Mechanical and mathematical modeling. Basic physical models and concepts of mechanics. Why you should study Mathematics or Mechanics

The most common entrance exams are:

  • Russian language
  • Maths ( a basic level of)
  • Physics - a profile subject, at the choice of the university
  • Informatics and information and communication technologies (ICT) - at the choice of the university

Professions

"Mechanics and math modeling"- a specialty that allows in the future to make a choice from quite a large number interesting professions:

  • Researcher,
  • engineer,
  • mathematician,
  • analyst,
  • supervisor,
  • researcher,
  • teacher of physical and mathematical disciplines,
  • specialist in mathematical modeling.

Academic bachelors have the opportunity to work in any field of science, industry, production, management related to mathematics, engineering, physics, mechanics and programming.

Description of specialty

During their studies, students acquire scientific knowledge on computer modeling of various mechanical processes. Students study computational mathematics, mechanics and biomechanics, the theory of stability of electromechanical devices, the degree of elasticity, density and plasticity of materials. They master the static and dynamic strength of various objects and other sciences, one way or another related to theoretical mechanics, mathematics, engineering, sopromat.

In the process of learning, students develop the ability to analytical thinking, study the basics of economics and production management, learn to put into practice the basics of fundamental mathematics, mechanics, physics and other natural sciences.

A feature of training in the specialty "Mechanics and Mathematical Modeling" is a large number of standard hours devoted to workshops. Where students have a unique opportunity to apply their theoretical knowledge in the case, analyze and synthesize specific information. Some of the workshops are devoted to working with computer-mathematical modeling programs designed to simulate technological processes on a monitor screen.

Graduates find application for their knowledge in engineering centers of industrial companies, gas and oil industries, transnational corporations, research and design bureaus, including foreign ones, involved in the development of new engineering technologies.

The main subjects in training in the specialty

  • Mechanics of deformable bodies and media.
  • Mathematical modeling and computer engineering.

In addition, students study philosophy, history, foreign language and OBZh (basics of life safety). Compulsory disciplines: physical culture and applied physical culture.

Terms of study

The term for obtaining full-time education in the specialty"Mechanics and mathematical modeling" is 4 years (including holidays). Part-time and distance learning, by decision of the administration, can be extended for a period of six months to a year.

Skills and abilities acquired during training

  • Ability to solve complex problems using information and communication technologies.
  • Usage mathematical analysis in the field of theoretical and applied mechanics, resistance of metals, geometry, differential equations and probability theory.
  • Work with specialized programs for modeling and optimization of technological processes.
  • Doing research work independently or in a group.
  • Solving problems of mechanical modeling without the participation of a PC (if the situation requires it).
  • Adapting your knowledge to the organization educational process in the field of their competence (physics, mechanics, mathematics, computer science).
  • Organization of pedagogical, scientific, managerial and production-technological activities.

During the training, the bachelor acquires the professional skills necessary for competent engineering and analysis of complex mechanical objects by means of computer and / or physical analysis.

Speciality "Mechanics and Mathematical Modeling" is a branch of applied mathematics that deals with the mathematical modeling of complex physical processes in solids ah, liquids, gases and plasma.

During the training, students receive deep fundamental knowledge in the field of mathematics and programming, classical mechanics. In addition, students are taught a wide range of special disciplines in various areas of modern mechanics. Significant is the amount of training in the field of informatics, programming, IT-technologies.

During their studies, students will learn:

  • Apply mathematical methods and algorithms of computational mathematics in solving problems of mechanics and analyzing applied problems
  • Participate in the work of research seminars, conferences, symposiums, as well as organize them
  • Engage in the preparation of scientific articles and scientific and technical reports
  • Process general scientific and scientific and technical information
  • Apply fundamental knowledge in the field of mechanics in the preparation and conduct of experimental research
  • Carry out research work in the field of mechanics and mathematical modeling
  • Conduct experimental studies in mechanics
  • Use specialized software complexes when solving problems of mechanics
  • Analyze the results of research and production and technological activities
  • Teaching physical and mathematical disciplines and computer science in general education and secondary professional educational institutions in specialized training

A significant part of the graduates devotes themselves to a research career. But the direction has an applied application. In production, specialists can be engaged in calculations of power and thermal loads on the surface of aircraft, the creation of new materials and alloys with a shape memory effect, the design of installations for the production and transportation of oil and gas, etc. Specialists in mechanics and mathematical modeling are required in research institutes and centers, to enterprises of the mining complex, to aircraft design bureaus.

