Applied Problems Of Mechanics Research Articles

Development of a software solution to an applied mechanics problem based on numerical methods

The present work delves into the significance of material selection in the manufacturing of tools for milling operations and determines their suitability through a detailed analysis of strength and behavior during material processing. To enhance longevity and optimize production, the utilization of mathematical models and numerical methods, notably the least squares method and the solution of systems of linear algebraic equations (SLAE) employing the Gaussian elimination method with pivot selection, is proposed. These methods are applied for the approximation of experimental data and the analysis of material characteristics, ensuring precision in the evaluation of its properties. Situations where only partial data is known are investigated, along with simplifications in the computation of known functions. The study encompasses software for numerical computation and visualization of various problem types, effectively addressed through the aforementioned methods. The software algorithm for data approximation involves storing information in a text file, user input of variables, and selection of the quantity and type of basis functions. After the user inputs of parameters, the program formulates a system of equations based on selected functions, determines approximation coefficients, and generates a graph for an objective assessment of results. With a user-friendly interface, users can easily interact with the program, input values, and analyze results through graphical representation, streamlining the workflow and facilitating the comprehension of obtained data. The approximation of functions using numerical methods proves to be efficiently applicable in diverse fields for addressing applied mechanics problems.

A general framework for probabilistic sensitivity analysis with respect to distribution parameters

Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximisation and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.

Solution of Integral Equations Using Local Splines of the Second Order

Splines are an important mathematical tool in Applied and Theoretical Mechanics. Several Problems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elements and Splines. In this paper, we consider the construction of computational schemes for the numerical solution of integral equations of the second kind with a weak singularity. To construct the numerical schemes, local polynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. The results of the numerical experiments are given. This methodology has many applications in problems in Applied and Theoretical Mechanics

AI-Timoshenko: Automatedly Discovering Simplified Governing Equations for Applied Mechanics Problems From Simulated Data

Abstract The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler–Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems.

International Scientific Conference “Fundamental and Applied Problems of Mechanics” (FAPM-2020). Moscow, 2–4 December, 2020. Materials of the Сonference. Part 1

Compiled by P.M. Shkapov, M.I. Dyachenko The next scheduled conference was held in 2020, the year of the 190th anniversary of the founding of Bauman Moscow State Technical University — one of the leading technical universities in Russia, the one that gave rise to many higher technical educational institutions, scientific and pedagogical schools in the field of engineering and technology. The conference was held on the basis of the Scientific and Educational Complex “Fundamental Sciences” and the Department of “Theoretical Mechanics” named after Professor N.E. Zhukovsky and brought together scientists from research institutions of the Russian Academy of Sciences, universities of the Russian Federation, well-known foreign mechanical scientists. The conference aimed at introducing new research carried out by Russian and foreign scientific and educational institutions in various areas of mechanics. Part 1 presents Plenary reports, as well as materials from Sections 1 and 2. Part 2 contains materials from Sections 3, 4 and 5. Working languages of the conference: Russian and English. Conference website: http://fn.bmstu.ru/coferences-sec-fs/item/1011-fapm-2020

Международная научная конференция «ФУНДАМЕНТАЛЬНЫЕ И ПРИКЛАДНЫЕ ЗАДАЧИ МЕХАНИКИ», посвященная 100-летию со дня рождения академика Константина Сергеевича Колесникова (Москва, 10–12 декабря 2019 г.)

Compiled by P.M. Shkapov, M.Yu. Barkin, E.V. Melkumova Since 2012 conferences "Fundamental and Applied Problems of Mechanics - FAPM" have been regularly held at Bauman Moscow State Technical University. The conferences are hosted by the Scientific and Educational Complex "Fundamental Sciences" and the Department of Theoretical Mechanics named after Professor N.E. Zhukovsky. Scientists from leading scientific institutions of the Russian Academy of Sciences and universities of the Russian Federation, as well as foreign scientists majoring in mechanics take part in this event. The main objective of the conference held in 2019 was to present new research conducted in various fields of mechanics in Russian and foreign scientific and educational institutions. In 2019, the FAPM-2019 conference was dedicated to the 100th birthday of academician Konstantin Sergeyevich Kolesnikov (1919–2016), one of the pioneers in space exploration, the creator of a scientific and pedagogical school on the dynamics of rocket-space systems, oscillation theory, the front-line soldier, acknowledged mechanical scientist of Bauman University until his recent death in the 97th year of life. In connection with K.S. Kolesnikov's anniversary, many reports placed emphasis on the studies which developed and continued his scientific and educational research in modern conditions. Conference website: http://www.fn.bmstu.ru/coferences-sec-fs/item/885-fapm-2019

