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The influence of the material properties of a pre-stressed cylinder containing a compressible inviscid fluid on the dispersion of axisymmetric quasi-Scholte waves is studied. It is supposed that the inhomogeneous pre-stresses in the cylinder are caused by the fluid pressure acting on the internal face surface of the cylinder before the wave propagation. The motion of the cylinder during wave propagation is described by the so-called three-dimensional linearized equations of the theory of elastic waves in bodies with initial stresses, and the flow of the fluid, by the linearized Euler equations. For solving the corresponding eigenvalue problem, the discrete–analytical solution method is employed and the related dispersion equation is solved numerically. The dispersion curves containing the first roots of the dispersion equation refer to quasi-Scholte waves, which play an important role in helping to understand the solid–fluid dynamic interaction. A study of the influence of the cylinder material properties on the character of these curves is the main novelty of the present paper. The numerical results are presented and discussed on. For this purpose, steel, aluminum, lucite, and soft rubber are selected as cylinder materials, and water is chosen as the fluid. It is established, in particular, according to the numerical results, that an increase in the shear wave velocity in the cylinder material causes an increase in the propagation velocity of quasi-Scholte waves. [ABSTRACT FROM AUTHOR]

Experimental tests of a seven-bolted connection with an asymmetric contact area between the joined elements are presented. The research is divided into two stages. In the first one, the connection is preloaded in a three-pass cycle. In the second stage, the connection is loaded with a monotonic alternating force applied at an angle of 30 degrees to the contact surface of the joined elements to generate compressive and shear forces in the connection. The tests are carried out with the use of the INSTRON 8850 testing machine. As a result, the courses of forces in the bolts measured with the use of resistance strain gauges and the relative displacements between the joined elements measured with an extensometer are shown. In the second part, the modeling of the connection in the convention of the finite element method is presented. The joined elements are modeled with the use of spatial finite elements, and the fasteners, as the hybrid elements made of deformable beams, rigid heads, and rigid nuts. The paper is completed with a comparison of the results obtained from the measurements and calculations, based on which the conclusions important from the point of view of the FEM analysis are drawn. [ABSTRACT FROM AUTHOR]

The paper deals with the study of the influence of the inhomogeneous residual stresses caused by the "contact" of a cut on the dispersion of axisymmetric longitudinal waves in a two-layer hollow cylinder. According to the classification of Guz, this study is carried out using the second version of the small initial deformation of the linearized 3D theory of elastic waves in bodies with initial stresses. The discrete analytical method developed by the authors is used to solve the corresponding field equations. Numerical results illustrating the influence of residual stresses on the dispersion curves are presented and discussed. The magnitude of the residual stresses is estimated by the intersection (cutting) angle as a result of contacting, through which the residual stresses occur in the layers of the cylinder. [ABSTRACT FROM AUTHOR]

The paper performs a citation analysis of publications of mechanicians of the National Academy of Sciences of Ukraine (NASU) based on information tools developed by the Thomson Reuters Institute for Scientific Information. Two groups of mechanicians are considered: representatives of the S. P. Timoshenko Institute of Mechanics of the NASU (NASU members, heads of departments) and members (academicians) of the NASU Division of Mechanics. Three elements of the Citation Report (Results Found, Citation Index (Sum of the Times Cited), h-index) are presented for each scientist. This paper may be considered as a follow-up on the papers [–] published by Prikladnaya Mekhanika ( International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

The paper presents a brief historical sketch of nanotechnology and scientific analysis of nanoparticles, nanoformations, and nanomaterials. Certain aspects of the state of the art and promising trends in the nanomechanics of materials and relationships among macromechanics, mesomechanics, micromechanics, and nanomechanics are analyzed [ABSTRACT FROM AUTHOR]

The paper analyzes the level of coverage and citation of publications by mechanicians of the National Academy of Sciences of Ukraine (NASU) in the Scopus database. Two groups of mechanicians are considered. One group includes 66 doctors of sciences of the S. P. Timoshenko Institute of Mechanics as representatives of the oldest institute of the NASU. The other group includes 34 members (academicians and corresponding members) of the Division of Mechanics of the NASU as representatives of the authoritative community of mechanicians in Ukraine. The results are presented for each scientist in the form of two indices—the total number of publications accessible in the database as the level of coverage of the scientist’s publications in this database and the h-index as the citation level of these publications. This paper may be considered to continue the papers [–] published in Prikladnaya Mekhanika (International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