Awarded qualification

Mechanic. Applied Mathematician - professional qualification of a specialist

Positions held

  • Programmer
  • mechanical engineer
  • Mathematician
  • Math teacher
  • Mathematical Modeling Specialist

Main results, results of work and plans for the future

Undergraduate

In 2015, the first graduation of bachelors took place in the direction with a profile "Experimental mechanics and computer simulation in mechanics". Eight people out of ten who entered the Department of TiPM in 2011 successfully defended their graduation theses and received bachelor's degrees in engineering.

The developed curriculum for the preparation of a bachelor in the direction "Mechanics and Mathematical Modeling" proved its high quality. In comparison with the previous program of the specialist in "Mechanics", non-core subjects were removed, the ratio between the physical and mathematical cycle of disciplines and special courses, the physical and mechanical workshop and the computational experiment was balanced. At the official level, training has been introduced to work with the universal "heavy" calculation complex ANSYS (ANSYSInc., USA), which is one of the three main finite element complexes used in industry to develop new technology. Based on the experience gained and in connection with the further development of the federal state educational standard the undergraduate curriculum will continue to improve and optimize for the needs of high-tech production.

As a result, the achieved level of mastering the basic educational program of the bachelor's graduate turned out to be higher than the specialist's graduate (4.1 vs. 3.8), and the presented bachelor's theses, despite the shorter preparation time, "beat" the diplomas of specialists (4.6 vs. 4.2). At the same time, the solved scientific and practical problems themselves aroused keen interest among the members state commission and lengthy discussions.

Master's degree

This year the first enrollment for the new master's program was carried out "Dynamics and strength of complex mechanical systems" directions "Mechanics and Mathematical Modeling". Nine people came to us, including graduates of the bachelor's degree program "Experimental Mechanics and Computer Simulation in Mechanics".

The bachelor's degree level is only the first level in the system of Russian and world education. It provides a basic theoretical level and gives some practical skills. However, in order to solve the main task of the Russian industry today - the creation in the shortest possible time of globally competitive and demanded products of a new generation - specialists of a new formation are needed - "engineering and technological special forces", whose training can only be carried out on master's programs focused on the high-tech sector of the economy. This is the program we offer to our undergraduate students.

Engineers of the 21st century are research and development engineers who own all the world-class advanced technologies, are able to “break through walls”, “solve unsolvable problems”, make innovative breakthroughs, and ultimately ensure the creation of a new generation of industrial products.

Distribution, practice

The distribution this year has been more active than ever, which is associated with the end of the specialist's programs and the double graduation. However, there was no particular interest in specialist graduates compared to bachelor graduates. The "hunger" for the development engineers of new technology is only increasing. Mechanical engineers are in demand in all branches of mechanical engineering: heavy, energy, auto, ship, aircraft and rocket manufacturing. We were visited by both old partners (Galich Truck Crane Plant, Federal Nuclear Center - Scientific Research Institute of Technical Physics, Progresstekh-Dubna LLC, Gazpromtrubinvest OJSC), as well as new ones, among which the Experimental Machine-Building Plant named after A.I. Myasishchev, engaged in the creation of aviation, aerospace, aerostatic and landing equipment. It was there that most of the mechanical graduates of this year went to the design department for a very decent salary.

Industrial practice 3rd year bachelor's degree "Mechanics and Mathematical Modeling" went very well. After a long break, the students worked in the super-equipped materials testing laboratory of the Dipos Group of Companies (Ivanovo), in the Proton Innovation Center (Vladimir). I would especially like to note the practice at the enterprise "GosMKB" Raduga "named after. A.Ya. Bereznyak (Dubna), which produces high-speed aircraft, and in the Moscow engineering center of a large international company FESTO, Germany.

