Mechanics Of Deformable Solid Body Research Articles

ПРИМЕНЕНИЕ МЕТОДОВ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА ДЛЯ КОМПЬЮТЕРНОГО МОДЕЛИРОВАНИЯ ФРАКТАЛЬНЫХ ПОВЕРХНОСТЕЙ

The paper considers the possibility of using artificial intelligence methods for computer modeling of fractal surfaces. Fractals act as a mathematical model for creating a random surface relief. The random profile is constructed using the random displacement method, which is an algorithm for generating random functions with a spectrum. Surfaces are defined with the help of data arrays, which are checked by the self-similarity condition. Based on the defined arrays, models are built using the Weierstrass function. The algorithm for constructing surfaces has been refined and improved using machine learning neural network generative models. Thus, instead of simply creating a fractal surface using random functions, the generator creates fractal surfaces based on the distribution learned during training. The verification criterion is an algorithm based, in general, on a mathematical Monte Carlo method. The obtained results show the realism of the constructed fractal surfaces using neural networks. The models of the obtained surface reliefs can be used in modeling contact mechanics, mechanics of deformable solid bodies.

Cold resistance of steel beam prestressed by wall drawing

Introduction. The purpose of the article is a generalized analysis of existing methods for determining of structural steel elements behaviour in extreme conditions of subzero temperatures and their use to assess the cold resistance of steel beams prestressed by drawing of a thin wall. Subject of study is structural steel. Object of study is bimetallic steel beam prestressed without rods.Materials and methods. The study is based on the mechanics of deformable solid bodies, studies of the mechanical characteristics of steel and its behaviour at considerable subzero temperatures, taking into account stress concentrators and the probability of brittle cracks in the beam elements.Results. The impact strength analysis of steels C440 and C245 used in the flange plates and wall of prestressed beam was carried out. It is found that during the structure operation in the temperature range from minus 45°C to minus 55°C, cold resistance of the beam elements is ensured. It is proved that actual normal stresses in the extreme fibers of the prestressed beam web section are lower than the allowable stresses during plastic deformation of the wall material and, according to the theory of M. Huber, R. Mises and H. Hencky, the probability of brittle cracks in stress concentrators zone is low. It is found that the absence of stiffeners along the beam wall reduces plastic deformations caused by welding, reduces the number of extra elements in the structure and increases the material’s cold resistance.Conclusions. The high stability of prestressed beam wall enables designing it quite thin and increasing its cold resistance. The stressed state of the structure, reduction of its weight, thinning of wall, absence of welding stress concentrators, and reduction of the number of extra elements in the beam testify to the cold resistance of the material of the beam pre-stressed by wall drawing.

100-years’ story of success: photoelasticity — LSR–MICE – MSUCE

Introduction. The 100-years’ history of MICE – MSUCE is also a history of establishment and flourishing of one of the world’s most powerful experimental school of development and application of the photoelasticity method in the investigation of the stress state of civil and special structures. Reliable forecast of the stress state of buildings and structures under static, thermal and dynamic impacts is an indispensable prerequisite of safe operation provision of civil structures during the construction and the operation. The photoelasticity method, allows, along with the analytical methods of the mechanical science, for continual study of the stress state of the object under test, being an experimental method efficiently used both in “standalone” mode and in conjunction with numerical methods. The goal and the objectives hereof: a retrospective development review of the photoelasticity method, in particular, of the contribution of LSR of MICE, and the assessment of the contemporary state of the method in terms of its actuality, novelty and practical significance of mechanical problem solutions, of stress-strain state studies of structures and buildings.
 
 Materials and methods. The subject hereof is the polarized light method or the photoelasticity method: development, problematics, solution methods of mechanical problems and studies of structures, applications.
 
 Results. The paper describes solution examples of vital problems by the photoelasticity method: stress analysis in the wedge-shaped notch zone of the area boundary, stress state problem under forced deformation in the block-basement contact area, stress state study of underground hydropower plant tunnel with the weir erected by pinpoint blasting. The performed analysis of the photoelasticity method and its contemporary level illustrates the opportunities provided by the method in solving of mechanical problems and in structural studies.
 
