International Master Degree Program Continuum Mechanics .
Institute of Applied Mathematics and MechanicsSt. Petersburg Polytechnic UniversityInstitute for Problems in Mechanical EngineeringRussian Academy of SciencesInternational Master Degree ProgramContinuum Mechanics:Fundamentals and Applications
Objective of the programMasters capable of formulating and solving awide range of problems arising in variousfields of continuum mechanics both mechanics of solids and fluids both fundamental researchand engineering applications interdisciplinarity in the spirit of the STEM educationconcept aimed at obtaining 21st centuryskills in science, technology, engineering,and elopment
Key facts 3Being enrolled in MSc Program “Continuum mechanics: fundamentals and applications”means practically oriented learning, mentoring and scientific guidance from prominentprofessors of the Institute of Applied Mathematics and Mechanics of St. PetersburgPolytechnic University (Departments of Mechanics and Processes Control,Hydroaerodynamics, Applied Mathematics, Continuum Mechanics), recognized scientistsfrom the Institute for Problems in Mechanical Engineering of Russian Academy ofScience that is one of the leading research institutions in the field of mechanics of materials,and invited professors from top world universities: TU Berlin, TU Delft, ÉcolePolytechnique, University of Illinois at Chicago.The focus is placed, on the one hand, on interdisciplinarity, which is a current trend inmechanics, and the program topics include phase transformations, mechanochemistry,biological systems etc., and on the other hand, on deep learning of basic subjects ofcontinuum mechanics and applied mathematics. As a result, the graduates will acquirecompetencies which are necessary to both fundamental and applied research in theoreticaland computational mechanics of solids, gas and fluids as a unit, and, thus, being prepared forprospective international careers.We possess not only the extensive experience in research and teaching, but also broadinternational contacts, which we are eager to share with our students for their future career.This provides academic mobility and internships at the universities all around the world.We also expect the MSc Program to be approved by ECMI (European Consortium forMathematics in Industry) that in turn will give additional opportunities for academic mobility.
Training courses2 years, full-time, regular and modular courses, 120 ECTS(30 ECTS for the Master’s Thesis) 4Fundamentals: Мechanics and Thermodynamics of Continua; Elasticity; Plasticity;Fracture Mechanic; Мicromechanics, Rods and Shells, Waves in Continua, FluidMechanics, Multiphase Flows, Turbulence Modeling, Research and Developments ofMechatronic Systems (42 ECTS)Computational Solid and Fluid Mechanics (8 ECTS)Mechanics and Applied Mathematics in Natural Sciences and Technologies: blocksof lectures given by leading scientists from European and USA universities on varioustopics in mechanics and applied mathematics (8 ECTS).Mathematical foundations: Tensor Calculus; Functional Analysis; Numerical methodsfor PDE’s; Reliable Modeling and Error Control (A Posteriory Error Analysis); AdvancedTopics in Probability, Stochastic Processes and Statistics (16 ECTS)Research and Modeling Seminar: all students are given a problem-project to solveeither individually or in minigroups, and the results are then discussed altogether (16ECTS)
Continuum mechanics: fundamentals and applicationsCurriculum1st semester (30 ECTS)Focus on basic competencies Mechanics andThermodynamics of Continua(5 ECTS) Mechanics of Solids (6 ECTS):2nd semester (30 ECTS)Focus on core professionalcompetencies Fracture Mechanics (3 ECTS) Мicromechanics in Strengthand Plasticity (3 ECTS)Elasticity, Plasticity Waves in Continua (3 ECTS) Fluid Mechanics (5 ECTS) Multiphase Flows (3 ECTS) Computational Solid and FluidMechanics (4 ECTS) Computational Solid and FluidMechanics (4 ECTS)3rd semester (30 ECTS)Focus on advanced knowledge Fracture Mechanics andMicromechanics of HeterogeneousMedia (5 ECTS) Mechanics of Rods and Shells (3ECTS) Research and Developments ofMechatronic Systems (3 ECTS) Turbulence Modeling (3 ECTS) Mechanics and AppliedMathematics in Natural Sciencesand Technology (4 ECTS) Mechanics and Applied Mathematicsin Natural Sciences and Technology (4ECTS) Advanced Math (6 ECTS) : Advanced Math (5ECTS): Advanced Math (5 ECTS):Functional Analysis I;Numerical methods for PDE’s I;Tensor Calculus.Functional Analysis II;Numerical methods for PDE’s II.Reliable Modeling and Error Control;Parallel Algorithms for ScientificApplications;Advanced Topics in Probability, StochasticProcesses and Statistics. Research and ModelingSeminar (4 ECTS)5 Research and Modeling Seminar (7 Research and ModelingECTS)Seminar (5 ECTS)4th semester (30 credits): MSc Thesis
Modular coursesRegular courses, strengthened by learning-by-doing and modular training.“Mechanics and Applied Mathematics in Natural Sciences and Technology” is a modularcourse during which leading scientists from top world universities offer studentschallenging courses and highlight cutting-edge issues. After the end of each module thecommunication and possible collaboration with the invited lecturer may be continued on-lineto provide support with research projects as well as theses.Modules:Rational Electrodynamics of Materials (Prof. W. H. Müller)Nonlinear deformation of solids in particular rubber (Prof. W. H. Müller)Perturbation Methods for Nonlinear Continuous Dynamical Systems(Prof. W. T. van Horssen)Fatigue and shakedown (Prof. Eric Charkaluk)Experimental and Theoretical Fracture Mechanics(Prof. Alexander Chudnovsky)6
