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Functional analysis --- Numerical methods of optimisation --- Operational research. Game theory --- Fluid mechanics --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- kansrekening --- mechanica --- optimalisatie --- Mechanics, Analytic. --- Calculus of variations. --- Mathematical optimization. --- Analytical mechanics --- Kinetics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Isoperimetrical problems --- Variations, Calculus of --- Mecànica --- Càlcul de variacions --- Càlcul variacional --- Problemes isoperimètrics --- Màxims i mínims --- Anàlisi funcional --- Desigualtats variacionals (Matemàtica) --- Dominis convexos --- Equacions de Hamilton-Jacobi --- Funcions de Lagrange --- Principis variacionals --- Teoria de Morse --- Teoria del punt crític (Anàlisi matemàtica) --- Mecànica clàssica --- Mecànica de sòlids --- Mecànica newtoniana --- Física --- Acceleració (Mecànica) --- Aptitud per a la mecànica --- Biomecànica --- Deformacions (Mecànica) --- Elasticitat --- Energia mecànica --- Estabilitat --- Estàtica --- Física matemàtica --- Fluids --- Fricció --- Gasos --- Gravetat --- Hidràulica --- Hidrodinàmica --- Hidrostàtica --- Màquines de vapor --- Massa (Física) --- Mecànica analítica --- Mecànica orbital --- Mecànica relativista --- Moments d'inèrcia --- Moviments mecànics --- Pèndol --- Propietats de la matèria --- Resistència de materials --- Sòlids elàstics --- Teoria del moviment ondulatori --- Teoria del potencial (Matemàtica) --- Termodinàmica --- Vibració --- Viscositat --- Cinemàtica --- Dinàmica --- Enginyeria --- Energia --- Maquinària --- Moviment

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This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on "Calculus of Variations in Mechanics and Related Fields". The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

Functional analysis --- Numerical methods of optimisation --- Operational research. Game theory --- Fluid mechanics --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- kansrekening --- mechanica --- optimalisatie

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Stringent industrial requirements of sophisticated performances and of circumstantial control for micro-devices or nanotechnology manufactures, and other types of machinery at multiple scales, can be satisfied often only by resort to or allowance for complex materials. The adjective 'complex' beckons to the fact that the substructure influences gross mechanical behaviour in a prominent way and interactions due to substructural changes are represented directly. The description of the mechanical behaviour of complex bodies proposes a wide class of challenging problems from macroscopic-to-nano-wo

Microstructure. --- Materials science. --- Atomic structure. --- Molecular structure. --- Nanostructured materials. --- Nanomaterials --- Nanometer materials --- Nanophase materials --- Nanostructure controlled materials --- Nanostructure materials --- Ultra-fine microstructure materials --- Microstructure --- Nanotechnology --- Structure, Molecular --- Chemical structure --- Structural bioinformatics --- Structure, Atomic --- Atomic theory --- Material science --- Physical sciences --- Materials --- Matter --- Morphology --- Micromechanics --- Stereology --- Constitution

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This distinctive textbook aims to introduce readers to the basic structures of the mechanics of deformable bodies, with a special emphasis on the description of the elastic behavior of simple materials and structures composed by elastic beams. The authors take a deductive rather than inductive approach and start from a few first, foundational principles. A wide selection of exercises, many with hints and solutions, are provided throughout and organized in a way that will allow readers to form a link between abstract mathematical concepts and real-world applications. The text begins with the definition of bodies and deformations, keeping the kinematics of rigid bodies as a special case; the authors also distinguish between material and spatial metrics, defining each one in the pertinent space. Subsequent chapters cover observers and classes of possible changes; forces, torques, and related balances, which are derived from the invariance under classical changes in observers of the power of the external actions over a body, rather than postulated a priori; constitutive structures; variational principles in linear elasticity; the de Saint-Venant problem; yield criteria and a discussion of their role in the representation of material behavior; and an overview of some bifurcation phenomena, focusing on the Euler rod. An appendix on tensor algebra and tensor calculus is included for readers who need a brief refresher on these topics. Fundamentals of the Mechanics of Solids is primarily intended for graduate and advanced undergraduate students in various fields of engineering and applied mathematics. Prerequisites include basic courses in calculus, mathematical analysis, and classical mechanics. [Publisher]

Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Solid state physics --- Applied physical engineering --- toegepaste mechanica --- wiskunde --- fysica --- mechanica --- Continuum mechanics. --- Elastic solids. --- Milieux continus, Mécanique des --- Solides élastiques

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Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Granular materials --- Matériaux granulaires --- Mathematical models. --- Modèles mathématiques --- Mathematical Theory --- Materials Science --- Mathematics --- Chemical & Materials Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Engineering. --- Mathematics. --- Physics. --- Amorphous substances. --- Complex fluids. --- Industrial engineering. --- Production engineering. --- Industrial and Production Engineering. --- Mathematics, general. --- Mathematical Methods in Physics. --- Soft and Granular Matter, Complex Fluids and Microfluidics. --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Complex liquids --- Fluids, Complex --- Amorphous substances --- Liquids --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Science --- Construction --- Industrial arts --- Technology --- Bulk solids --- Materials --- Mathematical physics. --- Physical mathematics --- Physics --- Soft condensed matter