Mathematical theory of elasticity

The first systematic investigations in this area fulfilled for solution of torsion and bending problems of prismatic bars. During 1947-1948 the method reducing the solution of research problems to the regular infinite system of algebraic equations had been suggested by Nagush Kh. Arutunyan . On the basis of this method the problems of torsion and bending, widely used in mechanical engineering and construction of bars with different geometrical forms, were investigated.Since 1954 the multilateral investigations dedicated to study of plane, spatial, contact and mixed boundary value problems of elasticity theory, have been fulfilled. A numerous interesting problems of new class have been solved. During the construction of above mentioned problems' solutions, the mathematical methods of dual, triple-integral and other functional equations were generalized and developed. Significant number of works was dedicated to the problems of interaction of deformable bodies, as well as to different classes of stress concentrators (punches, holes, cracks, inclusions, elastic stringers). The contact interaction problems of elastic compound bodies of complicated configuration with determinate and indeterminate contact boundaries had been considered.

Nagush Kh. Arutunyan firstly introduced the direction of contact problems between thin-walled stringers and massive elastic bodies. In the frame of different contact models application, a numerous theoretically important and practically interesting results had been obtained. The important results obtained in the theory of elasticity represented in the works of N. Arutunyan, B.Abramyan, A.Babloyan, V.Tonoyan, A.Mkrtchyan, S.Mkhitaryan, E.Grigoryan, V.Makaryan, V.Hakobyan and others.

Interesting results in the mathematical theory of elasticity were obtained during the research of torsion, bending and contact problems of inhomogeneous anisotropic elastic bodies. ( V.Sarkissyan)

In 1965 the theory of elasticity of bodies, which have various resistance to tension and pressure, (theory of different modulus elasticity) was developed by S.Ambartsumyan, A.Khachatryan. On the basis of this theory a number of classic problems were solved.

From 1955 up to now the investigations in the field of concentration of stresses in elastic bodies were still in progress. It is shown that in order to avoid from high stressed state as well as provide a low-stressed state in angular point of connection surface it is necessary to select geometrical and physical parameters of compound elastic bodies in appropriate way. The results obtained by Karapet S.Chobanyan became the basis of these investigations. In 1978 he was awarded with Diploma No 102 for Discovering (in former USSR). By common efforts of R.Aleksanyan, A.Khachikyan first of all, and the others, this direction obtained its further theoretical and experimental development. On the basis of low-stress phenomenon investigation in the angular points of compound bodies, made from non-linear elastic materials, the boundaries of low-stressed area in longitudinal shear, in plane strain and stress state, in plates bending were obtained. ( M.Zadoyan)