Solid Body Mechanics Research Articles

Матрична алгебра В як евклідовий простір

Representation of information by means of hypercomplex numerical systems is used in various problems of science and technology: in classical mechanics, solid body mechanics, electrodynamics, radio electronics, computer animation, and others [1]. Often a hypercomplex system (that is, a system whose elements are considered to be hypercomplex numbers) is understood as any finite-dimensional algebra over a field. An important place among such algebraic structures is occupied by matrix algebras. The impossibility of constructing algebras with division does not at all mean the impossibility of constructing algebras without division, but their properties are close to the first ones (use of defined division). Since each algebra of finite rank can be monomorphically immersed in some complete matrix algebra, this caused, so to speak, an inverse approach to the construction of new algebras. A certain subalgebra stands out from a complete matrix algebra, which is a matrix representation of an algebra of finite rank. It is the implementation of such an approach that makes it possible to endow elements of algebra of finite rank with matrix characteristics, in particular, a canonical representation of algebra elements is constructed through the spectral representation of a matrix, and the algebra itself is endowed with a topological structure through one of the matrix norms. At the same time, an additional condition is often imposed, that it be an algebra over the field of real or complex numbers. The article constructs a real algebra of finite rank, the elements of which are matrices of the second order with the same sum of rows and columns. We endowed it with a norm and a scalar product, demonstrating that it is a Euclidean space. This algebra is a matrix representation of the algebra of hypercomplex numbers, which we called binary in our research [4].

MATHEMATICAL MODELS OF HUMAN RESPIRATORY AND BLOOD CIRCULATORY SYSTEMS

Aim. To analyze modern approaches to mathematical modeling of human respiratory and blood circulatory systems. Methods. Comprehensive review of scientific literature sources extracted from domestic and international resources databases. Results. Historical information and modern data concerning mathematical modeling of human functional respiratory and blood circulatory systems were summarized and analyzed in present ¬review; current trends in approaches to the construction of these models were revealed. Conclusions. Currently, two main approaches to the mathematical modeling of respiratory and blood circulatory systems exist. One of them is the construction of models of the mechanics of respiration and blood circulation. They are based on the models of mechanics of solid deformable body, thermomechanics, hydromechanics, and continuum mechanics. This approach uses complex mathematical apparatus, including Navier-Stokes equation, which makes it possible to obtain a number of theoretical results, but it is hardly usable for real problems solutions at present time. The second approach is based on the model of F. Grodins, who represented the process of breathing as a controlled dynamic system, described by ordinary differential equations, in which the process control is carried out according to the feedback principle. There is a significant number of modifications of this model, which made it possible to simulate various disturbing influences, such as physical activity, hypoxia and hyperemia, and to predict parameters characterizing functional respiratory system under these disturbing influences.

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.

SOLUTIONS OF THE PROBLEM OF RANDOM VIBRATIONS IN HEREDITARY-DEFORMABLE SYSTEMS USING IMPULSIVE FUNCTIONS

In recent years, probabilistic-statistical methods for studying various problems of mechanics of solid deformable bodies are being applied more than ever. The principal part of its field of application is the development of a general theory of strength and a hereditarily deformed solid. As known, the theory of random oscillations is increasingly being used in technology. Current research is aimed to present a numerical-analytical approach for studying the dynamic response of a hereditarily deformable system to unsteady input influences. It is established that the dynamic reaction of hereditarily deformable systems to an arbitrary form of random perturbations can also be represented as the Duhamel integral if the impulse transition function satisfies special Cauchy problems for the integro-differential equation (IMU). A study proposes an accurate analytical solution to the IMU of an impulsive transition function in existing weakly singular Rzhanitsyn-Koltunov nucleuses.

МОДЕЛЮВАННЯ ПРОЦЕСУ ДЕФОРМАТИВНОСТІ БУРОНАБИВНИХ ПАЛЬ ЗА МГЕ

Designing reliable and ekonomicznych modern construction projects, which are themselves large-scale structures, is relevant, so the proper use of soil mechanics is especially important when design and construction. Soil mechanics is the mechanics of natural dispersed (finely crushed ) bodies, includes both the laws of theoretical mechanics (mechanics of solid brand neszhimaemoi bodies) and the patterns of structural mechanics (the laws of prognosti, plasticity). The success of foundation engineering as a whole is tied to its scientific base - soil mechanics. The boundary stress state of the soil at a given point of otvechaet such stress condition, when a slight additional effect of narushaet the existing balance and makes the ground in an unstable condition in the soil mass occur of the sliding surface, discontinuities, subsidence and broken strength between its particles and aggregates. Such a stress state of soils must be considered as invalid if construction on their facilities. Therefore, for engineering practice, it is very important to be able to estimate the maximum possible loading on the soil in which it will still be in equilibrium, ie, will lose strength and stability. In connection with increase in volumes use of bored piles is a necessity of developments of modern predictive methods for the determination of their carrying capacity with the involvement of computers as the main challenge in the design of structures is an engineering assessment of the load-bearing capacity of soil based ... In working on numerical BEM modeled the process of deformation of the bored SAI. Questions of strength, bearing capacity , stability of soils is a task of the General theory of limit equilibrium, the beginning of which was laid by the works of M. Coulomb, L. Prantl.

