Shvab'yuk V. Development of models and methods of estimation of stress-displacement relations of composite elements of shell constructions at their contact interaction.

The solution of scientific problem of elaboration of new models and methods of the stress-deformed state of composite elements of shell construction with rigid punches under localized loads. Two-dimensional models of ortho- tropic shells, plates and beams with the account of transversal shear, transversal normal stresses and displacements have been developed. A hypothesis about the possibility of decomposition of components of the vector of casing arbitral point in the form of trancated power series along the lateral coordinate has been used for the construction of the models. From the Lagrange's variational principle for full potential energy of elastic system the author received a system of five differential equations in partial derivatives of 14-th order, and variational equalities for formulation of seven limit conditions on the casing borders. Axisymmetrical problem of transversal-isotropic roads plates bending on the elastic half-space under localized loading is considered with the help of Hankel 's method of integral transforms. The dependency of contact displacements and stresses distribution on the contact area quantity of transversal-anisotropy plates is investigated. The stresses and displacements values are compared with the corresponding results of elasticity theory. Thus, the generalized theory of shells and plates indicates that at their analysis one should take into account not only the corrections for lateral shear deformation but also the corrections for lateral normal stresses and deformations. The latter ones may in some cases (contact problems) considerably exceed the shear corrections and play the leading role.