Boundary contour method for plane problems in a dual formulation with linear elements (Q2717039)

This paper is concerned with the plane strain problem of homogeneous and isotropic elastic solids in a dual formulation. In the first part of the paper the author presents the basic field equations in terms of stress functions and rotation, and establishes the matrix of fundamental solutions. A reciprocity relation and the fundamental matrix are used to obtain representations of Somigliana type. Then, the boundary value problems are reduced to the study of integral equations. The author proves that the integrands of corresponding boundary integral equations are divergence-free provided that the unknown functions satisfy the field equations. An implementation is carried out with linear approximation. Two examples are given to illustrate the method.