Residual technological stresses in the winding of the stator of large electrical machines

Conclusions Equations were derived for calculating RTS in the gap part and the zone of bending the coils and bars of the stator winding; it was shown that in calculating the RTS in the bending zones, it is necessary to take into account the presence of residual stresses in the copper of the bar. The calculated and experimental results indicate the high concentration of the stresses _X in the bending zones, These regions are most critical from the view-point of possible disruption of the monolithic nature and reduction in the electrical strength of the housing insulation.Paper presented at the Fifth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1983).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 868–872, September–October, 1983.     

Experimental study of the effect of technological parameters on the residual stresses in thin-walled coiled parts

The effect of the parameters of heat treatment and programmed winding under tension on the residual stresses in thin-walled coiled parts made from glass plastic by the "dry" winding of a heated glass strip on an unheated mandrel is studied experimentally. The effect of the thickness of the parts on the maximum radial residual stresses is considered. A method is proposed for regulating the residual stresses in parts with very thick walls.Translated from Mekhanika Polimerov, No. 1, pp. 75–80, January–February, 1972.     

State of stress and strain of a multilayered composite flexible pipe reinforced by helical carcass

Conclusion The model of a composite flexible pipe reinforced by a helical carcass, suggested in the present article, makes it possible to reduce the problem of calculating its strength and rigidity to the calculation of a multilayered anisotropic shell. It was established that when the flexible pipe is exposed to internal pressure and axial load, two states of equilibrium in regard to untwisting of the pipe are possible, and they are attained with different combinations of the winding angles of the reinforcing elements in the longitudinally bearing layers. The characteristics of strength and rigidity of a flexible pipe depend in different ways on the winding angles of the reinforcing elements. An analysis of these dependences makes it possible to choose rational winding angles in combination with the specified requirements that the parameters of strength and rigidity of the newly devised pipes have to satisfy.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1061–1067, November–December, 1987.     

Design of anisotropic thin-walled rods consisting of flat strips of symmetrical cross section

Conclusion The approach demonstrated in [1] for deducing generalized rod models from equations for uniform and isotropic folded structures in which the strips are rigidly joined in bending was expanded to the case of symmetrical anisotropic structures. Thus, we have developed an effective approach for global structural analysis of thin-walled three-dimensional structures made of composites. Here, we examined the feasibility of using the method of initial parameters to solve the differential equations in certain special cases. In the general case, global structural analysis requires the use of powerful numerical methods. In the case of an isotropic material, use can be made of methods of solving first-order canonical differential equations or methods based on a solution obtained by means of quasi-unidimensional finite elements. The application of the last approach to the case of composite materials will be demonstrated in a future article.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 641–649, July–August, 1989.     

Statistical characteristics of the mechanical constants of glass-reinforced plastics

The results of statistical treatment of experimental data on the physicomechanical properties of glass-reinforced plastics, based on alkali-free, aluminoborosilicate glass fibers (composition NS-55/6) with paraffin as lubricant and epoxyphenolbutyral composition EFB-4, obtained from tensile tests on flat specimens prepared by "wet" winding on a mandrel, are given. The data can be used for evaluating the effect of the scatter of the mechanical constants of a composite material on the efficiency of a structure and its elements.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1125–1128, November–December, 1972.     

Calculation of the residual stresses and strains in wound reinforced-plastic products

A method is proposed for determining the residual stresses and strains in wound glass-reinforced plastic products. The fabrication process is divided into five stages: winding, heating polymerization, cooling, and removal from the mandrel. The initial stresses that develop during winding and the subsequent stress increment associated with heating are taken into account. Polymerization is treated as a process during which the mechanical and thermophysical properties of the material change. Chemical shrinkage of the resin and its filtration through the fiberglass are disregarded. Equations are derived for the residual radial and peripheral stresses in the finished product, for the residual change in inside diameter, and for the temperature at which the product is released from the mandrel during the cooling process. The experimental data relating to two types of wound products are discussed. The results of a computation of the residual stresses and the residual changes in inside diameter are compared with the experimental data.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 134–139, January–February, 1969.     