Fundamentals of the General Theory of Resistance of Reinforced Concrete Elements and Structures to Power Influences

The article outlines the basic elements of the general theory of concrete and reinforced concrete deformation: the model of reinforced concrete elements and structures resistance to power influences; defining hypotheses necessary for the implementation of this model; criteria of the limiting state onset of the reinforced concrete elements and structures. These elements are joined together by a system of equations of a deformed solid body mechanics which is transformed into a statically distinguishable by means of additional analytical dependences.

Specific Features of Fluoroplastic Band Bending with Due Account of Various Modularity of Material

The paper considers a technological process for production of sealing rings by winding a band work-piece on a cylindrical caliber mandrel with subsequent endurance under load and further cutting of a spiral in rings and also studies the possibility to obtain products while using a method for cold forming of a work-piece which excludes thermal stabilization operation. Taking into account the fact that fluorine plastic is a high-plastic material even at very low temperatures such technology looks quite real. Therefore winding of a band on a mandrel, endurance of a spiral work-piece without heating but under conditions of force action within the time which is necessary for completion of relaxation processes, and the subsequent cutting in rings will allow to obtain finished ring products of the required size. However fluoroplastic has specific mechanical properties and a number of specific features which are revealed during deformation process. Its deformation behavior considerably differs from behavior of low-molecular materials and therefore it requires a solid approach while using the existing theoretical base and developing calculation methodologies. While taking into consideration the fact that fluorine plastic is high density material and has structure with high degree of crystallinity, the mechanism of deformation behavior in it under conditions of a force field is mainly similar to metal behavior that allows to use methods and approaches for calculation of fluoroplastic products which are accepted in mechanics of solid bodies. However the applied calculating formulae require a certain correction and adaptation to specific features of mechanical fluoroplastic properties, one of which is its various rigidity at stretching and compression that is revealed in case of winding band work-piece on a mandrel. Fluorine plastic is a material with various modularity and its rigidity is higher during compression than under stretching and consequently in the case of band bending a neutral axis of section is displaced from the center of gravity to the area of compressed fibers, and the area of stretching is increasing. High elasticity at stretching and increase of this area lead to large accumulation of elastic deformations causing springing after unloading and changes in size of a finished product. These facts must be taken into account while calculating and designing a mandrel tool, it is also necessary to keep in mind various modularity of a material and possibility that a section being led to an uniform rigidity may take some other shape due to this. Calculation methodologies have been developed by the authors for both versions of section that take into consideration directly or indirectly a material with various modularity and which do not contradict each other and which are rather precisely proved by experimental data.

Топологическая оптимизация конструкции диска турбины при действии термомеханических нагрузок

This article presents a study of topology optimization to obtain a new form of an axisymmetric structure using mathematical tools of solid body mechanics and finite elements analysis and taking into account the effect of thermal and mechanical loads. The problem of minimizing the compliance of a rotating turbine disk is solved sequentially, with a given of the volume constraint. First, temperature distribution is obtained in the design area, then the problem of determining the stress-strain state is solved taking into account the thermo-effect, and finally, topology optimization is performed using the moving asymptotes method. The results of calculations for different optimization scenarios are compared: operating at different volume fractions and different rotational speeds of the turbine disk; with and without thermal loading. A comparison of the optimized model obtained by implementing the developed program in the MATLAB environment, and structures created using ANSYS APDL and ABAQUS (TOSCA) is presented. The form of the optimized disk allows its manufacturing by both traditional as well as additive methods.

Residual resource of power resistance during building structures deformation

Modern scientific research and design developments, based on the fundamental principles of physics, mechanics and thermodynamics, are developing in a phenomenological direction. This implementation is found both in traditional integrated models of reinforced concrete using the advantages of computer technology, and in discrete models following the grid methods of solid deformable body mechanics. Discrete models in content and chronology over time are hereditary with respect to integral models. The theoretical basis for calculating the residual life of the force resistance to deformation, determines the stiffness of the cross sections of reinforced concrete elements with a maximum bending moment and with zero bending moment are presented in this article.

Forecasting Durability of Construction Composites on the Basis of Liquid Rubber

Initial theoretical propositions based on S.N. Zhurkov’s concept about termo-fluctuation approach to mechanics of destruction and solid bodies straining is formulated, formulas of dependence limits functionality of solid composites are described in the article. Physical constants of six rubber polymeric concrete composition are experimentally detected, the results of experiments are analyzed and described. The prediction and enhancement problem of working capacity for the polymeric construction materials come to detection of relationship between power, temperature and temporal limits of the material use. The optimal composition of rubber polymeric concrete from the power, temperature and temporal durability point of view is detected from the experiments results.

