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Voronkov V.N.,Central Scientific Research Institute for Engineering TsNIIMash
Mechanics of Solids | Year: 2016

Complex systems whose subsystems interact at finitely many points are considered. The couplings are given by linear homogeneous differential relations. The problem of determining the coupling parameters is solved. To this end, the system oscillations are represented as linear combinations of harmonic responses of the subsystems. For each point of coupling, one can construct a system of linear algebraic equations for the parameters (rigidities) of this coupling. The method is intended for determining the values of rigidities of the couplings between blocks of spacecraft carriers. The analytic model of a simplest structure is carried out as an example. © 2016, Allerton Press, Inc.

Bykov D.L.,Central Scientific Research Institute for Engineering TsNIIMash | Konovalov D.N.,OT Kontakt Ltd. | Mel'nikov V.P.,The Federal Center for Dual Use Technologies Soyuz | Osavchuk A.N.,The Federal Center for Dual Use Technologies Soyuz
Mechanics of Solids | Year: 2010

The filled polymer materials exhibit viscoelastic properties in a wide time range including the millisecond range (~10-2-10 ms) characteristic of different shock loadings of structures made of these materials. We propose a method for the identification of the filled polymer material relaxation kernel in the millisecond time range; this method is based on a shock loading test of a cylindrical sample made of this material. In this test, the disk indenter acceleration is measured by using a piezotransducer. The test scheme does not impose any rigid constraints on the sample dimensions. In particular, it is possible to use samples of typical dimensions of the order of 10 cm, for which the conditions that the sample material is representative of the structure material are necessarily satisfied. The relaxation kernel parameters are identified by numerical minimization of the theoretically predicted indenter velocity deviation from the velocity-time dependence obtained by integrating the acceleration transducer readings. The minimization problem is solved by using a genetic algorithm. The problem of theoretical prediction of the indenter velocity is solved numerically by using a reduced computational scheme whose parameters are chosen from the minimum condition for the deviation from the prediction obtained in the framework of the detailed computational scheme. The use of the reduced computational scheme permits decreasing the computational costs by 3-4 orders of magnitude compared with the detailed computational scheme, which is a necessary condition for the practical applicability of the genetic algorithm in identification problems. We present examples of relaxation kernel identification in the range of 0.1-10ms from the results of the test where the disk indenter raised to the height of 1m falls on the sample end surface. © 2010 Allerton Press, Inc.

In the proposed theory of plasticity, the deviator constitutive relation has a trinomial form (the vectors of stresses, stress rates, and strain rates, which are formed form the deviators, are coplanar) and contains two material functions; one of these functions depends on the modulus of the stress vector, and the other, on the angle between the stress vector and the strain rate, the length of the deformation trajectory arc, and the moduli of the stress and strain vectors. The spherical parts of the stress and strain tensors satisfy the relations of elastic variation in the volume. We obtain conditions on the material functions of the model which ensure the mathematical wellposedness of the statement of the initial–boundary value problem (i.e., the existence and uniqueness of the generalized solution, and its continuous dependence on the external loads). We also describe the scheme for solving the initial–boundary value problem step by step using the model and present the expression for the Jacobian of the boundary value problem at the time step. These results are formalized as a subprogram for prescribing the mechanical properties of the user material in the finite-element complex ABAQUS, which allows one to calculate the structure deformations on the basis of the proposed theory. © 2015, Allerton Press, Inc.

Bykov D.L.,Central Scientific Research Institute for Engineering TsNIIMash | Martynova E.D.,Moscow State University
Mechanics of Solids | Year: 2013

A method for determining the material functions of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) with preliminary mechanical damage was developed. The proposed method is based on an analysis of the differences between two graphs of the stress dependence on time obtained in tension with the same constant speed of two specimens made of the same filled polymer material. One of the specimens was not preloaded, and the other was preloaded. The reduced time [1] contained in the NETAVEM constitutive relations and its dependence on the actual time are determined by the distances from the stress axis to two points corresponding to the same stress value and lying on the graphs for the damaged and undamaged specimens. The relaxation kernel is determined in the experiment with the undamaged specimen. These two material functions and the curve obtained for the damaged specimen are used to obtain the NETAVEM aging function, and then the function of viscosity can be calculated. As a result, all characteristics of the damaged material become known, and the strength of structures made of this material can be calculated. © 2013 Allerton Press, Inc.

Peleshko V.A.,Central Scientific Research Institute for Engineering TsNIIMash
Mechanics of Solids | Year: 2016

The deviator constitutive relation of the proposed theory of plasticity has a three-term form (the stress, stress rate, and strain rate vectors formed from the deviators are collinear) and, in the specialized (applied) version, in addition to the simple loading function, contains four dimensionless constants of the material determined from experiments along a two-link strain trajectory with an orthogonal break. The proposed simple mechanism is used to calculate the constants of themodel for four metallic materials that significantly differ in the composition and in the mechanical properties; the obtained constants do not deviate much from their average values (over the four materials). The latter are taken as universal constants in the engineering version of the model, which thus requires only one basic experiment, i. e., a simple loading test. If the material exhibits the strengthening property in cyclic circular deformation, then the model contains an additional constant determined from the experiment along a strain trajectory of this type. (In the engineering version of the model, the cyclic strengthening effect is not taken into account, which imposes a certain upper bound on the difference between the length of the strain trajectory arc and the module of the strain vector.) We present the results of model verification using the experimental data available in the literature about the combined loading along two- and multi-link strain trajectories with various lengths of links and angles of breaks, with plane curvilinear segments of various constant and variable curvature, and with three-dimensional helical segments of various curvature and twist. (All in all, we use more than 80 strain programs; the materials are low- andmedium-carbon steels, brass, and stainless steel.) These results prove that the model can be used to describe the process of arbitrary active (in the sense of nonnegative capacity of the shear) combine loading and final unloading of originally quasi-isotropic elastoplastic materials. In practical calculations, in the absence of experimental data about the properties of a material under combined loading, the use of the engineering version of the model is quite acceptable. The simple identification, wide verifiability, and the availability of a software implementation of the method for solving initial–boundary value problems permit treating the proposed theory as an applied theory. © 2016, Allerton Press, Inc.

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