Optimization of a cylindrical shell of reinforced plastic with a filler under dynamic loading

Conclusions 1. The numerical investigation of profiles of functions of the physical constraints carried out in this work allows us to assume that problems of optimal design of shells of reinforced plastics, strengthened by an elastic filler, for purposes of stability (static and dynamic) under axial compression, in the given formulation, are problems of convex programming. This guarantees uniqueness of their solution and allows us to use gradient methods for a numerical realization.2. Optimal shells of a composite material have a smaller mass than equivalent shells of high-strength metal alloys. The gain in the expenditure of the material is ensured not only as a result of higher specific characteristics of the composite, but basically as a result of optimizing the reinforcement structure of the pack of orthotropic layers of the shell.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 879–885, September–October, 1977.     

An accurate method to predict the stress concentration in composite laminates with a circular hole under tensile loading

The paper presents a theoretical-numerical hybrid method for determining the stresses distribution in composite laminates containing a circular hole and subjected to uniaxial tensile loading. The method is based upon an appropriate corrective function allowing a simple and rapid evaluation of stress distributions in a generic plate of finite width with a hole based on the theoretical stresses distribution in an infinite plate with the same hole geometry and material. In order to verify the accuracy of the method proposed, various numerical and experimental tests have been performed by considering different laminate lay-ups; in particular, the experimental results have shown that a combined use of the method proposed and the well-know point-stress criterion leads to reliable strength predictions for GFRP or CFRP laminates with a circular hole. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 531–570, July–August, 2007.     

The deformation of a half-space with a gradient elastic coating under arbitrary axisymmetric loading

An analytical-numerical method of solving the Neumann boundary-value problem for an elastic half-space with a gradient elastic coating is proposed. The problem is formulated and the construction of the fundamental solution (Green’s function) is described. The method enables a solution of the problem to be obtained for a fairly wide class of types of non-uniformity of the medium, and effects related to the non-uniformity are investigated analytically. A procedure for calculating the displacement, stress and strain fields is described. Particular attention is devoted to analysing the mechanical characteristics in the transition region from the coating to the elastic substrate.     

Compound vibrator method of determining the complex deformation characteristics of polymeric materials

The propagation velocities c and logarithmic decrements in the longitudinal and shear modes, used for calculating the complex deformation characteristics of polymeric materials, can be simultaneously determined by means of a compound vibrator with a mechanical clamp. Relations are obtained for determining c and when the other end of the specimen is free or fixed and with allowance for the mechanical losses in the measuring rod. The method has been tested on specimens of P-4020E polyethylene at various temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 116–123, January–February, 1970.     

Problems of the theory of deformation of polymeric materials under complex loading

Research on problems of the theory of deformation of polymeric materials under complex loading based on a synthesis of creep theories and the local strains theory is reviewed.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.M. V. Lomonosov Moscow State University. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 434–443, May–June, 1972.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965     

Effect of the starting structure of a polymer on the time dependence of its strength under cyclic loading

The stress dependence of the logarithm of the cyclic life for different modifications of the same polymer is represented by a fan of straight lines that converge upon extrapolation to zero stress at a single point log A_cy, which differs from the analogous extrapolation point log A_st. The possible causes of this effect are discussed.Ioffe Physico-Technical Institute, AS USSR, Leningrad. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1008–1013, November–December, 1968.     

Compromise optimization of a rectangular composite plate subjected to biaxial thermal loading and buckling under the action of shear

The compromise optimization of the structure and geometry of a laminated anisotropic composite plate subjected to biaxial thermal shear loading is considered. From the known properties of the monolayer and given values of a variable structural parameter, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal and transverse thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 471–478, July–August, 2008.     

The problem of the equilibrium of a plate reinforced with stiffeners

The problem of the equilibrium of a non-linear plate reinforced with stiffeners is considered. The idea of a generalized solution of the problem as a critical point of the energy functional of an elastic system is introduced and the existence of a generalized solution of the problem is proved. The convergence of Ritz' method within the framework of this problem and also of the conformal versions of the finite-element method, constructed on the basis of Ritz' method, is validated. Similar problems were discussed in [1–3].