Speciality "Mechanics and math 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 systems in 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.
Designed syllabus preparation of a bachelor in the direction "Mechanics and Mathematical Modeling" proved his 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, ultimately ensure the creation of industrial products new generation.
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.
- Undergraduate
- 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 and many humanities. Thanks to the development of this science, humanity has made an impressive technological breakthrough over the past century. Without mathematics, the development of physics, chemistry, engineering, programming, architecture and many other disciplines is impossible. Without knowing mathematics it is impossible to build a house, design an internal combustion engine, create a computer program. Mathematics is a tool, a tool for others scientific disciplines, with 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 will be understood in any country.
Without knowledge of mathematics to live in modern world impossible in the era of globalization. But if the elementary foundations of this science are enough for most people, then for successful work in some areas human activity deep knowledge of this discipline is required.
Perhaps in the future the line between mathematics and other sciences will be erased, but now specially trained mathematicians are absolutely necessary in science-intensive industries of any profile, in sociology, politics and education.
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 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 this particular situation can be neglected or not.
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 side,
when considering the daily rotation of the Earth around own axis it is impossible to apply the “material point” model for the Earth.
When studying the motion of a body or a system of bodies, when the concept material point cannot be used, it is often useful to apply another physical model 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.
characteristic feature Such a movement is that the trajectories of all material points that make up a rigid body have the same shape and size and, with a parallel displacement, can be combined with each other.
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.
Benefits of learning
- Fundamental mathematical training, providing the possibility of active work in the most difficult areas modern mechanics; deep knowledge of programming, which allows to carry out computer simulation of processes and phenomena in various systems
- Availability of existing scientific schools that allow students to actively engage research work directly to the University
- An outstanding team of teachers and researchers who provide training in all areas of modern mechanics
- Work on unique experimental facilities in their own laboratories, a combination of theoretical and experimental approaches, allowing graduates to comprehensively explore the most complex problems of mechanics
- Mastering applied programs for solving problems of theoretical mechanics, hydroaeromechanics and elasticity theory (ANSYS, FLUENT, etc.) and creating your own algorithms and programs for specific problems of modern mechanics on the most modern computer technology
Notable teachers
- N. F. Morozov - Head of the Department of Elasticity Theory of St. Petersburg State University, Academician of the Russian Academy of Sciences, Professor, Doctor of Physical and Mathematical Sciences. Specialist in the nonlinear theory of elasticity, mathematical methods of fracture mechanics. Author of over 200 publications in Scopus and Web of Science
- P. E. Tovstik - Head of the Department of Theoretical and Applied Mechanics of St. Petersburg State University, Professor, Doctor of Physical and Mathematical Sciences, laureate of the State Prize of the Russian Federation, Honored Scientist of the Russian Federation, Commander of the Order of Honor, Honorary Professor of St. Petersburg State University. Specialist in the field of asymptotic and numerical methods V theoretical mechanics, the theory of thin-walled structures, solid mechanics and nanomechanics. Author of over 250 scientific works, including ten monographs and textbooks
- Yu. V. Petrov - Professor of St. Petersburg State University, Head of the Department "Extreme States of Materials and Structures" IPME RAS, Corresponding Member of RAS, Professor, Doctor of Physical and Mathematical Sciences. Specialist in the dynamic theory of elasticity and plasticity, physics and mechanics of shock-wave processes, dynamics of deformation and destruction of solids, detonation and explosion. Author of over 200 publications in Scopus and Web of Science
- E. V. Kustova - Head of the Department of Hydroaeromechanics, St. Petersburg State University, Doctor of Physical and Mathematical Sciences, Professor of the Russian Academy of Sciences. Specialist in the field of the kinetic theory of transfer and relaxation processes in non-equilibrium reacting gases, studies of heat and mass transfer on the surface of aircraft entering the atmosphere of Earth and Mars. Author of more than 200 scientific papers, including more than 120 publications in Scopus and Web of Science, five monographs and textbooks
Future career
Practice locations
Education involves the passage of educational, research and industrial practice on the basis of departments and scientific laboratories St. Petersburg State University.
List of key professions
Graduates of the program are ready for success professional activity in research, design and design institutes, in the construction industry, mechanical engineering, in the rocket and space industry, biomechanics, robotics and other areas of technology and natural science related to the development and application of mathematical methods. They can work as specialists in research and development work in the field of mathematical modeling, scientific and applied research for science-intensive high-tech industries, production and technological activities. Pedagogical work in the field of secondary general and vocational education is possible.
Organizations where graduates work
Graduates of the program continue their studies in the master's program at St Petersburg University and other universities, work in institutes Russian Academy sciences, at the enterprises of the State Corporation Roscosmos, at the subsidiaries of PJSC Gazprom Neft, at the enterprises of JSC United Shipbuilding Corporation, JSC Concern VKO Almaz-Antey, at the Krylov State Research Center, the Central Institute of Aviation Motors named after P.I. Baranova (CIAM), enterprises of the Mavis Investment Group of Companies, at the Izhora Plant, at the shipbuilding NPO Almaz, at the Obukhov Plant, at the FGU Rubin.
