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• ## Pure bending of hereditary viscoelastic rectangular plates

On the basis of the proposed Timoshenko S. P. solution of the problem of pure bending of an elastic rectangular plate under the action of moments of constant intensity acting on its boundary, the theory of bending of viscoelastic plates fixed in the vertices is proposed for the first time. The proposed solution uses the hereditary theory taking into account the hypothesis of N. H. Harutyunyan about the constancy of the coefficient of transverse deformation. For the first time, a method of recalculation of the distributed transverse load applied on the surface of the plate at equivalent moments of constant intensity, time-dependent and applied at the edges, is proposed. For the first time with the help of this theory, the problem of bending a plate pinched at a single angular point distributed by a transverse load is solved. As examples, calculations of rectangular plates under the action of their own weight are given.

Keywords: roller blade, horizontal mixer, optimization, design, process, material procurement, machining, reduction of production costs

• ## Spatial equations of mechanics of composite solid for viscoelasticity models containing in one-dimensional case of two elastic and one viscous element

For the first time, in the generalization to the spatial case of a one-dimensional viscoe-lasticity model for one viscous and two elastic elements, the stress deviators, deformations, and also the stress and strain rates were used. It is established that the model of a standard viscoelastic body (standard linear solid model) is more universal. The second model cannot be used to solve problems for a weighty body, or dynamic problems, since leads to the solution of an auxiliary physically unjustified boundary or initial-boundary value problem for doubled values of the accelerations. It means that the second model can be applied only to the solution of quasistatic problems for weightless bodies. It is established that the model of a standard viscoelastic body (standard linear solid model) is applicable only to the study of unsteady creep, while the second model is suitable for investigating the steady rheological behavior of a weightless material. Generalization of both models viscoelasticity for composite body was created. The effective Kravchuk-Tarasyuk values of the Poisson ratio, the Young's modulus, and the viscosity of composite material were defined.

Keywords: deviator of stresses, deviator of strains, deviator of stress rates, deviator of strain rates, viscosity, standard linear solid model

• ## Determination of the yield stress of the material by static indentation

For the first time, using the simplest model of an elasto-ideally-plastic coating, a relationship between the Meyer hardness and the absolute value of the yield stress of the material under compression was established for all types of indenters used for static hardness testing. The necessity for an accurate determination of the thickness of the layer in the simplest coating model is eliminated, when using the Prandtl bilinear diagram corresponding to an elasto-perfectly-plastic material as the equation of state. If the linear dimension of the test mark of the hardness is equal to 90 percent of the linear dimension of the total contact area, taking into account the elastic deformations, than the Meyer hardness is the absolute value of the compressive yield strength for the material under compression.

Keywords: surface hardness, Meyer hardness, yield strength, ball indenter, conic indenter, pyramidal indentor