This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.

This book presents a selection of cutting-edge methods that allow readers to obtain novel models for nonlinear solid mechanics. Today, engineers need more accurate techniques for modeling solid body mechanics, chiefly due to innovative methods like additive manufacturing-for example, 3D printing-but also due to miniaturization. This book focuses on the formulation of continuum and discrete models for complex materials and systems, and especially the design of metamaterials. It gathers outstanding papers from the international conference IcONSOM 2019

This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

This book focuses on nonlinear finite element analysis of thin-walled smart structures integrated with piezoelectric materials. Two types of nonlinear phenomena are presented in the book, namely geometrical nonlinearity and material nonlinearity. Geometrical nonlinearity mainly results from large deformations and large rotations of structures. The book discusses various geometrically nonlinear theories including von Karman type nonlinear theory, moderate rotation nonlinear theory, fully geometrically nonlinear theory with moderate rotations and large rotation nonlinear theory. The material nonlinearity mainly considered in this book is electroelastic coupled nonlinearity resulting from large driving electric field. This book will be a good reference for students and researchers in the field of structural mechanics.

This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

This volume presents the latest research and industrial applications in the areas of mechanism science, robotics and dynamics. The respective contributions cover such topics as computational kinematics, control issues in mechanical systems, mechanisms for medical rehabilitation, mechanisms for minimally invasive techniques, cable robots, design issues for mechanisms and robots, and the teaching and history of mechanisms. Written by leading researchers and engineers, and selected by means of a rigorous international peer-review process, the papers highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations. They reflect the outcomes of the 8th European Conference on Mechanism Science (EuCoMeS) in 2020.

This book is an homage to the pioneering works of E. Aero and G. Maugin in the area of analytical description of generalized continua. It presents a collection of contributions on micropolar, micromorphic and strain gradient media, media with internal variables, metamaterials, beam lattices, liquid crystals, and others. The main focus is on wave propagation, stability problems, homogenization, and relations between discrete and continuous models.

This book provides a comprehensive coverage of the theory and principle of the Hoek-Brown (HB) failure criterion, methods or guidelines for estimating the HB input parameters, and the methodology of application of the HB criterion in rock engineering projects. It aims to help researchers, engineers and research students who work in the area of rock mechanics and mining engineering. Academics can quickly obtain an overview of the state of the art of the theory and principle of the Hoek-Brown criterion by reading the book before they advance their researches on the topics related to rock failure criteria. Geotechnical engineers can select appropriate Hoek-Brown input parameters for the design and analysis of rock engineering projects with the help of the principles introduced in this book. Research students may use the book as a textbook to learn the principle of rock mechanics related to rock mass properties.

The book addresses computational methods for solving the problem of vibration, response, loads and stability of a helicopter rotor blade modeled as a rotating beam with flap or out-of-plane bending. The focus is on explaining the implementation of the finite element method in the space and time domain for the free vibration, aeroelastic response and stability problems. The use of Floquet analysis for the aeroelastic stability analysis of rotor blades is also shown. The contents of the book will be useful to researchers in aerodynamics and applied mechanics, and will also serve well professionals working in the aerospace industry.

The author presents current work in bond graph methodology by providing a compilation of contributions from experts across the world that covers theoretical topics, applications in various areas as well as software for bond graph modeling.
It addresses readers in academia and in industry concerned with the analysis of multidisciplinary engineering systems or control system design who are interested to see how latest developments in bond graph methodology with regard to theory and applications can serve their needs in their engineering fields.
This presentation of advanced work in bond graph modeling presents the leading edge of research in this field. It is hoped that it stimulates new ideas with regard to further progress in theory and in applications.

This book offers a comprehensive and timely report of size-dependent continuum mechanics approaches. Written by scientists with worldwide reputation and established expertise, it covers the most recent findings, advanced theoretical developments and computational techniques, as well as a range of applications, in the field of nonlocal continuum mechanics. Chapters are concerned with lattice-based nonlocal models, Eringen's nonlocal models, gradient theories of elasticity, strain- and stress-driven nonlocal models, and peridynamic theory, among other topics. This book provides researchers and practitioners with extensive and specialized information on cutting-edge theories and methods, innovative solutions to current problems and a timely insight into the behavior of some advanced materials and structures. It also offers a useful reference guide to senior undergraduate and graduate students in mechanical engineering, materials science, and applied physics.

In this book, the authors use molecular dynamics simulations to conduct a comprehensive study of the compression/superheating limit and phase transition of 2D (monolayer, bilayer, and trilayer) water/ice constrained in graphene nanocapillaries. When subjected to nanoscale confinement and under ultrahigh pressure, water and ice behave quite differently than their bulk counterparts, partly because the van der Waals pressure can spark a water-to-ice transformation, known as the metastability limit of two-dimensional (2D) liquids. From a mechanical standpoint, this liquid-to-solid transformation characterizes the compression limit (or metastability limit) of 2D water. The findings presented here could help us to better understand the phase behavior of 2D confined water/ice.