Basic questions of mechanics

Kinematics

Mechanics studies the simplest forms of motion found in the material world, which are united by the common name, mechanical motion.

Under the mechanical movement we will understand the change in the relative position of one material object in relation to another material object. This is one of the most important properties of mechanical motion: its relativity.

The main questions that arise when trying to characterize the mechanical movement of a given material object are as follows:

1. How does this object move?, that is, what is the type and nature of its relative motion?

2. Why does this object move in this way and not otherwise?, that is, what are the reasons that cause this particular type and nature of the movement of the object in question?

The search for an answer to the first of these questions is dealt with by the section of mechanics - kinematics, the second - dynamics.

Conclusions: mechanical movement relatively and is the simplest form of motion of matter. Basic questions of mechanics: How and why does a material object move?

Depending on the properties of a material object, the nature and type of its movement, the simplest physical models are used in mechanics:

material point (particle) - an object (body), the dimensions of which can be neglected in comparison with the characteristic size of the movement in which this object participates.

Here we should pay attention to the relative nature of the concept and its abstractness. Any real object has a finite size, which in a given specific situation may or may not be neglected.

For example, considering the motion of the Earth around the Sun, it can be considered a material point, since the radius of the Earth R z = 6400 km is much less than the radius of its orbit around the Sun R s = 1.5 × 10 8 km. On the other hand,

By revising daily rotation The earth around its own axis cannot be applied to the earth with the “material point” model.

When studying the motion of a body or a system of bodies, when the concept of a material point cannot be used, it is often useful to apply another physical model, which is called system of material points.

The essence of this model is that any body or system of bodies, the movement of which needs to be studied, is mentally divided into small sections (material points), the dimensions of which are much smaller than the dimensions of the body or system of bodies. In this case, the study of the motion of a body or a system of bodies is reduced to the study of the motion of individual sections of the system, that is, the material points that make up this system. In this case, one should, of course, take into account whether the material points interact with each other or not.



A particular case of the “system of material points” model in mechanics is the model called solid:

Solid - is a system of material points, mutual arrangement which does not change during this movement.

Pay attention to the relativity of this model.

The limiting case of a rigid body model is an absolutely rigid body. In an absolutely solid body, the distance between any arbitrary particles does not change under any conditions. A perfectly rigid body is an abstract model, since no real body has this property.

To describe the movement of a material point, a model is used - trajectory .

Trajectory of movement An imaginary line along which a given material point moves is called.

If this line is a straight line or its segment, then they say that the motion of the material point is rectilinear, otherwise the motion is curvilinear. To describe the types of motion of a rigid body, models of translational and rotational motion are used.

Translational called such a motion of a rigid body, in which any straight line, fastened to this body, during its movement remains parallel to itself.

A characteristic feature of such a movement is that the trajectories of all material points that make up a solid body have the same shape and size and can be combined with each other with a parallel displacement.

rotational called such a motion of a rigid body in which all its material points move in circles. In this case, the centers of these circles are located on one straight line, called the axis of rotation.

Arbitrary motion of a rigid body can always be represented as a set of simultaneous translational and rotational motions.

Conclusions: The main physical models of mechanics are a material point, a system of material points and a rigid body. The movement of a material point is determined by the concept of “trajectory of movement”. Trajectories are either straight or curved. The motion of a rigid body can be reduced to two forms: translational and rotational.

The profession lies at the intersection of mathematics, physics and computer science. Students learn to predict the physical processes occurring in solids, liquids, gases and plasmas using mathematical modeling methods. To do this, you have to use complex computer programs, and sometimes you have to create them yourself. Moreover, if it is impossible to use a computer, graduates should be able to solve the problem in other ways. In the curriculum, much attention is paid to physical disciplines, primarily mechanics. Also, students get acquainted with computer science, programming and robotics. Specialization depends on what kind of objects the graduate decides to model: solids, liquids or gases. Such a branch of science as engineering biomechanics is becoming popular - the study of the properties of living tissues and the design of artificial body parts. *

* Kit academic disciplines and learning bias

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