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This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It also presents the necessary mathematical framework, namely tensor algebra and tensor calculus, by using an inductive approach, which makes it particularly suitable for beginners. In general, the book can be used in undergraduate classes on continuum theory and, more specifically, in courses on continuum mechanics, for students of physics and engineering alike. The benefits for the readers consist of providing a sound basis of the subject as a whole and of training their ability for solving specific problems in a rational manner. For this purpose the general laws of nature in terms of the balances for mass, momentum, and energy are applied and combined with constitutive relations, which are material specific. Various examples and homework problems illustrate how to use the theory in daily practice. Numerous mini-biographies have been added to the mathematical text for diversion and amusement.

Classical continuum physics. --- Continuum mechanics. --- Engineering. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Continuum mechanics --- Fluid mechanics. --- Electromagnetism --- Mathematical models. --- Mathematics. --- Hydromechanics --- Mechanics of continua --- Continuum physics. --- Mechanics. --- Mechanics, Applied. --- Materials science. --- Theoretical and Applied Mechanics. --- Classical Continuum Physics. --- Materials Science, general. --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mechanics, applied. --- Materials. --- Classical and Continuum Physics. --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Materials --- Material science --- Physical sciences --- Classical field theory --- Continuum physics --- Physics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory

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This book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis.

Materials Science --- Applied Mathematics --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Continuum mechanics. --- Deformations (Mechanics) --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Elastic solids --- Mechanics --- Rheology --- Strains and stresses --- Structural failures --- Mechanics. --- Mechanics, Applied. --- Planetology. --- Solid Mechanics. --- Classical Mechanics. --- Planetary sciences --- Planetology --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory

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This book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis.

Solar system --- Classical mechanics. Field theory --- Fluid mechanics --- Applied physical engineering --- zonnestelsel --- ingenieurswetenschappen --- planeten --- mechanica

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Fluid mechanics --- Solid state physics --- Materials sciences --- Applied physical engineering --- materiaalkennis --- toegepaste mechanica --- mechanica

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This book commemorates the 75th birthday of Prof. George Jaiani – Georgia’s leading expert on shell theory. He is also well known outside Georgia for his individual approach to shell theory research and as an organizer of meetings, conferences and schools in the field. The collection of papers presented includes articles by scientists from various countries discussing the state of the art and new trends in the theory of shells, plates, and beams. Chapter 20 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Shells (Engineering) --- Boundary value problems. --- Mathematical models. --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Structural shells --- Elastic plates and shells --- Structural analysis (Engineering) --- Plates (Engineering) --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Mathematical Modeling and Industrial Mathematics. --- Models, Mathematical --- Simulation methods --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory