Edison Abramidze

A refined theory of flexible layered shells with orthotropic layers of variable thickness is considered. The theory assumes that each layer has a local rotation angle due to lateral shear. This makes it possible to derive equations whose order does not depend on the number of layers. The basic equations and calculation results are presented for a three-layer orthotropic toroidal shell under axisymmetric loading

The deformation of flexible multilayer circular cylindrical shells of variable stiffness is studied under a refined theory that accounts for the inhomogeneity of transverse shear strains. The effect of variation in the thickness at constant weight on the stress–strain state of a shell is analyzed

A version of a refined theory of deformation of flexible multilayered shells of revolution with layers of variable thickness is considered which takes into account non-homogenity of deformation of lateral shear strains. Using the approach for shells of revolution we get a non-linear boundary value problem for the system of ordinary differential equations. The solution of this problem is obtained using the methods of linearization and discrete orthogonalization. Based on the given approach we investigate the concrete examples of the stress-strain state of shells under the action of temperature field. Some numerical results are also discussed.

The nonlinear deformations of elastic spherical shells closed at a pole before and after critical loads are considered. A system of differential equations for the solution of the considered problem is obtained. A numerical solution of the system of differential equations is realized in a particular example.

For the numerical realization of problems of deformed multilayered ellipsoidal geometrically non-linear shells we give a give a non-linear system of differential equations, which provides the solution of these class of problems. This system is obtained on the basis of a version of the refined theory, which takes into account the non-homogeneity of shifts along the layers.            

For the purpose of studying and further numerical realization of the problems of nonlinear deformation of layered shells, nonlinear theories based on the hypotheses of Kirchhoff-Love and polygonal chains are used. For the numerical realization of problems of this class, on the basis of these theories, nonlinear systems of differential equations are obtained for solving problems of nonlinear deformation of layered shells. A particular example of deformation of a layered shell is given. The numerical solution of this example is carried out by numerical realization of systems of nonlinear differential equations obtained on the basis of the mentioned theories. Based on the comparison and proper analysis of the obtained numerical results, some conclusions were drawn.

Based on one of the variants of the improved theory, in the case of axisymmetric loading of a layered cylindrical shell by local surface force, for solution of the nonlinear deformation task the system of decision differential equations is obtained for this class. A particular case of deformation of cylindrical shell is considered, an appropriate analysis based on the results obtained from numerical realization of the example is stated

Based on one of the variants of improved theory, in the case of axisymmetric loading of layered cylindrical shell by local surface force and temperature field, for numerical solution of the nonlinear deformation task is obtained for this class the system of decision differential equations.

A particular example of deformation of cylindrical shell is considered. It is given an appropriate analysis based on the results obtained from numerical realization of the example.