Mechanical and mathematical modeling. Basic physical models and concepts of mechanics. Organizations where graduates work

Bachelor's degree
• 01.03.01 Mathematics
• 01.03.02 Applied mathematics and computer science
• 01.03.03 Mechanics and mathematical modeling
• 01.03.04 Applied Mathematics

Specialty
• 01.05.01 Fundamental mathematics and mechanics

The future of the industry

What technologies should a state have in order to be strong and independent in the 21st century? Space, nuclear energy, encryption, design, humanitarian technologies - mathematics is needed for all these and many other technologies, without which the future is unthinkable.

Mathematics is the basis, the basis for all natural sciences and many humanities. Thanks to the development of this science, humanity has made an impressive technological leap over the last century. Without mathematics, the development of physics, chemistry, engineering, programming, architecture and many other disciplines is impossible. Without knowing mathematics, you cannot build a house, design an internal combustion engine, or create a computer program. Mathematics is a means, a tool for other scientific disciplines, with the help of which you can translate the real properties of an object or system into abstract mathematical symbols and build models of the future operation of the system or object. Mathematics is a universal language that can be understood in any country.

Without knowledge of mathematics to live in modern world impossible in the period of globalization. But if the elementary fundamentals of this science are enough for most people, then for successful work in some areas human activity requires in-depth knowledge of the discipline.

Perhaps in the future the line between mathematics and other sciences will be erased, but now specially trained mathematicians are absolutely necessary in knowledge-intensive industries of any profile, in sociology, politics and education.

Main results, results of work and plans for the future

Bachelor's degree

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

Designed syllabus bachelor's degree in "Mechanics and mathematical modeling" has proven its high quality. Compared to the previous specialty program in Mechanics, non-core subjects were removed, the ratio between the physical and mathematical cycle of disciplines and special courses, physical and mechanical practical work and computational experiment was balanced. At the official level, training has been introduced to work with the universal “heavy” calculation complex ANSYS (ANSYSIInc., USA), which is one of the three main finite element complexes used in industry for the development of new equipment. Based on the experience gained and in connection with further development Federal state educational standard, the undergraduate curriculum will continue to be improved and optimized to meet the needs of high-tech production.

As a result, the achieved level of mastery of the main educational program of a bachelor’s graduate turned out to be higher than that of a specialist graduate (4.1 versus 3.8), and the submitted bachelor’s final works, despite the shorter preparation time, “beat” specialist diplomas (4.6 versus 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 undergraduate program “Experimental Mechanics and Computer Modeling in Mechanics.”

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

Engineers of the 21st century are research and development engineers who are proficient in all advanced world-class technologies, capable of “breaking through walls”, “solving unsolvable problems”, making innovative breakthroughs, and ultimately ensuring the creation of industrial products of a new generation.

Distribution, practice

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

Industrial practice 3rd year bachelor's degree "Mechanics and mathematical modeling" was very successful. After a long break, the students worked in the super-equipped materials testing laboratory of the Dipos Group of Companies (Ivanovo), at 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 the 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 under the general name, mechanical motion.

By mechanical movement we will understand a 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 motion of a given material object are the following:

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

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

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

Conclusions: Mechanical motion is relative and is simplest form movement 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 you should pay attention to the relative nature of the concept and its abstractness. Any real object has finite dimensions, which in a given specific situation can or cannot be neglected.

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

When considering the daily rotation of the Earth around its own axis, it is impossible to apply the “material point” model to the Earth.

When studying the motion of a body or 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 whose movement needs to be studied is mentally divided into small areas (material points), the dimensions of which are significantly smaller than the size of the body or system of bodies. In this case, the study of the movement of a body or system of bodies comes down to the study of the movement of individual sections of the system, that is, the material points of which this system consists. In this case, one should, of course, take into account whether the material points interact with each other or not.

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

Solid - This is a system of material points, the relative position of which does not change during a given movement.

Note 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. An absolutely 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 is called an imaginary line along which the movement of a given material point occurs.

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

Progressive This is the movement of a rigid body in which any straight line attached to this body remains parallel to itself during its movement.

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

Rotational is the movement 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 motion”. Trajectories can be rectilinear or curvilinear. The motion of a rigid body can be reduced to two forms: translational and rotational.

The most common entrance exams:

• Russian language
• Mathematics (basic level)
• Physics is a specialized subject, at the choice of the university
• Computer science and information and communication technologies (ICT) - at the university's choice

Professions

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

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

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, strength materials.

During the learning process, students develop analytical thinking abilities, study the fundamentals of economics and production management, and learn to apply in practice the fundamentals of fundamental mathematics, mechanics, physics and other natural sciences.

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

Graduates find application of 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.

Basic subjects when studying for a specialty

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

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

Duration of training

Duration of full-time education in the specialty"Mechanics and mathematical modeling" is 4 years (including holidays). Full-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

• Solving skills complex tasks by the method of information and communication technologies.
• Use of mathematical analysis in the field of theoretical and applied mechanics, strength 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 mechanical modeling problems without the participation of a PC (if the situation requires it).
• Adapting your knowledge to the organization of the educational process in your field of competence (physics, mechanics, mathematics, computer science).
• Organization of pedagogical, scientific, managerial, production and technological activities.

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

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

During their studies, 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. The amount of training in the field of computer science, programming, and IT technologies is significant.

During their studies, students will learn:

• Apply mathematical methods and algorithms of computational mathematics in solving mechanics problems and analyzing applied problems
• Participate in research seminars, conferences, symposia, as well as organize them
• Prepare scientific articles and scientific and technical reports
• Process general scientific and scientific-technical information
• Apply fundamental knowledge in the field of mechanics when preparing and conducting experimental research
• Conduct research work in the field of mechanics and mathematical modeling
• Conduct experimental research in mechanics
• Use specialized software systems to solve mechanical problems
• Analyze the results of research, production and technological activities
• Teach physical and mathematical disciplines and computer science in general education and secondary vocational schools educational institutions during specialized retraining

A significant proportion of graduates devote themselves to research careers. But the direction also has practical applications. In production, specialists can calculate power and thermal loads on the surface aircraft, the creation of new materials and alloys with 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, in enterprises of the mining complex, in aircraft design bureaus.

Assigned qualification

Mechanic. Applied mathematician - professional qualification of a specialist

Positions held

• Programmer
• Mechanical Engineer
• Mathematician
• Mathematics teacher
• Mathematical Modeling Specialist