This paper presents a brief survey of the Series of Scientific Monographs "Stability and Control: Theory, Methods and Applications" published during 1995–2002 at the Gordon and Breach Science Publishers (UK) and the Taylor and Frances Publisher (USA). The Series comprises 22 volumes and is encyclopedic in the field of stability and control theories. Moreover, the history of appearance and realization of the idea of publishing the Series is outlined. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of evaluation of scientific publications as a part of the general problem of scientific information environment. A discussion on objective citation (entitled “Proposal from the Timoshenko Institute” and took place on the Internet in July 2007) is reviewed. New criteria (h-index, g-index) are discussed. A recent discussion by the mathematician community on the evaluation of scientific publications is presented. Some comments and proposals are formulated [ABSTRACT FROM AUTHOR]

The paper discusses the evaluation of scientific journals based on the Scopus database, information tools, and criteria. The SJR (SCImago Journal Rank) as the main criterion used by Scopus to evaluate scientific journals is considered. The Scopus and ISI systems are compared using information on the journal Prikladnaya Mekhanika ( International Applied Mechanics), a number of world-known journals on mechanics, and some journals on natural sciences issued by the National Academy of Sciences of Ukraine. Some comments and proposals are formulated. This paper may be considered as a follow up on papers published in Prikladnaya Mekhanika ( International Applied Mechanics) in 2005–2009 [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of N. N. Bogolyubov in recognition of his towering stature in nonlinear mechanics and theoretical physics, his remarkable many-sided genius, and the originality and depth of his contribution to the world’s science. The paper briefly describes Bogolyubov’s achievements in nonlinear mechanics, classical statistical physics, theory of superconductivity, quantum field theory, and strong interaction theory [ABSTRACT FROM AUTHOR]

The paper analyzes new publications on the brittle fracture mechanics of prestressed materials. It is found out that new scientific results published in the International Journal of Solids and Structures in 2002 are a particular case of the results obtained at the Institute of Mechanics 20 years ago [ABSTRACT FROM AUTHOR]

The results of experimental studies on the effect of randomly located circular holes of various number and diameters on the critical buckling force of longitudinally compressed cylindrical shells are presented in the form of curves of the critical buckling load versus the number, size, and total area of the random holes and the buckling patterns. The obtained data can be useful for predicting the residual load-bearing capacity of damaged shell structures. [ABSTRACT FROM AUTHOR]

The paper proposes an analytic procedure based on the method of characteristics to study the nonstationary thickness vibration of a piezoelectric layer polarized across the thickness and subjected to dynamic mechanical loading. The problem is solved for a suddenly applied harmonic mechanical load. The dynamic electroelastic state of the layer is analyzed [ABSTRACT FROM AUTHOR]

Nonclassical problems of fracture and failure mechanics that have been analyzed by the author and his collaborators at the S. P. Timoshenko Institute of Mechanics (Kiev, National Academy of Sciences of Ukraine) during the past forty years are considered in brief. The results of the analysis are presented in a form that would be quite informative for the majority of experts interested in various fundamental and applied aspects of fracture and failure problems including the identification of related mechanisms. This paper was prepared on invitation of the Editorial Board of the journal “Annals. The European Academy of Sciences” and may be considered as an Extended Pascal Medal Lecture (The 2007 Blaise Pascal Medal in Materials Sciences of the EAS) [ABSTRACT FROM AUTHOR]

The presence of compliant elements in biped running mechanisms generates a smoother motion and decreases the impact forces. Biological creatures that have a complicated actuation system with parallel and series elastic elements in their muscles demonstrate very efficient and robust bipedal gaits. The main difficulty of implementing these systems is duplicating their complicated dynamics and control. This paper studies the effects of an actuation system, including Hill-type muscles on the running efficiency of a kneed biped robot model with point feet. In this research, we implement arbitrary trajectories compatible with the initial condition of the robot, and we calculate the necessary muscle forces using an analytical inverse dynamics model. To verify the results, we execute the direct dynamics of the robot with the calculated control inputs to generate the robot's trajectory. Finally, we calculate the contractile element force of the muscles and its cost of transport, and we investigate the effects of the muscles' elements on reducing or increasing the cost of transport of the gait and maximum actuating forces. [ABSTRACT FROM AUTHOR]

The paper establishes the relationship between the solutions of the static contact problems of elasticity (no friction) for an isotropic half-plane and problems of electroelasticity for a transversely isotropic piezoelectric half-plane with the boundary perpendicular to the polarization axis. This allows finding the contact characteristics in the electroelastic case from the known elastic solution, without the need to solve the electroelastic problem. The contact problems of electroelasticity for different types of wedge-shaped punches (flat punch with rounded one or two edges, half-parabolic punch, and a periodic system of punches) are solved as examples [ABSTRACT FROM AUTHOR]

