On Design Models in Stability Problems for Corrugated Cylindrical Shells

Three design techniques for stability analysis of longitudinally corrugated cylindrical shells are examined. The first two account for the true geometry of the shell and the third one replaces the corrugated shell with an equivalent orthotropic shell using reduction formulas. The exact formulations employ classical and Timoshenko-type theories. The techniques are analyzed by an example of sinusoidally corrugated shells. It is shown that the exact formulation permits finding practically important relations for corrugation parameters, which raises considerably the specific critical loads.     

The temperature dependence of parachor

The results obtained in studying the temperature dependence of parachor are presented. The concepts of the parachor at the critical point and reduced parachor are introduced. The approach based on scaling principles and the assumption of a universal character of changes in crossover functions at critical exponents was used to obtain a universal temperature dependence of the reduced parachor. The dependence of the parachor at the critical point on the critical molar volume was established. The constituents of parachor were determined for halogenated hydrocarbons.     

Stability of corrugated composite noncircular cylindrical shells under external pressure

Cylindrical shells consisting of cylindrical panels of smaller radius and subjected to uniform external pressure are analyzed for stability. The geometrical parameters of the shells are approximated by Fourier series on a discrete set of points. The Timoshenko theory of shells is used. The solution is represented in the form of trigonometric series. It is shown that short-and medium-length shells with cylindrical panels are advantageous over circular shells. By selecting appropriate parameters of the panels, keeping the mass of the shell constant, it is possible to achieve a significant gain in critical loads. The shells under consideration are less effective than isotropic shells. Shells with sinusoidal corrugation under external pressure are of no practical interest __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 91–102, December 2007.     

On the canonical equations of Kirchhoff-Love theory of shells

The paper outlines a procedure to derive the canonical system of equations of the classical theory of thin shells using Reissner’s variational principle and partial variational principles. The Hamiltonian form of the Reissner functional is obtained using Lagrange multipliers to include the kinematical conditions that follow from the Kirchhoff-Love hypotheses. It is shown that the canonical system of equations can be represented in three different forms: one conventional form (five equilibrium equations) and two forms that are equivalent to it. This can be proved by reducing them to the same system of three equations. For problems with separable active and passive variables, partial variational principles are formulated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 99–107, October 2007.     

Stability of longitudinally corrugated cylindrical shells under uniform surface pressure

The buckling problem for longitudinally corrugated cylindrical shells under external pressure is solved. The solution makes practically exact allowance for the geometry and buckling modes of the shell. The inaccuracy of the results is due to the assumption that the subcritical state is momentless. Shells consisting of cylindrical panels of smaller radius and noncircular shells with sinusoidal corrugations are analyzed for stability. The practical applicability of such shells is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 66–79, October 2007.     

Influence of imperfect bonding of the components on the mechanical properties and stability of cylindrical nanocomposite shells

An approach to determining the effective characteristics of nanocomposites with well-known methods of micromechanics is proposed. The irregular distribution of discrete bonds between a nanofiber and the polymeric matrix over the fiber circumference is taken into account. The area with a great number of bonds is modeled by a continuum and the area with a small number of bonds is modeled by a discontinuity. The dependence of the mechanical characteristics of nanocomposites on the volume fraction of the reinforcement and the size of the imperfect-bonding zone is studied. The performance of such materials in structures is demonstrated by stability design of cylindrical shells