Preface

In December 13-15, 2018 Bauman Moscow State Technical University held the International Conference “Fundamental and Applied Problems of Mechanics”. The main purpose of this conference is to present new research results in various areas of mechanics held in Russian and foreign scientific and educational institutions. One of the important tasks of the conferences “Fundamental and applied problems of mechanics” (FAPM), which are regularly held at Bauman Moscow State Technical University, is also the disclosure of links with the research of N.Ye. Zhukovsky and the presentation of the development of its results in modern conditions. This year the conference is dedicated to the 140th anniversary of the Department of Theoretical Mechanics, which is one of the oldest departments of Bauman Moscow State Technical University was founded by Nikolay Egorovich Zhukovsky in 1878.One of the important tasks of the conferences “Fundamental and applied problems of mechanics” (FAPM), which are regularly held at Bauman Moscow State Technical University, is also the disclosure of links with the research of N.Ye. Zhukovsky and the presentation of the development of its results in modern conditions.Traditions laid by N.E. Zhukovsky in the department, continue to be maintained and developed. New young teachers, graduate students and students are connected to the scientific, pedagogical, methodical and social activities, which is the key to the further successful development of the department in modern conditions.

Fundamental and Applied Problems of Mechanics - 2017

PREFACEIn October 24-27, 2017 Bauman Moscow State Technical University held the International Conference “Fundamental and Applied Problems of Mechanics” dedicated to the 170th anniversary of the birth of the great Russian scientist Nikolay Egorovich Zhukovsky. The primary goal of this conference is to present new research results in various branches of mechanics, carried out by Russian and international scientific and educational institutions. The anniversary of N.E. Zhukovsky suggests focusing in particular on the studies that evolve and elaborate on his scientific and teaching-oriented investigations, updating them for the world of today. The conference was attended by Dr. Christian Bizouard (Director of IERS Earth Orientation Centre, Observatoire de Paris), Prof. Dr. Shuanggen Jin (Head of Satellite Navigation and Remote Sensing Group, Chinese Academy of Sciences), Prof. V.V. Sadovnichii (Member of RAS, Rector of Lomonosov Moscow State University) and other famous scientists. The scientists showed their great potential in studying various problems in numerous fields of science and technology, as well as applying new approaches, which develop and improve methods of mechanics.Nikolay Egorovich Zhukovsky is the great Russian scientist, founder of applied aerodynamics, “father of the Russian aviation”, creator of TsAGI, the Central Aerohydrodynamic Institute, founder of Theoretical Mechanics Department, Professor of the Imperial Moscow Technical School and Moscow University.Professor N.E. Zhukovsky’s scientific work initiated a new era in development of mechanical science and technology. N.E. Zhukovsky is not only responsible for a large number of important discoveries in mechanics, but he is also a scientist who dramatically changed the role of science in engineering. One of his biggest achievements is that he was able to combine the most subtle theoretical research with experience and direct all the power of these methods to study physical and technical phenomena, to solve major engineering problems. N.E. Zhukovsky realized and showed that mechanics can develop further, only being constantly enriched by experimental data, as it was in the days of Galileo, and in such a combination it will become an instrument of unprecedented strength for studying the phenomena of nature, for the advance of technology. All future and present day scientists, engineers, and researchers should know Nikolay Yegorovich Zhukovsky’s prophetic words, which he said in 1898 at the Tenth Congress of the Russian Naturalists: “A man … will fly, not leaning on the strength of his muscles, but on strength of their reason”.

Fundamental and Applied Problems of Mechanics - 2017

List of International Organising Committee of the FAPM-2017 available in this pdf.

Fundamental and Applied Problems of Mechanics - 2017

List of Academician Committee of FAPM-2017 (International Advisory Council) available in this pdf.

Fundamental and Applied Problems of Mechanics - 2017

List of Photo available in this pdf.

Direct and Inverse Problems of Thermomechanics Concerning the Optimization and Identification of the Thermal Stressed State of Deformed Solids

We describe the main stages of the development of investigations originated by Prof. Vihak in the fields of the theory and methods of optimal control over the thermal processes and thermal stressed state of deformed solids, theory of inverse problems of heat conduction and thermomechanics, and the mathematical methods in the mechanics of deformable solids. We indicate the existence of close relationship between the obtained theoretical results and the applied problems of thermal power engineering motivating investigations of this kind. We describe a significant contribution made by the researchers of the Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of the Ukrainian National Academy of Sciences to the development of investigations in these fields. The prospects of further development of these studies are analyzed and some facts from the life and creative activity of Prof. V. М. Vihak are presented.