Current approaches to the citation analysis of scientific publications are outlined. Science Citation Index, Impact Factor, Immediacy Index, and the selection procedure for Essential Science Indicators—a relatively new citation analysis tool—are described. The new citation evaluation tool has yet not been discussed adequately by mechanicians [ABSTRACT FROM AUTHOR]

The main results of research on some nonclassical problems of fracture/failure mechanics are analyzed. These results have been obtained by the author and his followers at the Department of Dynamics and Stability of Continua of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials; it is published in Prikladnaya Mekhanika (55, No. 3, 2019). The third part is Other Nonclassical Problems of Fracture/Failure Mechanics; it is published in Prikladnaya Mekhanika (55, No. 4, 2019). [ABSTRACT FROM AUTHOR]

The principal results of research on some nonclassical problems of fracture/failure mechanics have been analyzed. These results have been obtained by the author and his followers at the Department of Continuum Dynamics and Stability of the Tymoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review: – first problem is fracture of composites compressed along the reinforcement; – second problem is short-fiber model in stability and fracture of composites under compression; – third problem is end-crush fracture of composites under compression along the reinforcement; – fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks; – fifth problem is shredding fracture of composites stretched or compressed along the reinforcement; – sixth problem is fracture of materials under compression along parallel cracks; – seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces); – eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling. About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review. This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials. The third part deals with other nonclassical problems of fracture mechanics. [ABSTRACT FROM AUTHOR]

A new type of combined honeycomb structure produced by optimally organizing the hexagons and square unit cells is proposed. The related equivalent elastic parameters are studied based on the strain energy equivalent theory. A numerical simulation method is used to verify the correctness of the equivalent mechanical model. A good agreement between the simulation values and theoretical solutions is observed. The study of mechanical properties of the combined honeycomb structure shows the great advantages in mechanical properties as compared with the traditional hexagonal honeycomb structure. With the same equivalent density, the in-plane equivalent elastic modulus of the new combined honeycomb is improved to 22%, the shear modulus enhanced to 95%. The external equivalent elastic modulus and shear modulus are improved to 33% and 29%, respectively. The carried out study provides a theoretical basis for the combined honeycomb structure's further research and also gives a new way to improve the current honeycomb sandwich. [ABSTRACT FROM AUTHOR]

A two-dimensional problem of the theory of elasticity is solved for a circular disk with an inclined edge crack, on a finite section of the boundary of which uniformly distributed pressure and tangential forces (friction forces) are applied. The contact load is balanced by concentrated forces and moment applied in the center of the disk. Contact with the friction of the crack faces is allowed. The problem is reduced to solving a system of two complex singular integral equations of the first kind with the Cauchy kernel. Numerical values of the stress intensity factors are obtained, depending on the location of the contact load on the disk boundary, as well as on the crack length and friction coefficients at the contact load application section and between the crack faces. The solution is presented using a railroad wheel as an example. [ABSTRACT FROM AUTHOR]

The novelty of the presented results is the deriving of exact solutions of axisymmetric poroelasticity problems for finite solid and hollow cylinders. The statement of these contact problems is given under the assumptions of Biot's model for poroelastic materials. A simulation of the poroelastic response of a cylinder is implemented using the apparatus of boundary problems. By the method of integral transforms, the original boundary problem is reduced to a one-dimensional boundary problem in the transform domain. Based on the exact solution of the latter one, it is manageable to derive the explicit formulas for displacements, stress, and pore pressure. The investigation of contact stress and pore pressure distribution inside the cylinder regarding its geometrical ratios, type of applied loading, and poroelastic material is carried out. [ABSTRACT FROM AUTHOR]

The reaction of a radial flexible ring with flanges in the supports of machine rotors to radial displacement has been studied. Two models of deformation and contact interaction of an elastic element with two rigid bodies positioned inside and outside of the ring have been developed. These models are based on variational statements with respect to the unknown forces and displacements. The options of gap and offset on both sides of the contact between the ring and the rigid bodies have been considered. A substantially nonlinear static reaction of the ring to radial displacement has been established. Radial reaction curves have been obtained across a wide range of design parameters, enabling a well-justified choice of an elastic damper with the desired stiffness properties. [ABSTRACT FROM AUTHOR]

