Minimization of the weight of ribbed cylindrical shells made of a viscoelastic composite

The minimization of the weight of ribbed viscoelastic composite cylindrical shells under a long-term external pressure is considered. The shells are strengthened with six inner stiffening rings with identical geometric parameters and a square cross section. It is assumed that the shell material obeys the linear law of hereditary creep and the displacements across the shell wall are distributed according to the Timoshenko hypothesis. The shell must withstand an external pressure of –0.5 MPa without the loss of stability for an unlimited time. The parameters of optimization are the intensity of reinforcement and thickness of its covering and the height and width of the stiffening rings. It is found that the weight of an optimum ribbed shell is 24% lower than that of an optimum cylindrical shell without ribs.     

Optimal reinforcement of a material in a known state of stress

The problem of minimizing the total reinforcement of a material in a known state of stress is considered. In the proposed geometric formulation the problem reduces to the determination in normal stress space of the shortest path from a point representing the state of stress to the region of strength. Examples of the determination of the relative area of reinforcement in three-dimensional and plane states of stress are given for characteristic regions of strength: for plane stress and plane strain the calculations lead to expressions that permit the relative areas of reinforcement to be determined directly.Kucherenko Central Scientific-Research Institute of Building Structures, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 922–930, September–October, 1971.     

Effectiveness of radially reinforced bodies of revolution

The relative effectiveness of glass-reinforced plastics with radial as compared with tangential reinforcement (obtained, for example, by winding) as a material for bodies of revolution subjected to external hydrostatic pressure is examined.     

相对遗传环

本文给出了左相对遗传环的概念及刻划.讨论了左相对遗传环与左遗传环,左半遗传环的关系,并给出了左遗传环的几个新的刻划.最后,证明了左相对遗传环(相对于左模范畴的生成元)的左理想的自同态环是左半遗传的;左相对遗传环(相对于左模范畴的内射生成元)上的有限生成相对投射模的自同态环是左半遗传的等结果.     

Strength of an organic/glass fiber-reinforced textolite in plane stress

Conclusions An analysis of the results of testing hybrid glass organic textolites, containing layers of glass and organic fabric reinforcement in various proportions, along characteristic simple short-time quasi-static loading paths served as a basis for determining a family of strength surfaces for plane stress in the plane of reinforcement. The strength of the five materials investigated is described by a second-order surface equation with allowance for the difference in compressive and tensile strengths. The dependence of the strength surface tensor components entering into the strength equation on the structure parameter representing the relative content of organic and glass fabric in the hybrid textolite is investigated and described. The results obtained can be used in practical calculations for determining the optimum ratio of organic to glass fabric in hybrid material with allowance for the specific requirements to be met by the strength properties of the material when used for structural purposes.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1021–1026, November–December, 1979.     

Stability of hydrostatic-pressured FGM thick rings with material nonlinearity

Buckling behaviors of elastoplastic ceramic/metallic functionally graded material (FGM) rings are investigated by using the first order shear deformation theory. The hydrostatic-pressured rings are assumed to be in both the plane-stress case and the plane-strain case, which lead respectively to a uniaxial and a biaxial elastoplastic stress states in prebuckling stage. A uniform strain hypothesis helps to deal with the elastoplastic stress states. By introducing in the graded material properties, the constitutive model of FGMs is formulated under the framework of J₂ deformation theory. By considering the kinetic relations of von-Kárman type and employing the principle of virtual displacement, the equilibrium equations and the buckling governing equations of FGM circular rings are formulated, and the analytical solution of the anisotropic rings is obtained. Finally, the elastoplastic buckling problem is numerically solved through a semi-analytical method, which is proposed to seek the real circumferential strain of FGM rings at the buckling point and determinate the elastoplastic buckling critical hydrostatic pressure. The effects of the inhomogeneous and geometrical parameters on the buckling critical load and the position of the elastoplastic interface are discussed. Results show that, in both the plane-stress and the plane-strain cases, the elastoplastic critical loads are generally lower than their elastic counterparts due to material flow, and the plane-strain critical load is generally larger than the plane-stress one. The elastoplastic critical load does not always decrease monotonously with the increase of the inhomogeneous parameters, which is quite different from their elastic counterparts.     

