Rational and Applied Mechanics

Rational and Applied Mechanics

Author: Nikolai Nikolaevich Polyakhov

Publisher: Springer Nature

Published: 2021-08-30

Total Pages: 526

ISBN-13: 3030640612

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Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied​ for the integration of equations of motion, and the elements of special relativity theory are presented. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.


Rational and Applied Mechanics

Rational and Applied Mechanics

Author: Nikolai Nikolaevich Polyakhov

Publisher: Springer

Published: 2021-06-07

Total Pages: 474

ISBN-13: 9783030641177

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Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.


Rational and Applied Mechanics

Rational and Applied Mechanics

Author: Nikolai Nikolaevich Polyakhov

Publisher: Springer

Published: 2021-04-13

Total Pages: 516

ISBN-13: 9783030640606

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Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied​ for the integration of equations of motion, and the elements of special relativity theory are presented. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.


Advances in Applied Mechanics

Advances in Applied Mechanics

Author:

Publisher: Academic Press

Published: 2014-11-21

Total Pages: 535

ISBN-13: 0128003022

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Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. - Covers all fields of the mechanical sciences - Highlights classical and modern areas of mechanics that are ready for review - Provides comprehensive coverage of the field in question


Empirical Design in Structural Engineering

Empirical Design in Structural Engineering

Author: Thomas Boothby

Publisher: Emerald Group Publishing

Published: 2023-10-10

Total Pages: 129

ISBN-13: 0727766341

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Through case studies from North America, Europe and Asia, Empirical Design in Structural Engineering shows that empirical design is practised much more widely than is generally understood,that it can make a valuable contribution to structural engineering design, and can be found embedded within the procedures of rational engineering design.


Mechanics of Fatigue

Mechanics of Fatigue

Author: Vladimir V. Bolotin

Publisher: CRC Press

Published: 1999-06-24

Total Pages: 210

ISBN-13: 9780849396632

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Mechanics of Fatigue addresses the range of topics concerning damage, fatigue, and fracture of engineering materials and structures. The core of this resource builds upon the synthesis of micro- and macro-mechanics of fracture. In micromechanics, both the modeling of mechanical phenomena on the level of material structure and the continuous approach are based on the use of certain internal field parameters characterizing the dispersed micro-damage. This is referred to as continuum damage mechanics. The author develops his own theory for macromechanics, called analytical fracture mechanics. This term means the system cracked body - loading or loading device - is considered as a mechanical system and the tools of analytical (rational) mechanics are applied thoroughly to describe crack propagation until the final failure. Chapter discuss: preliminary information on fatigue and engineering methods for design of machines and structures against failures caused by fatigue fatigue crack nucleation, including microstructural and continuous models theory of fatigue crack propagation fatigue crack growth in linear elastic materials subject to dispersed damage fatigue cracks in elasto-plastic material, including crack growth retardation due to overloading as well as quasistationary approximation fatigue and related phenomena in hereditary solids application of the theory fatigue crack growth considering environmental factors unidirectional fiber composites with ductile matrix and brittle, initially continuous fibers laminate composites Mechanics of Fatigue serves students dealing with mechanical aspects of fatigue, conducting research in fracture mechanics, structural safety, mechanics of composites, as well as modern branches of mechanics of solids and structures.


Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Author: Jörg Schröder

Publisher: Springer Science & Business Media

Published: 2010-08-04

Total Pages: 361

ISBN-13: 3709101743

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Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.