 Conclusions. Is the experimental school of the photoelasticity method of LSR–MICE – MSUCE really the sunk Atlantis? The development of the experimental mechanics of deformable solid bodies is characterized by progressive proximity of experimental and numerical analysis research methods. The physical modelling, in particular, the polarized light method, allows for obtaining stress-strain state diagrams of structures, or solutions of mechanical problems, feasible for assessment or for calculation result corrections, that is why the polarized light method retains actuality and practical significance. The development of the deformable solid body mechanics determines the significance of the physical modelling, including the polarized light method. The benefit of the polarized light method is the continuity of mechanical problem solutions which is especially important when local areas with specific features of the stress strain behaviour are considered. Modern technologies of material property studies, invention of new materials lead to creation of new mechanical models, for adequacy assessment of which physical modelling methods are required, in particular, the polarized light method.

Physics of martial arts: Incorporation of angular momentum to model body motion and strikes.

We develop a physics-based kinematic model of martial arts movements incorporating rotation and angular momentum, extending prior analyses. Here, our approach is designed for a classroom environment; we begin with a warm-up exercise introducing counter-intuitive aspects of rotational motion before proceeding to a set of model collision problems that are applied to martial arts movements. Finally, we develop a deformable solid-body mechanics model of a martial arts practitioner suitable for an intermediate mechanics course. We provide evidence for our improved model based on calculations from biomechanical data obtained from prior reports as well as time-lapse images of several different kicks. In addition to incorporating angular motion, our model explicitly makes reference to friction between foot and ground as an action-reaction pair, showing that this interaction provides the motive force/torque for nearly all martial arts movements. Moment-of-inertia tensors are developed to describe kicking movements and show that kicks aimed high, towards the head, transfer more momentum to the target than kicks aimed lower, e.g. towards the body.

On modeling of airflow in human lungs: constitutive relations to describe deformation of porous medium

Within the framework of a multilevel mathematical model to describe the evolution of functional disorders of the human organism under the influence of environment factors, a mathematical model of the "meso-level" of the human respiratory system is developed. The article is deals with the development of the meso-level model - the formulation of a constitutive model to describe the airflow in a porous lung medium. Human lungs filled with small airways and alveoli, with air contained in them, are modeled by an elastically deformable saturated porous medium enclosed in an internal chamber with varying volume (movable walls). Conceptual and mathematical statements are presented. Air movement in the deformable porous medium of lungs is described by ratios of the mechanics of deformable solid body and filtration theory. As an element of this sub-model an analytical solution is obtained for an auxiliary geometrically linear problem of the all-round compression of an elastic thin-walled hollow sphere filled with air to determine the rate of mean stress of the two-phase medium of the lungs, taking into account the interaction between the lung tissue and the air contained in the lungs. To confirm the hypothesis on the acceptability of a linear solution of an auxiliary problem for large deformations, a similar problem was numerically solved in a geometrically nonlinear formulation. The results show that the obtained analytical solution is in satisfactory agreement with the solution of a similar problem in a nonlinear formulation both for calm and deep breathing, which indicates the possibility of using the former in the construction of the considered sub-model.

Once Again on Preliminary Reference Earth Model

AbstractWe studied the isotropic ball using data of Preliminary Reference Earth Model (PREM). It is shown that such a ball should be either destructed or gone into a more stable equilibrium state with uneven distributed deformation under thermobaric condition of the inner core. Body elastic waves with real velocities cannot propagate in it. This manuscript is devoted to study the situation from the standpoint of nonlinear geomechanics. A number of necessary principles of Mechanics of Deformable Solid Body (MDSB) is given at the beginning of the analysis. A brief review of the published latest experimental work is performed. It is established that proper attention to the role of the MDSB principles in micro‐scale (nano) experiments of the physical level has not been given. Deformation properties of solid bodies are emphasized in microscale and macroscale. Application of linear acoustoelasticity and extrapolation of Birch's linear law of the inner core and use of an idea on variability of elasticity moduli with the increase of pressure and temperature have contributed to obtained pseudo data for the geological medium of the Earth's core instead of linear data on the physicomechanical properties. It is proposed that parallel to elimination of the indicated disadvantages, collection, processing and interpretation should be performed using nonclassically linearized approach. This set of necessary actions is offered as the “key” of geomechanical analysis. The proper application will allow conducting similar analysis concerning other solid‐state structures of the Earth.

Continuous and discrete models in the mechanics of deformable solid bodies

Continuous and discrete models in the mechanics of deformable solid bodies

Continuous and discrete models in the mechanics of deformable solid bodies

The study provides an overview of modelling possibilities for the mechanical behaviour of media. The discrete, continuous or differential geometric as well as the discrete nature and continuous description grid continuum model in particular are highlighted. We point out that the differential geometric model is based on the concept of continuity and interprets a continuous medium model. We reveal that the grid continuum model is based on the application of numerical method and interprets a discrete medium model.