Nonlinear contact problems for thin-walled elements of constructions

Some one-dimensional contact problems for plates and shells are considered for one-side contact with a rigid base. Contrary to analogous papers about the zone of contact, we use applied theories of contraction of Winkler type, which are obtained from equations of elasticity theory by asymptotic methods together with bending equations of thin-walled elements. The possibility of deviation of shells needs a definition of a contact zone in the process of solution of the problem from the condition of continuity of bending and its derivatives up to the second order inclusive. Some conclusions are made with respect to the optimal projects of reinforcement of shells taking into account their deviation.Translated from Dinamicheskie Sistemy, No. 8, pp. 40–45, 1989.     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations

Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an appropriate, critical quadrature rule; this allows the elimination of the flux and Lagrange multiplier parameters so as to obtain equations in the scalar variable, which will define the finite volume method. Following this derivation with different mixed finite element spaces leads to a variety of finite volume schemes. In particular, we restrict ourselves to finite volume methods posed over rectangular partitions and begin by studying an efficient second-order finite volume method based on the Brezzi–Douglas–Fortin–Marini space of index two. Then, we present a general global analysis of the difference between the solution of the underlying mixed finite element method and its related finite volume method. Then, we derive finite volume methods of all orders from the Raviart–Thomas two-dimensional rectangular elements; we also find finite volume methods to associate with BDFM ₂ three-dimensional rectangles. In each case, we obtain optimal error estimates for both the scalar variable and the recovered flux.     

Filament-wound rings tested by the application of concentrated loads

The stiffness and strength of rings and ring segments of fiber-reinforced materials have been investigated theoretically and experimentally in short-time tests with concentrated loads applied in the plane of the specimen. It is shown that the low shear resistance and the geometric nonlinearity must be taken into account in testing thick- and thin-walled specimens, respectively. The equations and graphs presented make it possible to allow for these effects in analyzing the test results or in design calculations. Experiments on unidirectional glass-reinforced plastics indicate good agreement with the proposed theoretical equations.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 719–727, July–August, 1969.     

Correlation of the elastic characteristics of Arimid PM with the elasticity modulus of its crystal lattice

Studies were made of the elastic characteristics (longitudinal elasticity modulus, elastic recovery) of Arimid PM fibers and of the longitudinal elasticity modulus of the crystal lattice of these samples. The elasticity modulus of the crystallites was determined by x-ray diffraction studies of loaded fibers. It is shown that the studied samples practically instanteneously recover their starting length after removing the load; the sample and its crystal lattice have comparatively low elasticity moduli with nearly identical values. Based on this data, reasons are discussed for the high elastic recovery of Arimid fibers and for the low elasticity modulus of its crystal lattice.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 771–773, September–October, 1972.     

A model for taking into account the nonlinearity of properties of a semifinished product in the force analysis of the winding of composite materials

Conclusions 1. The proposed method of accounting for the nonlinearity of properties of a semifinished product by a piecewise-linear approximation of its stress—strain diagram greatly refines the calculation of stresses induced during the process of winding a product.2. A numerical analysis has revealed the ranges of values of the winding parameters where replacing the nonlinear model by simpler linear models for the calculation is appropriate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 231–240, March–April, 1977.     

Moduli of elasticity of crystal lattices of polyamides and crystallike elements of amorphous poly(amido acids)

From the displacement of meridional reflections on large angle x-ray diffractograms of fibers from polyimides PM, PFG, DFOFG and the corresponding poly(amido acids) during their elastic deformation along the axis, determinations were made of the elasticity moduli of crystalline lattices of polyamides and of the crystallike elements of amorphous poly(amido acids).Collaborator in the Structural-Chemical Laboratory of the Academy of Sciences of Hungary; participated in this study during probation in the Laboratory of Physical Chemistry of Polymers, Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, in 1971.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, Vol. 6, pp. 1014–1020, November–December, 1972.     

