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ABSTRACT: The paper outlines an approach to identifying the principal dynamic-instability domain for systems composed of shells of revolution
with different shapes under axisymmetric periodic loading. The original problem is reduced to one-dimensional eigenvalue problems
with respect to the meridional coordinate. Results of calculations for a specific shell system are presented
Keywordsshell system–periodic load–dynamic instability domain
International Applied Mechanics 05/2012; 47(2):186-194.
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ABSTRACT: An approach to studying the vibrations of statically loaded nonthin inhomogeneous anisotropic shells of revolution with complex
geometry is developed. The approach is based on a nonclassical theory of shells that takes into account transverse shear and
reduction. The expediency of allowing for these factors in the analysis of natural frequencies is confirmed by specific examples
Keywordslayered shells of revolution-prestress-nonclassical model-transverse shear-reduction-numerical analytical solution
International Applied Mechanics 04/2012; 46(3):279-286.
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ABSTRACT: A method of studying the natural vibrations of highly inhomogeneous shells of revolution is developed. The method is based
on a nonclassical theory of shells that allows for transverse shear and reduction. By separating variables, the two-dimensional
problem is reduced to a sequence of one-dimensional eigenvalue problems. The inverse iteration method is used to reduce these
problems to a sequence of inhomogeneous boundary-value problems solved by the orthogonal sweep method. The capabilities of
the method are illustrated by solving certain representative problems and comparing their solutions with those obtained using
the three-dimensional theory of elasticity, the classical theory of shells, and the refined Timoshenko model
International Applied Mechanics 01/2007; 43(9):980-987.
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ABSTRACT: We propose a procedure for the solution of the contact problem for preliminarily loaded anisotropic shells of revolution as
applied to the evaluation of the stressed state of pneumatic tires. We use the principal relations of the nonclassical model
of shells with regard for all types of transverse deformation. The preliminary stresses induced in the shell by axisymmetric
loads of various kinds are taken into account as parametric terms in the linearization of the initial geometrically nonlinear
equations of medium bending. The corresponding two-dimensional boundary-value problems are solved with the help of a combination
of analytic and numerical approaches. By using a structure simulating pneumatic tires as an example, we study the influence
of internal pressure on the size of the contact zone with rigid base, the characteristic of loading, and static stiffness.
Strength of Materials 01/2007; 39(3):275-283. · 0.23 Impact Factor
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ABSTRACT: A nonclassical model of shells that accounts for transverse shears and reduction is used to develop a method for solving the
contact problem for inhomogeneous anisotropic shells of revolution subject to a field of mechanical and thermal loads. The
prestresses are described by parametric terms in the linearized geometrically nonlinear equations of the second-order theory
of flexible shells. The influence of the prestressed state of shells interacting with a flat surface on the contact area and
the distribution of contact pressure is analyzed. Some computational features of the technique are discussed
International Applied Mechanics 09/2006; 42(10):1137-1144.
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ABSTRACT: A method is proposed to solve the contact problem for laminated anisotropic shells of revolution. The method is based on a two-dimensional model that accounts for transverse shears and reduction. Also the method is based on the method of successive approximations, the generalized pseudo-force method, and a numerical-analytical method of solving boundary-value problems. The results obtained for a cylindrical shell of complex thickness structure are compared with those obtained in three-dimensional formulation
International Applied Mechanics 04/2005; 41(5):520-525.
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ABSTRACT: The class of stress problems for orthotropic shells of revolution loaded along narrow ring zones or by forces concentrated in the meridional direction is analyzed on the basis of a refined model. It is established that the solutions of these two problems for essentially anisotropic shells do not fully agree
International Applied Mechanics 01/2004; 40(2):213-217.
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ABSTRACT: An approach is proposed for refined solution of stress problems for elastic systems consisting of coaxial shells of revolution. Transverse shear and reduction are taken into account. Multivariant calculations made for orthotropic cylindrical shells with elliptical end-plates allow us to analyze the influence of the semiaxis ratio and intermediate supports on the stress–strain state of the shell systems under consideration
International Applied Mechanics 01/2003; 39(5):587-594.
