Theory of composite grid shells

The grid shells formed by a system of edges are currently used in structures of various destination. In the last years, geodesic grid structures manufactured of modern composite materials by the winding method find increasingly wider applications in rocket-space technology as rocket transfer modules, spacecraft bodies, and load-carrying components of space platforms which have the form of cylindrical or conic shells. Grid composite shells are considered as promising elements of the passenger aircraft wing, empennage, and fuselage structures of sufficiently irregular shapes. In the present paper, general equations of the theory of composite grid shells are derived and their possible simplifications are considered.     

On the formulation of contact problems of shells and plates

The equations of motion in terms of resultants and the constitutive equations in the theory of shells and plates are ordinarily derived from the three-dimensional equations relative to an interior surface, often taken to be the middle surface in the reference configuration of the shell-like body. This usual formulation is not, in general, applicable to contact problems of shells for which one of the major surfaces, e.g., the upper surface, is specified as the reference surface. The present paper is concerned with the transformation relations between the relevant variables (and hence also the response functions) of the traditional formulation and one which can be obtained relative to one of the major surfaces. Our derivations, carried out both from the three-dimensional equations and by a direct approach, utilize only the conservation laws and the field equations without recourse to constitutive equations. Hence, the results are applicable to any shell-like medium and their validity is not limited to elastic shells alone.     

On some problems of plastic buckling of plates and shells

This paper gives the stress-strain relations of the variational types on the basis of an assumption concerning the small deformation in the theory of elasto-plasticity.The compact form of fundamental equations of plastic buckling of the plates and shells is obtained in terms of secant modulus.     

On numerical solution of dynamic problems in the theory of reinforced shells

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 50–56, May 2006.     

Discretized solution of junction problems in shells

Summary A discretization method based on a shifting field is presented. For plate flexure this is a congruent field of displacements, for plate extension an equilibrium configuration of stresses, for shells a mixed system. The main purpose of the present investigation is to establish a procedure for the numerical analysis of shell intersection problems.

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Sommario Si presenta un metodo di discretizzazione che si vale di un campo mobile, di spostamenti congruenti per gli stati flessionali della piastra, di tensioni equilibrate per gli stati estensionali, di spostamenti e tensioni per il guscio. Scopo essenziale della ricerca è la costruzione di un procedimento per l'analisi numerica dei problemi di intersezione dei gusci.

     

Two-dimensional statics problems of noncircular cylindrical shells

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev, Translated from Prikladnaya Mekhanika, Vol. 27, No. 10, pp. 90–95, October, 1991.     

On solution of problems of dynamics of plates and shells with local structure heterogeneities

A general approach to the solution of nonstationary problems of the theory of shells with local structure heterogeneities is proposed. The approach is based on representation of solutions for the systems of differential motion equations of shell theory in the form of expansions in terms of free forms of vibrations (FFV). Two implementations of the approach, involving FFV expansions of certain members and FFV expansions of the system as a whole, are considered. The capabilities of the approach are illustrated by results for specific problems. In the first implementation, we determine the dynamic stress-strain state of a square plate with three rod supports. A round plate connected to a coaxial circular cylindrical shell is considered as an example of FFV expansion of the system as a whole. Special Design and Engineering Office, S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 46–53, October, 1999     

On symmetry of shells

Here, we consider transformations of generalised coordinates in describing the symmetry of shells.     

On one iteration method for solving problems on the stress-strain state of thin shells

Decomposition methods are used in solving problems on the stress-starin state of thin shells. The problem is reduced to the iterative solution of a system of equations that have a simpler structure and permit constructing a computing parallel-integration algorithm. The stress-strain problem is solved by an example of a shallow spherical shell. The effect of the curvature of the shell on the number of iterations necessary for reaching the accuracy prescribed is studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 98–103, June, 2000.     

One-dimensional problems in the stability of thin shells

Summary Algebraic conditions, sufficient for the infinitestimal stability of elastic shells in the class of one-dimensional perturbations from homogeneous ground states, are considered. A necessary and sufficient condition for superstability is also deduced.The shells are modelled according to the director theory. Unlike three-dimensional elastic continua, the strain energy depends on the displacement components and not only on their gradients. This plays a central role in the analysis of these problems.