The indentation method as a method of assessment of loading and degradation of mechanical characteristics of the material

On the basis of the calculation of a series of model problems on pressing a hard spherical indenter into a half-space from a reinforcing material we show the possibility of using the indentation for the simultaneous determination of effective stresses, as well as the yield strength of the material. The methodology leans upon an approach based on finding unknown parameters from the condition of minimization of discrepancies in the data of registration experimental registration of displacement fields by electronic speckle pattern interferometry, which result from indentation, and their corresponding calculated displacement fields found on the basis of a numerical solution of a series of boundary value problems of deformed solid-body mechanics.

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.

Theoretical investigation of crack formation in tungsten after heat loads

Transient events such as ELMs in large plasma devices lead to significant heat load on plasma-facing components (PFCs). ELMs cause mechanical damage of PFCs (e.g. cracks). The cracks appear due to stresses caused by thermal extension. Analytical calculations of the stresses are carried out for tungsten. The model only takes into account the basic features of solid body mechanics without material modifications (e.g. fatigue or recrystallization). The numerical results of the model demonstrate good agreement with experimental data obtained at the JUDITH-1, PSI-2 and GOL-3 facilities.

Coupling Molecular Dynamics and Continua with Weak Constraints

One of the most challenging problems in dynamic concurrent multiscale simulations is the reflectionless transfer of physical quantities between the different scales. In particular, when coupling molecular dynamics and finite element discretizations in solid body mechanics, often spurious wave reflections are introduced by the applied coupling technique. The reflected waves are typically of high frequency and are arguably of little importance in the domain where the finite element discretization drives the simulation. In this work, we provide an analysis of this phenomenon. Based on the gained insight, we derive a new coupling approach, which neatly separates high and low frequency waves. Whereas low frequency waves are permitted to bridge the scales, high frequency waves can be removed by applying damping techniques without affecting the coupled share of the solution. As a consequence, our new method almost completely eliminates unphysical wave reflections and deals in a consistent way with waves of arbitrary frequencies. The separation of wavelengths is achieved by employing a discrete -projection, which acts as a low pass filter. Our coupling constraints enforce matching in the range of this projection. With respect to the numerical realization, this approach has the advantage of a small number of constraints, which is computationally efficient. Numerical results in one and two dimensions confirm our theoretical findings and illustrate the performance of our new weak coupling approach.

Dynamics of extrusion landslides on bank slopes

The mathematical models proposed in this work based on concepts and methods of the mechanics of solid bodies, continuous medium mechanics, and the theory of capillarity and surface processes make it possible to describe quantitatively these processes and determine the parameters of “extrusion” landslides at all their development stages.

Problems of fracture mechanics of solid bodies with V-shaped notches

We present a survey of the research into the problems of fracture mechanics of solid bodies with V-shaped notches. The methods used for the solution of plane problems of the theory of elasticity in the domains with corner points on the boundary contours are analyzed. Special attention is given to the unified approach to the solution of the problems of stress concentration near sharp and rounded V-shaped notches in elastic domains. The fracture criteria for solid bodies with V-shaped notches are analyzed. On the basis of the solution of plane elastoplastic problem within the framework of the model of plastic strips for a plane with infinite rounded V-shaped notch, we propose a new deformation fracture criterion for quasibrittle bodies with sharp and rounded V-shaped notches.

Thebas experiment during the spanish soyuz mission cervantes

The educational experiment THEBAS, performed during the Cervantes Mission, was focused on illustrating the principles of dynamics ranging from the classic mechanics of solid bodies to the continuous media mechanics. The objective was to prepare a video for educational purposes. In this article the experimental setup used to perform the experiment is described. It consisted of transparent closed containers (having the same size and total mass) filled with solid spheres of different radii that were periodically oscillated in one dimension. The article also describes the experiment procedures and the technical problems encountered which caused that the experiment did not to work as expected.

In Memoriam: M. Eugene Merchant

In Memoriam: M. Eugene Merchant

Effluvia

Taking as a guiding theme his claim thatthere are effluvia from all things that have come to be, (DK B89), the author presents a reading of Empedocles that stresses the central role of effluvia in his natural philosophy. In presentations of Empedocles, the tradition has usually emphasized the importance of the elements-earth, air, water, fire, Love, and Strife. But as an alternative to that tradition, the author here argues that one must bring to the forefront the role of the effluvia, which give to Empedocles' cosmology a fluid, viscous character. The history of western natural science has been dominated by a mechanics of solid bodies following, however indirectly, in the tradition of the atoms and void of early Greek atomism. Empedocles represents a forgotten exception to that history, and the present paper attempts to return to his philosophy, unearth its fluid mechanical foundations, and present a challenging alternative to the dominant physical paradigm.