On the boundary integral formulation of the plane theory of elasticity with applications (analytical aspects)

A formulation of the plane strain problem of the theory of elasticity in stresses, for simply connected domains, is carried out in terms of real functions within the frame of what is known as the boundary integral method. Special attention is devoted to the problem of determination of the arbitrary constants appearing in the solution, in view of work in progress where numerical techniques are used. Relying on some mathematical results formulated in the appendix, simple applications concerning the first and the second fundamental problems for the circle and for the ellipse are given, which show the correctness of the formulation and the necessity of recurring to numerical techniques, once the geometry of the problem or the type of boundary conditions deviates from being simple. Following parts of the present work are devoted to the numerical treatment of the obtained system of equations, as well as to the theories of thermoelasticity and thermo-electromagneto-elasticity.