Wolfgang H. Müller

This book shows how continuum mechanics can be extended to describe phenomena that lie beyond the scope of classical mechanics and traditional constitutive theory. In many applications, the classical translational degrees of freedom are not sufficient. Rotational motion, internal variables, particle density, and physics-based concepts from mixture theory provide additional degrees of freedom that are needed to capture the behavior of complex materials. The book also introduces several recently developed concepts, including a producible microinertia tensor field that allows structural changes to be described directly at the continuum level. Besides the classical balance laws, the book discusses generalized balance equations, such as strain balances, and their role in continuum modeling. It also presents continuum formulations for electromagnetic phenomena and shows how these can be combined with mechanical descriptions within a common theoretical framework. The relation between microscopic models and macroscopic continuum theories is examined, and homogenization methods are used to establish the connection between these different levels of description. The concepts presented are applied to a broad range of problems, including granular materials, damage and fracture, phase transitions, and electrodynamic phenomena. The book is intended for researchers and graduate students in continuum mechanics, applied mathematics, physics, and engineering who are interested in modern extensions of continuum theory and their applications.

This book presents various dynamic processes in non-uniform piezoceramic cylindrical and spherical bodies based on numerical methods. It discusses different variants of nonhomogeneous structural polarized piezoceramic materials in the shape of cylinders and spheres, and highlights the validation of the reliability of the results obtained by numerical calculations. The content is based on an outlined theory and methods of three-dimensional electroelasticity problems.

This book presents various dynamic processes in non-uniform piezoceramic cylindrical and spherical bodies based on numerical methods. It discusses different variants of nonhomogeneous structural polarized piezoceramic materials in the shape of cylinders and spheres, and highlights the validation of the reliability of the results obtained by numerical calculations. The content is based on an outlined theory and methods of three-dimensional electroelasticity problems.

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It includes the necessary applied mathematical framework of tensor algebra and tensor calculus, using an inductive approach particularly suited to beginners. It is geared toward undergraduate classes in continuum theory for engineers in general, and more specifically to courses in continuum mechanics. Students will gain a sound basic understanding of the subject as well as the ability to solve engineering problems by applying the general laws of nature in terms of the balances for mass, momentum, and energy in combination with material-specific relations in terms of constitutive equations, thus learning how to use the theory in practice for themselves. This is facilitated by numerous examples and problems provided throughout the text.

This brief book presents solutions of stress-strain problems for a wide class of anisotropic inhomogeneous shells obtained by the refined model. Studying these problems results in severe computational difficulties due to partial differential equations with variable coefficients resulting from the constitutive relations of the original model. To solve this problem the book uses spline-collocation and discrete-orthogonalization methods. It analyses the influence of geometrical and mechanical parameters, of various kinds of boundary conditions, and of the loading conditions on the distributions of stress and displacement fields in shallow, spherical, conical, and noncircular cylindrical shells. The dependence of the stress-strain pattern on shell thickness variations is studied. The authors solve the problem also for the case of the thickness varying in two directions. They study how a variation in shell thickness influences the stress-strain state and consider noncircular cylindrical shells with elliptical and corrugated sections are considered. The results obtained during numerous calculations support the efficiency of the discrete-orthogonalization approach proposed in the monograph for solving static problems for anisotropic inhomogeneous shells when using the refined model.

These two-partition books present essential approaches to numerical-analytical solutions of problems in the mechanics of shells with various structures and shapes based on refined and spatial models. Further, it examines the mechanical behavior of shallow, circular and noncircular, conical, spherical, and functionally graded shells obtained by the refined model. The book investigates the stress-strain state and free vibrations of finite-length cylinders in spatial formulation (3D elasticity theory). Further, it analyzes the influence of geometrical and mechanical parameters, of boundary conditions, and of the loading character on both the distributions of stress and displacement fields, and on the dynamical characteristics in these shells and cylinders. Lastly, it discusses in detail the validation of reliability for the results obtained bynumerical calculations. As such, it complements the first part of the book, the volume Recent Developments in Anisotropic Heterogeneous Shell Theory: Applications of Refined and Three-dimensional Theory.

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 viewpointof rational continuum theory and numerical analysis.

This volume focuses on the relevant general theory and presents some first applications, namely those based on classical shell theory. After a brief introduction, during which the history and state-of-the-art are discussed, the first chapter presents the mechanics of anisotropic heterogeneous shells, covering all relevant assumptions and the basic relations of 3D elasticity, classical and refined shell models. The second chapter examines the numerical techniques that are used, namely discrete orthogonalization, spline-collocation and Fourier series, while the third highlights applications based on classical theory, in particular, the stress-strain state of shallow shells, non-circular shells, shells of revolution, and free vibrations of conical shells. The book concludes with a summary and an outlook bridging the gap to the second volume.