Some aspects of modeling and identification of inhomogeneous residual stress

Investigations of problems on mechanics of deformable solid body under residual (or initial, or pre-) stress state play a very important part in strength-and-stability assessment and in reconstruction of inhomogeneous properties. The present paper describes different theoretical aspects of modeling of residual stresses (RS). We compare several RS models for the vibrational problems for beams and plates and estimate numerically RS effect on their dynamical characteristics: frequency-response functions and eigenfrequency spectrum. We formulate and investigate the inverse problem on an identification of inhomogeneous plane RS state in a thin plate on the basis of the acoustic method. To solve the inverse problem, we propose two different approaches. We discuss the results of computational experiments on RS identification in detail and provide some practical recommendations on a selection of frequency range in order to obtain the highest reconstruction accuracy.

ТЕХНОЛОГИИ И ЗАДАЧИ МЕХАНИКИ КОМПОЗИЦИОННЫХ МАТЕРИАЛОВ ДЛЯ СОЗДАНИЯ ЛОПАТКИ СПРЯМЛЯЮЩЕГО АППАРАТА АВИАЦИОННОГО ДВИГАТЕЛЯ

The goal of this work is an analysis of modern technologies and problem definitions of mechanics of composite materials for production of outlet guide vane for new domestic aviation propulsion PD-14, planned for installation on the short-range and mid-range jet aircraft MS-21. Outlet guide vanes (OGV), also called flow straightening vanes, are radially disposed behind the fan to straighten out the airflow to reduce losses in the outer contour of the engine. Considering a large number of vanes in the engine, the weight reduction can be very significant due to using polymer composite materials (PCM) instead of the metal in OGV. It is predicted that the weight reduction of each vane, at certain approach to design, can reach 40 %. The results of literature search of composite materials application in the details of fan for aircraft jet engines of world top manufacturers are presented in this paper. The analysis of advanced techniques for production of composite outlet guide vane, such as prepreg technology with autoclave molding, resin transfer molding (RTM), the use of thermoplastic binders and press-materials was carried out. It was noted that the formulation and solution of complex problems of engineering mechanics of composite materials are necessary for high-rate realization of mechanical properties in constructions and reducing the occurrence of defects. The possible problem definitions of deformable solid body mechanics, describing such processes as filtration, physical and chemical conversion, visco-elastic-plastic deformation in heterogeneous medium, typical for composite materials production cycle were considered. The influence of autoclave molding parameters on the mechanical properties of several types of carbon fiber reinforced plastics (CFRP) was analyzed. Using the equations of mechanics of laminated composite plates and shells we calculated effective elastic and strength properties of quasi-isotropic CFRP. A comparative estimate of the effectiveness of composite materials application in the design of OGV was obtained.

Nondestructive Identification of Inhomogeneous Residual Stress State in Deformable Bodies on the Basis of the Acoustic Sounding Method

Analysis of inhomogeneous residual stress (RS) fields in bodies is one of the major problems of the mechanics of deformable solid bodies. In the present research the new techniques of identification of inhomogeneous RS in bodies are developed on the basis of surface displacement measurement in a set of points under vibrating sounding load. Corresponding nonlinear ill-posed inverse problems (IP) are formulated and solved numerically by means of iterative regularization. Based on computational experiments, the most advantageous sounding load types and frequency ranges providing the best reconstruction accuracy are revealed. The examples for a cantilever, a plate, a layer, and a cylindrical tube are presented.

Linear bendings of star-like bipyramids

This paper is a revised and an extended version of the article [A.D. Milka, Linear bending of star-like pyramids, Comptes Rendus Mecanique 331 (12) (2003) 805–810]. A family of polyhedra possessing unusual deformation properties is found. On one hand, models of these polyhedra admit free continuous large reversible bendings without visible distortions of the material. On the other hand, the polyhedra themselves are mathematically rigid and do not admit continuous bendings in the sense of O. Cauchy. The found polyhedra are called model flexors in order to distinguish them from theoretical flexors of R. Connelly. Bendings of the models are asymptotically exactly approximated by linear bendings of polyhedra. They represent a non-rigid, soft or retarded, loss of stability which corresponds to the loss of stability “in the small” in the sense of L. Euler. This new phenomenon in mechanics of deformable solid bodies may be considered as an original geometric catastrophe machine which supplements known physical models by E.C. Ziman and T. Poston.