The problem of elastic and limiting equilibrium of a shallow spherical shell weakened by a pair of rectilinear cuts along the meridian is considered in a two-dimensional statement. One is considered to be a contact crack capable of closing, while the other one — a narrow slit with free faces. The contact interaction of the crack faces under bending load is described using a contact model along a line in the front surface of the shell. The numerical solution to the problem is developed by the method of singular integral equations using the mechanical quadrature algorithm. The regularities of the contact reaction distribution on the closed crack faces are studied. The effect of the shell curvature and the relative location of the defects on the values of intensity coefficients of forces and moments and on the value of the fracture load is studied. [ABSTRACT FROM AUTHOR]

The parameters of a narrow small-scale plastic zone in an elastoplastic piece-wise homogeneous body undergoing a shear near the tip of an interfacial crack are calculated under plane strain conditions using the Wiener-Hopf method. Crack faces are in contact with friction. The plastic zone issuing out of the crack tip at an angle to a plane interface between media is modeled as the straight line of a displacement discontinuity involving two sections. Both tangential and normal displacements undergo the discontinuity at the section adjacent to the crack tip that models material destruction area. At the other section, only the tangential displacement experiences the discontinuity. The angle between the plastic zone and interface between the media is defined from the condition that the rate of energy dissipation in the zone is maximal. The sizes of the entire plastic zone, destruction zone and shear opening displacement of the crack in its tip are determined. It is studied how the friction of the crack faces, load, and the mechanical characteristics of the material influence on the parameters of the plastic zone and stress-strain state in the vicinity of the crack tip. [ABSTRACT FROM AUTHOR]

The plane problem on the effect of a moving load on an incompressible half-plane with inhomogeneity in the form of a thin surface layer is considered. The effect of the moving load, initial stresses, and mechanical parameters of elements of a layered foundation on the main characteristics of its stress-strain state is studied. [ABSTRACT FROM AUTHOR]

This paper, dedicated to the 20th anniversary of the independence of Ukraine (1991-2011), analyzes the activity of the S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, in 1991-2011. The major scientific achievements and their evaluation by the world's scientific community are briefly reported. The scientific staff and training activity of the Institute are discussed. New books (mînîgraphs, textbooks) and publications in scientific journals are mentioned. It is shown that the scientists of the Institute participate in the establishment of the scientific information environment [ABSTRACT FROM AUTHOR]

generalized form of the principle of virtual work where the virtual work is a time integral of virtual power is obtained. The corresponding Euler-Lagrange equation includes the divergence of the Lie derivative of stress. The equation of motion on the stress rate field is one of the results of this paper. A generalization of the acoustic tensor is obtained for a third-order wave. The generalized acoustic tensor seems the most important result of this paper. It can also be found by investigating an acceleration wave [ABSTRACT FROM AUTHOR]

The paper studies the radial nonstationary vibration of a piezoceramic cylinder polarized throughout the thickness and subjected to a dynamic electric load. A numerical algorithm for solving an initial–boundary-value problem using mesh-based approximations and difference schemes is developed. The dynamic electroelastic state of the cylinder subjected to a constant potential difference applied instantaneously is analyzed [ABSTRACT FROM AUTHOR]

The paper proposes a numerical approach to the problem of optimal control of low-thrust spacecraft in a strong central gravity field. The approach employs the solution of the averaged equations of optimal motion. For an optimal variable-thrust maneuver, it is shown that quasioptimal trajectories are close to the averaged ones. It is established that in the case of constant thrust, the averaged solutions can be used as a satisfactory first approximation for finding a quasioptimal solution by minimizing the discrepancy at the right end of the trajectory [ABSTRACT FROM AUTHOR]

The article is devoted to the six-volume series Uspekhi Mekhaniki ( Advances in Mechanics) and briefly discusses the state-of-the-art in and classification of modern mechanics, the motivation for publishing the series, and gives its characteristics and detailed description of all the six volumes, of which the first and second ones are already available to readers and the third will be in the near future [ABSTRACT FROM AUTHOR]

A numerical method for clamped thin rectangular plates carrying a uniformly distributed load and the exact solution of the governing equations are given. The solution is presented in a simple form suitable for direct practical use. The method is a very simple and practical approach. The results are compared with those reported in the previous papers [ABSTRACT FROM AUTHOR]

The paper provides an exhaustive account of the monographic heritage of Academician G. N. Savin, including a list of his 14 monographs available in the Library of Congress, USA, and ways (reading rooms and catalog numbers) of familiarizing oneself with them. The Library of Congress Online Catalog makes it possible to obtain information on these monographs via the Internet at any center of science in any country. Fifteen Savin’s monographs less known outside Ukraine are listed [ABSTRACT FROM AUTHOR]

