Abstract :
Piecewise-homogeneous bodies the interfaces or boundary surfaces of which are noncanonical in one or two coordinate directions are studied. For example, the laminated rock massifs forming various types of folded structures are objects of such a sort. By noncanonical surfaces we understand single-valued continuous surfaces. For simplicity, we consider first a modified semianalytical finite element method as applied in the plane problem of elasticity for symmetric domains. In the semianalytical finite element method (SFEM) [1], the nodal displacements are expanded in terms of orthogonal functions with respect to one of the coordinates, which reduces the dimension of the problem. In the traditional semianalytical scheme, the geometrical and physical properties of the material are independent of the coordinate with respect to which the expansion is performed. Unlike this, (he modified finite element method permits one to take into account both the inhomogeneity of the elastic characteristics of the medium and the change of the nodal coordinate in this direction.
