Some geometrically nonlinear problems of deformation of inelastic plates and shallow shells

This paper considers geometrically nonlinear problems of deformation of elastoplastic shallow shells and viscoelastoplastic plates where it is required to find kinematic loads for a given time interval such that a shell (plate) acquires prescribed residual deflections after these loads are applied and then removed. For some constraints, the correctness of the corresponding formulations (uniqueness of the solution and its continuous dependence on the problem data) is shown and iterative solution methods are justified.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 151–157, March–April, 2005.     

Dynamic stability of geometrically and physically nonlinear shallow shells with connectedness of the deformation and temperature taken into account

Saratov Polytechnic Institute. Translated from Prikladnaya Mekhanika, Vol. 25, No. 11, pp. 49–54, November, 1989.     

Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005.     

Canonical equations in the geometrically nonlinear theory of thin anisotropic shells

The functional in the principle of minimum potential energy of layered anisotropic shells with a nonlinear relationship between strains and displacements is transformed into a canonical integral that coincides with the functional in the Reissner principle. Partial forms of the functional are derived for problem formulations where the dimension can be reduced with respect to one of the coordinates. The canonical system of equations is linearized and then normalized. The boundary-value problem is solved by the numerical discrete-orthogonalization method. An anisotropic spherical shell under external compression is analyzed for stability as an example     

Modification of a generalized theory of shallow sandwich shells taking into account squeezing of the physically nonlinear filler

Zaporozh. University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 12, pp. 39–45, December, 1990.     

Analytical formulas of solutions of geometrically nonlinear equations of axisymmetric plates and shallow shells

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equations.     

Solvability of a class of second-order quasilinear boundary value problems

The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.     

Refined variant of a nonlinear theory of shells of the Timoshenko type and its use for calculating the initial post-critical behavior of long cylindrical shells

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 8, pp. 47–53, August, 1990.