Stability of composite prismatic rod of rectangular cross-section at central compression

Actuality of this study is not only in the fact that these problems are not solved for composite rods, but also in the fact that, unfortunately, despite of the huge interest in solving this problems it was still remained methodological inaccuracies in their solutions. Studies carried out led to the conclusion that the known equation of the losses of stability corresponds to only two schemes of constraints of ends of centrally compressed along the 0x axis rod: two fixed-ends in 0y direction, as well as fixation in 0y direction of the top end (it means the rod end of application of the force) and fixation in 0y direction of derivative of the equation of neutral layer of rod at the bottom end. The equation of Euler stability cannot be used to solve the problems of stability with the lower "clamped" and the free top ends. Applied in many papers increasing of order of differential equation for study of other schemes of fixation of rod ends has no mathematical justification. An equation for definition of the value of the first critical force was obtained depending on the concentration of the components in the composite material. The solution to the problem of stability for uniform aging viscoelastic material of rod was hold. The relaxation equation of the first critical load was defined. This solution is generalized to inhomogeneous composite material which consists of homogeneously aging viscoelastic components.

устойчивость стержней, вязкоупругие свойства твердых тел, композиционные тела, приближение Хилла кривизны композиционного стержня, эффективные деформационные и реологические свойства композиционного стержня, stability of rods, viscoelastic properties of solids, composite body, Hill approximation of curvature of the composite rod, effective deformation and rheological properties of the composite rod

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