National Research University“Saint Petersburg Polytechnic University”Since its foundation in 1899, SPbPU is one of the leadingtechnical universities in Russia and famous for manytalented scientists and researchers including 3 NobelPrize winners. Today SPbPU is the Russian top-ratedtechnical university noted for the quality of educationand scientific research. It comprises 11 lnstitutes inEngineering, Computer Science, Technical Physics,Power Engineering, Economics and Humanities withmore than 30000 students enrolled.In 2010 SPbPU received the prestigious status of“National Research University”. Modernization of theeducational system and integration of SPbPU within theEuropean higher educational system are the strategicpriorities of the university’s development policy.Providing answers to global challenges, SPbPU invitesyou to join its international educational programs.www.eng.spbstu.ru7
National Research University“Saint Petersburg Polytechnic University”8 Campus area – 102 ha Postgraduate programs – 92Buildings – 112Institutes – 12Total number of students – 26500Foreign students – 1900Undergraduate and graduateprograms – 92Teachers – 2730University staff – 6000
Institute of Applied Mathematics and MechanicsHighest level of theory combined with emphasis on applicationsInstitute of Applied Mathematics and Mechanics of SPbSPU was created on the basisof the Department of Physics and Mechanics. The combination of academic learningand scientific research is a principle stated by A.I. Ioffe, the founder of thedepartment. Nowadays this principle is fundamental in the Institute’s educationalprocess. The Institute’s academic staff consists of highly qualified professors,associate professors, and scientists.Teaching staff:63 Full Professors133 Associate Professors88 Assistant Professors9Students:518 BSc students193 MSc students42 PhD studentsResearch staff:61 personsTechnical staff:108 personsFirst curriculum forMechanics wasdeveloped by ProfessorStepan Timoshenko
Research in IAMM 10Mechanics of SolidsFluid MechanicsComputational Mechanics andMathematics. Computer Aided Engineeringbased on Finite Element Mechanics:Micro- and NanomechanicsMechanics of Discrete SystemsDynamics and Strength of MachinesMechatronicsBiomechanicsApplied Mathematics and StatisticsComputer Science
Institute for Problems in MechanicalEngineering of Russian Academy of SciencesIPME RAS was established in 1987. Now this is one of the recognizedscientific centers in the field of applied mechanics with focus on bothfundamental and engineering problems.Main research fields: mechanics of materials from nano- to macro phase transitions, including stress-induced transformations mechanochemistry defects and damage mechanics reliability of machines and constructions vibratory, wave and vibroimpact processes modelling control processes in complex physical and technicalsystemsThe Institute has close contacts with leading St. PetersburgUniversities. The Department of Mechanics and Processes Controlshares the responsibility for the Educational Program with Departmentof Continuum Mechanics affiliated by IPME RAS to the Universitywww.ipme.ru11
Prospective Program Partners12
How to get enrolledAdmissionrequirementsAdmission testsAdmissionprocedureCandidates are required to hold a Bachelor, Specialist orMaster degree in a related subject area. English languageproficiency at B2 level is required for all applicants .Examination in the field of mechanics and appliedmathematics and an interview with the program coordinator(optionally – via Skype).Written on-line application. Application deadline – June, 30.International applicants may find additional informationconcerning admission at the official website of SPbPU:http://imop-spbspu.ru/en/add ed/docs and tests int studentsManager of Admission office for international students:interadmisson@imop.spbstu.ruSemester startLength of programWinter semester – September, 1.Full program: 2 years, 120 ECTSSemesters: details are available upon requestinteradmisson@imop.spbstu.ru, mobility@spbstu.ruDegree awarded13Master of science (MSc)
Program scientific supervisorAlexander B. Freidin, Dr. Sci., Professor Professor of the Department of Mechanics and Processes Control,Chair of the Department of Continuum Mechanics, Institute ofApplied Mathematics and Mechanics of St. Petersburg PolytechnicUniversityHead of the Department of Mathematical Methods in Mechanics ofMaterials and Structures, Institute for Problems in MechanicalEngineering of the Russian Academy of il: alexander.freidin@gmail.comProgram coordinatorRoman Filippov, PhD., Associate Professor 14Department of Mechanics and Processes Control, Institute ofApplied Mathematics and Mechanics of St. Petersburg PolytechnicUniversitySenior researcher of the Department of Mathematical Methods inMechanics of Materials and Structures, Institute for Problems inMechanical Engineering of the Russian Academy of ail: rmnfilippov@gmail.com
Continuum mechanics: fundamentals and applications Curriculum 5 1st semester (30 ECTS) rd Focus on basic competencies Mechanics and Thermodynamics of Continua (5 ECTS) Mechanics of Solids (6 ECTS): Elasticity, Plasticity Fluid Mechanics (5 ECTS) Computational Solid and Fluid Mechanics (4 ECTS) Mathematics in Natural Sciences
Forward finite difference Finite difference Central finite difference Semi-analytical method Discrete derivative Analytical method Continuum-discrete method Continuum derivative Continuum-continuum method Source code transformation Computational derivative Operator overloading . Figure 2. Approaches to design sensitivity analysis.
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