Problems arising in the development of the scientific information environment are considered. Emphasis is on the building of international databases for periodical publications and monographs, evaluation of publications and journals, and objective citation. The activity of the S. P. Timoshenko Institute of Mechanics and the journal Prikladnaya Mekhanika (International Applied Mechanics) in this field is exemplified. Suggestions on how to ensure objective citation in articles are discussed [ABSTRACT FROM AUTHOR]

The paper investigates the benefits of implementing the semiactive control systems in relation to passive viscous damping in the context of seismically isolated structures. Frequency response functions are compiled from the computed time history response to pulse-like seismic excitation. A simple semiactive control policy is evaluated in regard to passive linear viscous damping and an optimal non-causal semiactive control strategy. The optimal control strategy minimizes the integral of the squared absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied. The optimization procedure involves a numerical solution to the Euler-Lagrange equations [ABSTRACT FROM AUTHOR]

The paper sets forth a modified preconditioned conjugate-gradient method with shifted aggregated multilevel preconditioning (MPCG_AMIS). The method is intended to solve large-scale natural-vibration problems. Such problems are typical for the finite-element analysis of buildings and other complex structures and bodies. Using a proper shift in preconditioning improves considerably the spectral properties of the preconditioner and, hence, improves convergence. Using the MPCG_AMIS allows us to avoid lock of convergence, which is the case in the conventional PCG method. The performance of the method is illustrated by examples [ABSTRACT FROM AUTHOR]

Some personal (and inevitably biased) thoughts pertinent to the Monte Carlo method are shared with the reader; in this mass production process of papers we are pausing and asking ourselves some nagging questions. Various aspects of the philosophy of the method are discussed. Its role in stochastic mechanics is elucidated and some questions are posed in view of promoting a further constructive discussion [ABSTRACT FROM AUTHOR]

The paper studies the effect of the discrete arrangement of ribs and their number on the number of dispersion curves for harmonic waves that have a deflection node on a rib's axis and propagate along a cylindrical shell. It is found out that these curves split and the distance between the split curves depends strongly on the torsional stiffness of the ribs [ABSTRACT FROM AUTHOR]

In the paper, primary attention is drawn to the determination of three-axial stresses. The basic relations for isotropic and quasiisotropic materials such as metals and alloys are derived, the measurement procedures are described, the accuracy of the method proposed is analyzed, and how this method is applied to the nondestructive determination of residual stresses arising in structural elements due to electrical welding is considered. This article is a complete report read at the ICTAM 2000 (Chicago, USA). An abstract was included in the ICTAM-2000 Abstract Book [ABSTRACT FROM AUTHOR]

The delayed fracture of an isotropic viscoelastic plate due to subcritical growth of a rectilinear microcrack of normal separation is studied. The paper deals with the development of the crack due to the stretching of the plate by uniformly distributed increasing and cyclic external loads applied perpendicularly to the crack line. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent integral operators of difference type, which describe the deformation of materials with time-dependent rheological properties. Numerical calculations are performed for resolvent integral operators with a kernel in the form of Rabotnov's fractional-exponential function. The kinetics of a crack with a tip zone commensurable with the crack length is studied. The results are compared with those obtained on the basis of the hypothesis on the thin structure of the crack tip. [ABSTRACT FROM AUTHOR]

Problems of parametric optimization of rod structure stated in terms of the nonlinear programming problem are considered. Use is made of the method of projection of the gradient of the cost function onto the surface of active constraints while eliminating the residuals in the violated constraints. The equivalent Householder transformations are proposed for the governing equations of the optimization method. They ensure the computational efficiency of the algorithm based on the gradient method. In addition, the equivalent Givens transformations are also proposed for solving the equations of the method. They ensure, in the cases described in this article, the acceleration of the iterative process by reducing the amount of computation. The reliability of the optimal solutions obtained using the proposed modification of the gradient method is confirmed by comparing the results of optimization of rod systems. The efficiency of the proposed improvement of the optimization method is also confirmed by the obtained absolute values of the maximum residuals in the constraints in a small number of iterations. [ABSTRACT FROM AUTHOR]

The stress–strain state of symmetric three-layer cylindrical shells under nonstationary loads is considered. The equation of vibrations of a shell with a light core reinforced with stiffening ribs under axisymmetric impulsive loading is derived. The members of the elastic structure are analyzed using the model of Tymoshenko's theory of shells and rods. Numerical results on the dynamics of the three-layer structure are obtained using the finite-element method. The significant effect of geometric and physical parameters of shell layers on the stress–strain state under axisymmetric internal impulsive loading is investigated. [ABSTRACT FROM AUTHOR]