A method of solving problems of the linear theory of elasticity (Q1075088)

Applying appropriate methods of functional analysis the mixed boundary value problem (bvp) for linear elasticity is examined and solved. By means of the so-called comparison medium the proper bvp is solved using the Green tensor. Two integral operators (projectors) P and Q are constructed, such that \(P+Q=Id\). Some properties of these operators are established. The solution of the problem considered is given in the form of Neumann series. Moreover convergence conditions are discussed. The potential energy is also represented in the form of series. The paper is interesting and the results may be applied to nonhomogeneous or anisotropic media.