Nonlinear parametric vibrations of cylindrical shells made from composite materials

The dynamic properties of a hinged shell made from a composite material and subjected to combined loads are investigated by means of an orthotropic model. The problem is solved by means of the geometrically nonlinear dynamic equations of the theory of sloping shells, set up on the basis of the Kirchhoff-Love hypothesis. Various cases of loading are considered, i.e., the combined action of a longitudinal pulsating load and an external static pressure and also of a pulsating external pressure and a static axial compression. The wave processes at the middle surface are not taken into account. The system of resolvents is obtained by consecutive application of the variation and averaging methods. The results of the calculations are presented graphically and are analyzed in detail.Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 531–539, May–June, 1973.     

Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry

A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007.     

Hamiltonian approach to studying thin shells of revolution made of composite materials

A method for constructing defining relations of the linear theory of shells of revolution in complex Hamiltonian form has been proposed. Based on the Lagrange variational principle, we have constructed a mathematical model of a multilayer orthotropic shell of revolution. We have obtained explicit expressions for the coefficients and right-hand sides of the Hamiltonian complex system of equations describing the statics of shells of revolution in terms of their rigid characteristics and acting loads. The Hamiltonian resolving system of linear differential equations, formulated in the axially symmetric case, has some specific properties facilitating both analytical studies and numerical procedures of their solution.     

Models of multicriterial optimization of structuring made of composite materials

Mechanics of Composite Materials -     

Dynamics and optimization of cylindrical composite shells

The stability of cylindrical composite shells under dynamic external pressure is discussed. A criterion for determining the load-carrying capacity based on Malmeister's equation with respect to bending parts of deformation is proposed. Optimization of the shell mass relative to various structural parameters has been carried out as a nonlinear programming problem. Numerical results are given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 81–87, January–February, 1995.