Towards ‘h-p adaptive’ generalized ANOVA

This paper presents a novel ‘h-p adaptive’ generalized analysis of variance decomposition (G-ANOVA) for high dimensional stochastic computations. Firstly, an iterative scheme based on variance based global sensitivity analysis is proposed to determine the optimal polynomial order and important component functions (p adaptivity) of G-ANOVA. Then, a homotopy algorithm is employed to determine the unknown expansion coefficients. Moreover, a novel distribution adaptive sequential experimental design (h-adaptivity) is utilized at each step and the accuracy of the G-ANOVA based surrogate model is computed using leave one out statistical test. It is observed that significantly less number of component functions are retained. As a consequence, the proposed approach is highly efficient and is applicable for solving problems involving large number of stochastic dimensions. Implementation of the proposed approach has been illustrated with four high dimensional applied mechanics problems. The proposed approach is found to yield accurate and efficient results. Finally, the proposed approach has been applied for structural reliability analysis of a large scale real life problem.

Generalization of the super ellipsoid concept and its application in mechanics

In this paper, we generalize the concept of super ellipsoid that was proposed by the French mathematician and mechanician Gabriel Lamé in 1818. Super ellipsoid itself represents a generalization of the ellipsoid, namely when the power n appearing in super ellipsoid equals 2, the conventional ellipsoid is obtained. In this paper the notion of super ellipsoid is further extended by introducing as many generally different powers, as is dictated by the dimensionality and the physics of the problem. Specifically, two different power parameters are introduced for the generalized super ellipse. Likewise, three generally different powers are adopted for the three-dimensional super ellipsoid etc. An applied mechanics problem is considered to demonstrate the efficiency of the notion of generalized super ellipsoids, namely we study the static behavior of an engine's crankshaft. Two to five geometric parameters specifying the crankshaft are treated as belonging to a generalized super ellipsoid set.

XIXth International Seminar/Workshop DIPED-2014

The XIXth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2014) was organized by the IEEE MTT/ED/AP Georgian and MTT/ED/AP/CPMT/SSC West Ukraine Chapters. This year, DIPED was held at the Tbilisi State University, Tbilisi, Georgia, on September 22–25. The Ivane Javakhishvili Tbilisi State University (TSU) and Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, NASU, Ukraine, were the co-organizers of DIPED-2014. The IEEE Antennas and Propagation Society, Electron Devices Society, and Microwave Theory and Tech niques Society provided the technical co-sponsorship for the seminar/workshop. The TSU provided the special financial support for the event that made it possible to extend the DIPED-2014 audience from outside Georgia (Figure 1). The IEEE Solid State Circuits Society and IEEE Ukraine Section were the supporting IEEE organizations.

Научная конференция "Фундаментальные и прикладные задачи механики", посвященная 135-летию кафедры теоретической механики имени профессора Н.Е. Жуковского (23–25 октября 2013 года)

Научная конференция "Фундаментальные и прикладные задачи механики", посвященная 135-летию кафедры теоретической механики имени профессора Н.Е. Жуковского (23–25 октября 2013 года)

The XIth All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics

The XIth All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics

Flexural vibrations of clamped-free rhombic plates with corner stress singularities. Part I: review of research

In this paper (part I) an ample review of the published literature of skew plate vibrations summarizes well over 100 references as background, bringing forth a need for accurate solutions incorporating stress singularity-based methodologies for analyzing this applied mechanics problem. Such an accurate method is presented in a part II companion paper for analysis of flexural vibrations of rhombic plates with all combinations of clamped and free edge conditions. The prime focus therein is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates. The strength of these singularities increases significantly as the obtuse angles at the corners increase. Frequency relations summarized herein from this review of Mindlin and Reddy skew plate vibrations research enable investigators to obtain accurate 3–4 significant digit upper bounds on exact solutions of shear deformable skew plates, including the effects of stress singularities, given analogous Kirchhoff skew (rhombic) plate frequency solutions, and thereby eliminating the need to solve the complicated equations of shear deformation theories including stress singularity effects published elsewhere.

X All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics

X All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics

Resolving applied-mechanics problems in creating Antonov transport aircraft

Some problems of flight mechanics encountered in creating transport aircraft designed by O. K. Antonov are described. To solve these problems, the Antonov ASTC used equations that describe the motion of aircraft under diverse conditions, including during cargo airdrop, under servotab control, and with multileg landing gears. The results of the theoretical and experimental studies as well as the practical work carried out to make aircraft structures of polymer composite materials are presented. Approaches to and a sequence of resolving problems of designing low-, medium-, and high-loaded structures are outlined. Photos of the most typical composite components and structures are shown