corresponding to the plane stress and plate bending problems, respectively; the equations are written in a symbolic, operator form and are equivalent to differential equations of infinite order. The homogeneous equations contain: the functions describing the internal state of stress and satisfying the 4th and 2nd order equations, respectively; the functions defined in the set of roots of the corresponding transcendental equations satisfying the Helmholtz equations and describing the boundary effect, and the functions defined in the set of real-valued eigenvalues, given in an explicit form, which satisfy the Helmholtz equations and describe the rotational field of displacements in the plate. Equations of the ,,more accurate'' theory are presented.