Numerical realization of the asymptotic averaging method for thermoelastic multidirectional composites

A zero approximation of the asymptotic averaging method is applied to investigate the structural stresses in the structures of spatially reinforced composite materials subjected to mechanical loading and high-temperature heating. A carbon-carbon composite material reinforced with anisotropic fibers in three mutually orthogonal directions in the ratio 111 is considered. According to the averaging method, the local functions, namely the components of the tensors of elastic moduli and thermoelasticity in a zero approximation, must be determined by solving a set of problems for a periodicity cell. The effective thermoelastic constants of the composite are found by averaging the local functions obtained over the periodicity cell. To calculate the structural stresses in constructions, the periodic local functions and the field of macrostrains, which is obtained from the solution of the averaged boundary value problem, must be known. The problems posed for the periodicity cell are solved by the method of finite elements. The average values of the local functions and the measures of deviation from them are examined for various temperatures and volume fractions of fibers of two different cross section shapes.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 455–464, July–August, 1999.     

Investigation of the principal dense-winding conditions for wound glass-reinforced plastic pipe

The dense-winding conditions have been found for glass-reinforced plastic pipe wound simultaneously with a large number of strands [conditions (15), (17), and (18)] and relations have been obtained for calculating the winding mechanism kinematics. Kinematic equations have been derived for dense winding by displacement of the strands in the pipe cross section, along the pipe axis, and in both directions at once.Glass-Reinforced Plastics Division of the All-Union Lenin Electrical Engineering Institute, Khar'kov. Translated from Mekhanika Polimerov, No. 6, pp. 1057–1064, November–December, 1970.     

Problems of the mechanics of winding thick-walled composite structures

Conclusions Dividing the winding process into individual stages, examination of the interply compliance of the composites, and the introduction of the circular metals made it possible to link the parameters of this process and, in particular, the tensioning force, with the properties of the completed component. It was thus possible to propose engineering methods of calculating thick-walled wound components with an allowance made for technological prior history. Structures for specific applications were constructed and a new technological method proposed and applied. These methods include the methods of producing spatial reinforced driveshafts whose load-carrying frame is produced on the basis of the system of the single filament. The studies examined in this work were used as a starting point for further investigations and development of the mechanics of winding in a number of scientific centers of the country.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 618–626, September–October, 1992.     

Elastoplastic deformations of metal pressure vessels reinforced with unidirectional glass-reinforced plastic

The design of cylindrical shells reinforced in the circumferential direction with high-strength elastic fibers is considered. The problem is solved on the basis of the deformation and flow theories. Relations are derived for the layer thickness required to obtain a structure of uniform strength and for the tension that must be applied to the glass tape during winding.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1069–1074, November–December, 1969.     

Determination of the thermal stresses in anisotropic shells of revolution

Using the relations of the improved model of layered anisotropic shells based on the straight line assumption taking account of the thermal compression over the thickness we obtain a resolvent system of equations for shells whose properties depend on temperature. We carry out a study of the stresses in a two-layer cylindrical shell formed by winding as a function of the winding angle. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 82–85.     

Determination of the mechanical indices of composite materials by testing multilayered samples

The mechanical indices of materials such as composites reinforced by braids and ribbons are difficult to determine by standard methods. Moreover, the indices of such materials may be greatly altered when they are converted into various structures. It has been suggested that these indices be determined by analyzing the structure testing data. The determination of linear and nonlinear elastic, plastic, and viscoelastic parameters of reinforced materials is discussed. A very simple structure, namely, cylindrical shells made by symmetric winding, is studied as an example. Equilibrium conditions are used to obtain resolving equations relative to the mechanical indices. Convergence of iteration methods is examined. The effect of the scatter of experimental data on the calculated results is analyzed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 607–615, September–October, 1995.     

Nonuniform isothermal curing of cylindrical products made of polymeric composites

Conclusion By increasing the curing temperature and reducing the winding rate, it is possible to obtain compressive radial stresses in a cylindrical product during the entire curing stage — which should prevent loss of integrity during the curing operation. When the duration of the curing process is limited, the magnitude of the compressive stresses will depend in an extreme manner on curing temperature. Meanwhile, in the general case, ensuring minimal residual stresses will not ensure the absence of tensile radial stresses during curing.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 873–877, September–October, 1988.