Rozwiązanie Zagadnienia Dwuwymiarowego przy Stałej Krzywiźnie Linii Izostatycznych

Considering the two-dimensional problem of the classical theory of elasticity in natural coordinates, the author expresses the equilibrium conditions in the form of two independent equations in the stress components. The general integrals of these equations are represented in a simple form, assuming constant curvature of the isostatic lines. This enables the expression of the state of stress in terms of two functions b and G, each being a function of only one variáble. An analysis of the compatibility condition leads to ordinary equations for the functions b and T. At the same time the differential equation for the LAMÉ parameter is obtained. For each curvilinear system oi reference appropriate five-parameter families of solutions are chosen. The boundary-value problem is illustrated by solving several particular cases.