New scientific researches of SPSUACE scientists in the field of models of covers of step-variable thickness provided a basis for a publication in a foreign magazine

Scientists of the St.-Petersburg state university of architecture and civil engineering studied models of shells of step-variable thickness. Results of these scientific researches provided a publication basis in «International Journal of Solids and Structures». The article of D.Sc. in engineering, professor Vladimir V. Karpov «Model of the shells having ribs, reinforcement plates and cutouts» was published in it. This journal is considered the most prestigious on subjects of the given scientific work and is indexed in Scopus and Web of Sсience.

D.Sc. in engineering, professor of SPSUACE Vladimir V. Karpov conducts scientific researches in the sphere of models of shells of step-variable thickness. His researches aim to study durability and stability of supported shell constructions which are used in aircraft construction, mechanical engineering, building and even rocket production. Results of the scientific researches of V.V. Karpov were used by Design office "Salute" at building space systems.

The basic ideas of ribbed shells were stated in the late forties of last century by V.Z.Vlasov and A.I.Lure. Both considered ribs as one-dimensional elements (cores). In this case it is not considered rigid fastening of ribs at crossing and some other factors influencing accuracy of calculations of stability of such shells.

In the model offered by V.V. Karpov, ribs are entered discretely taking into account their width, i.e. contact of a rib and shell occurs on a strip. In this case, it is also considered shear and twisting rigidity of ribs. Importance of such account was confirmed experimentally. To define the place of ribs’ attachment to the shell, there are used individual columnar functions equal to a difference of two individual functions. These functions are multiplied by height of ribs. Limiting transition from individual columnar functions to delta-functions receives a special case of the equations of the ribbed shells known earlier.

According to V.V. Karpov, the balance equations can be received if to equate to zero the first variation of functional of full potential energy of deformation of a shell (this functional represents the work of internal and external forces). The received variation equation can be transformed differently. Mathematical transformations allow to receive boundary conditions on a lateral surface of ribs.

. - If height of ribs in the equations is taken negative we will receive model of the shell weakened by cuts, and on border of cuts boundary conditions of free edge are satisfied, - V.V. Karpov comments his researches.

- In the article I state mathematical models of shells of step-variable thickness, i.e. shells which can have ribs, reinforcement plates and cutouts, and cutouts can be supported by rigidity ribs, - Vladimir Karpov says, - Using the received boundary conditions on a lateral surface of ribs, the method of constructive anisotropy considering shear and twisting rigidity of ribs was developed. It can be also applied to the shells weakened by often placed cuts.

In the article there is considered a variant of reinforcement of a shell by curvilinear ribs, ribs directed at an angle to co-ordinate lines, cuts of a curvilinear outline which can be supported by rigidity ribs. The scientist investigated influence of the account of various factors on stability of ribbed shells, and also showed efficiency of the offered model of a shell of step-variable thickness.

Results of researches of V.V. Karpov are applied in mechanical engineering, aircraft construction, building and rocket production.