Structure of nonlinear elastic relationships for the highly anisotropic layer of a nonthin shell

Laminated nonthin shells made of nonlinearly elastic fiber composites are considered. The composite material is assumed to be transversely isotropic in planes perpendicular to reinforcement. The asymptotic method and the condition of material stability are applied to analyze the structure of constitutive relations. To introduce a small parameter, the high stiffness in the reinforcement direction of the fiber composite is used. This allows us to obtain simplified constitutive relations containing functions with one or two arguments instead of five as in the initial general case. Kazan State Architectural Building Academy, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 615–628, September–October, 1999.     

Experimental Evaluation of the Effect of the Structure of Composite Rings on Their Properties in the Radial Direction

Based on the results of bending tests on cut glass-fiber-reinforced plastic rings with a longitudinal-circumferential reinforcement, their radial peel strength is evaluated. The effect of the fiber layout on the properties of the rings in the radial direction is investigated. It is shown that their radial tensile strength only slightly depends on the fiber layout but is basically determined by the properties of the polymer interlayer between the fibers. In radial tension, the presence of fibers in the polymer layer leads to a strain concentration, which results in a premature failure of the polymer phase of the composite. The strain-concentration factor cannot be used for an accurate prediction of the breaking stresses or strains of the composite, because of different failure modes of the pure resin and the composite.     

Experimental-theoretical study of thermal deformations of the KMU-8 structural CFRP

Conclusion The prediction techniques used herein make it possible to calculate with high accuracy the thermal characteristics of the material with the examined reinforcement schemes and make it possible to select the required reinforcement schemes in the design of articles made of a CM of the KMU-8 type. The use of particular reinforcement schemes makes it possible to obtain the desired values of the CLTE of the material in the required direction, and increase of the temperature in the CFRP working range does not lead to qualitative changes of these parameters.Translated from Meknanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 608–612, September–October, 1993.     

Virtually Gorenstein rings and relative homology of complexes

We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that all Gorenstein projective R-modules are Gorenstein flat. For such a ring R, we introduce the notion of relative homology functors of complexes with respect to Gorenstein projective (resp., flat) modules, and establish a balanced and a vanishing result for the homology functor.     

Evaluating the effect of whiskerization of the fibers of composites on the fundamental frequency of a laminated cylindrical shell

Conclusion The calculations showed that whiskerization of the reinforcement of the structural material of multilaminate shells makes it possible in some cases to increase the fundamental vibration frequency of the structure up to 15–20%. In combination with the well-known [1] effect of improved strength characteristics for a whiskerized composite in the transverse and shear directions, this finding allows us to conclude that whiskerized structural materials are more efficient than ordinary laminated composites in shell-type load-bearing structures. Here, the greatest benefit can be expected in the case of whiskers which have higher elastic moduli than the main reinforcement. Since considerably higher reinforcement intensities can be achieved in whiskerized laminated composites than in composites with a reinforcement characterized by an arbitrary three-dimensional structure, it can be concluded on the basis of the results obtained here that, at least for shells of moderate thickness (10 < R/h 50), whiskerized composites are the optimum structural material for load-bearing shells.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1022–1027, November–December, 1987.     

Minimizing the mass of cylindrical shells formed from a composite material with an elastic filler and designed for strength and stability under a combined loading

The mass of a multilayer cylindrical shell, formed from a composite material with an elastic filler and designed for strength and stability under the combined action of axial compression and external pressure, is minimized. The problem is formulated as one of nonlinear programming and is solved by Rossen's method of projection gradients. The strength of the material is established from analysis of the strength of the layers making up the entire bundle. Failure of an individual layer is determined from Malmeister's criterion. The structure of a shell with different external loads and the dependence of minimal mass on the stiffness of the filler and on the volume coefficient of reinforcement are investigated in numerous examples.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. K. Preikshas Shyaulyaisk Pedagogical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 289–297, March–April, 1976.     