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It includes the necessary applied mathematical framework of tensor algebra and tensor calculus, using an inductive approach particularly suited to beginners. It is geared toward undergraduate classes in continuum theory for engineers in general, and more specifically to courses in continuum mechanics. Students will gain a sound basic understanding of the subject as well as the ability to solve engineering problems by applying the general laws of nature in terms of the balances for mass, momentum, and energy in combination with material-specific relations in terms of constitutive equations, thus learning how to use the theory in practice for themselves. This is facilitated by numerous examples and problems provided throughout the text.

Das Buch führt in verschiedene Bereiche der Kontinuumstheorie ein, die für Ingenieure von Relevanz sind. Dazu gehören die Deformation des elastischen und des plastifizierenden Festkörpers, die Strömung reibungsfreier und reibungsbehafteter Fluide sowie die Elektrodynamik. Der Autor baut die Theorie im Sinne der Rationalen Mechanik auf, d.h. er unterscheidet zwischen Bilanz- und Materialgleichungen und erstellt daraus ein Feldgleichungssystem. Als mathematisches Hilfswerkzeug gibt er – sozusagen nebenbei – eine Einführung in die Tensoranalysis. Dabei wird sowohl der Indexkalkül als auch die absolute Schreibweise verwendet und gegenübergestellt. Das Buch wendet sich an Ingenieure und Physiker im Masterstudium.

Thermodynamics is the much abused slave of many masters • physicists who love the totally impractical Carnot process, • mechanical engineers who design power stations and refrigerators, • chemists who are successfully synthesizing ammonia and are puzzled by photosynthesis, • meteorologists who calculate cloud bases and predict föhn, boraccia and scirocco, • physico-chemists who vulcanize rubber and build fuel cells, • chemical engineers who rectify natural gas and distil f- mented potato juice, • metallurgists who improve steels and harden surfaces, • - trition counselors who recommend a proper intake of calories, • mechanics who adjust heat exchangers, • architects who construe – and often misconstrue – ch- neys, • biologists who marvel at the height of trees, • air conditioning engineers who design saunas and the ventilation of air plane cabins, • rocket engineers who create supersonic flows, et cetera. Not all of these professional groups need the full depth and breadth of ther- dynamics. For some it is enough to consider a well-stirred tank, for others a s- tionary nozzle flow is essential, and yet others are well-served with the partial d- ferential equation of heat conduction. It is therefore natural that thermodynamics is prone to mutilation; different group-specific meta-thermodynamics’ have emerged which serve the interest of the groups under most circumstances and leave out aspects that are not often needed in their fields.

Thermodynamics is the much abused slave of many masters • physicists who love the totally impractical Carnot process, • mechanical engineers who design power stations and refrigerators, • chemists who are successfully synthesizing ammonia and are puzzled by photosynthesis, • meteorologists who calculate cloud bases and predict föhn, boraccia and scirocco, • physico-chemists who vulcanize rubber and build fuel cells, • chemical engineers who rectify natural gas and distil f- mented potato juice, • metallurgists who improve steels and harden surfaces, • - trition counselors who recommend a proper intake of calories, • mechanics who adjust heat exchangers, • architects who construe – and often misconstrue – ch- neys, • biologists who marvel at the height of trees, • air conditioning engineers who design saunas and the ventilation of air plane cabins, • rocket engineers who create supersonic flows, et cetera. Not all of these professional groups need the full depth and breadth of ther- dynamics. For some it is enough to consider a well-stirred tank, for others a s- tionary nozzle flow is essential, and yet others are well-served with the partial d- ferential equation of heat conduction. It is therefore natural that thermodynamics is prone to mutilation; different group-specific meta-thermodynamics’ have emerged which serve the interest of the groups under most circumstances and leave out aspects that are not often needed in their fields.

Die enge Verbindung von Wirtschaft und Weltgeschehen verlangt nach einer exakten Untersuchung ihrer Notwendigkeit, Moglichkeiten und Grenzen. Die Okonomie wird auf ihre erlernbaren theoretischen Prinzipien, die Moglichkeiten ihrer Anwendung und die Bedingungen ihrer praktischen Durchsetzbarkeit hin untersucht. Ergebnis ist eine grundliche Neubestimmung des Verhaltnisses von Theorie, Anwendung und Praxis. Die historisch bekannten Wirtschaftsschulen und -richtungen werden auf ihren Geltungsanspruch hinterfragt. Politische und ideologische Rahmenbedingungen werden in ihrem Einfluss auf Privat- und Gemeinwirtschaft erlautert und Modelle zur Uberprufung von Wirtschaftspolitik und Wirtschaftsethik aufgezeigt."