Calculation of statically indeterminate composite beam elements by using refined boundary conditions and with account of their state diagrams

The effect of compliance of support units on the calculation of strength of composite beams with account of the nonlinear deformation diagram of the composite is examined. The basic equilibrium equations of the mechanics of deformable solid bodies are used to solve the problems of strength, rigidity, and displacements, with introduction into them extreme criteria for the parameters to be calculated. The procedure developed al lows one to find the final solutions by using iterative processes.

Linear bending of star-like pyramids

A family of polyhedra possessing unusual deformation properties is found. On one hand, models of these polyhedra admit free continuous large reversible bending without visible distortions of the material. On the other hand, the polyhedra themselves are rigid and do not admit continuous bending in the sense of the Cauchy definition. The found polyhedra are called model flexors in order to distiguish them from theoretical flexsors of Connelly. Bendings of the models are asymptotically exactly approximated by linear bendings of polyhedra. They represent a nonrigid, soft or slow, loss of stability that corresponds to the loss of stability in small accordingly to Euler. This new phenomenon in mechanics of deformable solid bodies may be considered as an original geometric machine of catastrophe. To cite this article: A.D. Milka, C. R. Mecanique 331 (2003).

On the three-dimensional stability loss problem of the viscoelastic composite plate

The three-dimensional linearized theory of stability (TDLTS) of deformable solid body mechanics is developed for the investigation of the three-dimensional stability loss problems of elements of constructions fabricated from the time-dependent composite materials. All procedures are made on the plate from the composite material that is modelled as homogeneous anisotropic linear viscoelastic material with normalised mechanical properties. As a stability loss criterion the values of time (critical time) for which the size of the initial imperfection starts to increase and grows indefinitely, is selected. By employing semi-analytical FEM modelling and Laplace transformation the numerical investigations are made. From the analyses of these results it is concluded that they can be significantly different from those obtained in the framework of the third-order refined plate theory.

A method of investigation of the general theory of stability problems on structural elements fabricated from viscoelastic composite materials

In the framework of the general theory of stability (GTS) the method for the investigation of the stability loss problems of the elements of constructions fabricated from the non-aging linear viscoelastic composite materials is proposed, with an example problem. The proposed approach is based on the investigation of the development of the initial insignificant imperfection of the considered elements of constructions in the framework of the geometrical non-linear exact equations of the deformable solid body mechanics. All investigations are carried out on the clamped strip. The numerical results (critical time) obtained in the framework of the proposed approach are compared with the numerical results found in the framework of the displacement based third order refined plate theory.

On problems of fracture of materials in compression along two internal parallel cracks

The fracture of materials under the action of compressive forces, directed along cracks which are parallel in plane cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type, used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening. The problems of such a class may be described only by using new approaches. One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics. It should be remarked here that this approach has been widely used in problems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.

Stability of Laminated Composites

The characteristic special feature of deformation behavior of modern laminated composite materials and structural elements fabricated from these materials, at current levels of loading and operating conditions is the occurrence of the purely three-dimensional stress-deformed state. In this process some specific mechanical phenomena and effects may occur, which is impossible to describe within the framework of applied or approximate approaches existing currently in deformable solid body mechanics. The structure of massive laminated materials may be included in this class of phenomena when the critical parameters of the problem depend only on the ratio between mechanical and geometrical characteristics of single layers and are independent of the dimensions and the form of the total laminated body as a whole. Since this phenomenon may be the beginning of the process of fracture of these materials, and the loss of the load-carrying capacity of structure elements fabricated from them, we consider below, in three-dimensional formulation, the problem of the surface and internal instability in laminated composite materials under compressive surface loads. The classification of the existing types of stability problems is presented for laminated materials and approaches for their solution presented in the literature. On the basis of three-dimensional linearized stability theory, within the framework of the piecewise-homogeneous media model, the general formulation of the most characteristic classes of stability problems of laminated materials is given in Lagrangian coordinates at small and finite, homogeneous and inhomogeneous precritical deformation. Analytic and variational methods of investigation of formulated problems are given with application to various models of laminated bodies models, in accordance with accepted stability criteria. The accuracy of these models is evaluated, based on the example of the solution of certain model problems; the range of application is given for existing applied and approximate approaches to the analysis of formulated problems. Results of solution of specific problems are given; specific mechanical effects, characteristic for the phenomenon considered, are found. Recommendations are formulated for engineering design and computational methods. New promising areas of research are pointed out for the problem of laminated composite materials stability.

Statics of Laminated and Fibrous Composites With Curved Structures

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.