Modern trends in the development of fibrous composites

The two main trends in the development of high-modulus composites are considered. Improved methods of calculation sensitive to the effects associated with the weak shear and transverse characteristics are reviewed. It is shown that the disadvantages of composites with a traditional arrangement of the reinforcement can be overcome. The properties of boron- and carbon-reinforced plastics with a traditional reinforcement structure are described and compared with those of three-dimensionally structured materials with two- or three-strand reinforcing. Whiskerized fiber reinforcement is also considered. A program of further research on high-modulus composites is outlined.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 541–552, May–June, 1972.     

Application of the finite-element method to improve the quasi-exact reinforcement theory of fibrous polymeric composites

In the paper, the WL quasi-exact reinforcement theory of fibrous polymeric composites is improved. An optimum compatibility condition related to the transverse shear problem for a unit cell, which brings solutions closest to reality, is derived. This condition is formulated in the form of a linear combination of maximum radial and circumferential displacements. Optimum coefficients of this combination are determined by comparing analytical and numerical solutions for a test specimen in the form of a rectangular thin plate, which is in a plane strain state and is subject to selected loading schemes. The analytic solutions are obtained for a homogenized material by using the WL reinforcement theory. The numerical solutions are found for an actual heterogeneous composite material by using the finite-element method, and they verify the WL reinforcement theory, in particular, the admissibility of Hills assumption. An analysis performed for two composite materials shows that the improved WL reinforcement theory gives adequate displacement fields.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 79–92, January–Febrauary, 2005.     

Model companion and model completion of theories of rings

Extending the language of rings to include predicates for Jacobson radical relations, we show that the theory of regular rings defined by Carson, Lipshitz and Saracino is the model completion of the theory of semisimple rings. Removing the requirement on the Jacobson radical (reduced to {0}), we prove that the theory of rings with no nilpotents does not admit a model companion relative to this augmented language.      

Load-bearing capacity of compressible plates of glass-fiber-reinforced plastic with different placement of the reinforcement

The effect of placement of reinforcement on the load-bearing capacity of circular and rectangular plates compressible in the reinforcement plane was evaluated experimentally. Four placement schemes for circular plates and nine for rectangular plates were investigated. Different schemes of supporting the edges were studied. Two mechanisms of exhaustion of the bearing capacity were revealed. A numerical evaluation and comparison of different placement schemes with respect to the value of the critical and breaking load are given. The role of the actual realization of clamping and nonlinearity of the material is shown. A comparison with analytic relations taking into account the characteristics of the material is given.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 646–653, July–August, 1972.     

Dynamics and self-propulsion of a spherical body shedding coaxial vortex rings in an ideal fluid

We describe a model for the dynamic interaction of a sphere with uniform density and a system of coaxial circular vortex rings in an ideal fluid of equal density. At regular intervals in time, a constraint is imposed that requires the velocity of the fluid relative to the sphere to have no component transverse to a particular circular contour on the sphere. In order to enforce this constraint, new vortex rings are introduced in a manner that conserves the total momentum in the system. This models the shedding of rings from a sharp physical ridge on the sphere coincident with the circular contour. If the position of the contour is fixed on the sphere, vortex shedding is a source of drag. If the position of the contour varies periodically, propulsive rings may be shed in a manner that mimics the locomotion of certain jellyfish. We present simulations representing both cases.     

The holomorphy rings of planar ternary rings with rational prime field

By a deep, recent result of Hartmann and Priess-Crampe any ordered planar ternary ring with rational prime field admits a natural order-compatible place into the reals. This allows us to extend the classical machinery about real places and spaces of orderings, the notion of real and relative holomorphy rings, the Kadison-Dubois representation for these rings, and the Brown-Marshall inequality to arbitrary planar ternary rings with rational prime field.     

Carrying capacity of thick-walled glass-reinforced plastic rings operating under pressure

Experimental data are presented on the carrying capacity and deformability of thick-walled rings made of unidirectional and two-way glass-reinforced plastic subjected to external and internal pressure. A limitation on the carrying capacity of the rings with increase in relative thickness is noted; an explanation of this effect is offered.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1130–1132, November–December, 1971.