This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing-for example, 3D printing- and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

This book focuses on the damage, fracture and fatigue of ceramic-matrix composites. It investigates tensile damage and fracture, fatigue hysteresis, and the properties of interfaces subjected to cyclic fatigue loading. Further, it predicts fatigue life at room and elevated temperatures using newly developed damage models and methods, and it analyzes and compares damage, fracture and fatigue behavior of different fiber performs: unidirectional, cross-ply, 2D and 2.5D woven. The developed models and methods can be used to predict the damage and lifetime of ceramic-matrix composites during applications on hot section components.Ceramic-matrix composites (CMCs) are high-temperature structural materials with the significant advantages of high specific strength, high specific modulus, high temperature resistance and good thermal stability, which play a crucial role in the development of high thrust weight ratio aero engines. The critical nature of the application of these advanced materials makes comprehensive characterization a necessity, and as such this book provides designers with essential information pertaining not only to the strength of the materials, but also to their fatigue and damage characteristics.

This book reviews the mathematical modeling and experimental study of systems involving two or more different length scales. The effects of phenomena occurring at the lower length scales on the behavior at higher scales are of intrinsic scientific interest, but can also be very effectively used to determine the behavior at higher length scales or at the macro-level. Efforts to exploit this micro- and macro-coupling are, naturally, being pursued with regard to every aspect of mechanical phenomena. This book focuses on the changes imposed on the dynamics, strength of materials and durability of mechanical systems by related multiscale phenomena. In particular, it addresses: 1: the impacts of effective dissipation due to kinetic energy trapped at lower scales 2: wave propagation in generalized continua 3: nonlinear phenomena in metamaterials 4: the formalization of more general models to describe the exotic behavior of meta-materials 5: the design and study of microstructures aimed at increasing the toughness and durability of novel materials

This book gathers 23 papers by top experts from 11 countries, presented at the 3rd Houston International Forum: Concrete Structures in Earthquake. Designing infrastructures to resist earthquakes has always been the focus and mission of scientists and engineers located in tectonically active regions, especially around the "Pacific Rim of Fire" including China, Japan, and the USA. The pace of research and innovation has accelerated in the past three decades, reflecting the need to mitigate the risk of severe damage to interconnected infrastructures, and to facilitate the incorporation of high-speed computers and the internet. The respective papers focus on the design and analysis of concrete structures subjected to earthquakes, advance the state of knowledge in disaster mitigation, and address the safety of infrastructures in general.

The book covers the theory of Michell structures being the lightest and fully stressed systems of bars, designed within a given domain, possibly within the whole space, transmitting a given load towards a given support. Discovered already in 1904 by A.G.M. Michell, the structures named after him have attracted constant attention due to their peculiar feature of disclosing the optimal streams of stresses equilibrating a given load and thus determining the optimal layout of bars. The optimal layouts emerge from among all possible structural topologies, thus constituting unique designs being simultaneously light and stiff. The optimal structures turn out to be embedded in optimal vector fields covering the whole feasible domain. Key features include: a variationally consistent theory of bar systems, thin plates in bending and membrane shells; recapitulation of the theory of optimum design of trusses of minimum weight or of minimal compliance; the basis of 2D Michell theory for a single load case; kinematic and static approaches; 2D benchmark constructions including Hemp's structures and optimal cantilevers; L-shape domain problems, three forces problem in 2D, bridge problems; revisiting the old - and delivering new - 3D benchmark solutions; extension to multiple load conditions; Prager-Rozvany grillages; the theory of funiculars and archgrids; the methods of optimum design of shape and material inspired by the theory of Michell structures, industrial applications. The book can be useful for graduate students, professional engineers and researchers specializing in the Optimum Design and in Topology Optimization in general.

This book focuses on surface layers fracture of cyclical contacting bodies (machine parts). Calculation models and calculating procedures of stress-strain states of cyclically contacting solids with cracks, are included. Recommendations for the optimization of operating parameters of joints (contact stresses magnitude, friction/lubrication conditions, materials crack resistance etc) for elements of rolling pairs (wheel-rail systems, backup roll - working roll of rolling mills etc.) and some fretting pairs are formulated.

This book is mainly based on the results of the EU-funded UE-FP7 Project EnCoRe, which aimed to characterize the key physical and mechanical properties of a novel class of advanced cement-based materials incorporating recycled powders and aggregates and/or natural ingredients in order to allow partial or even total replacement of conventional constituents. More specifically, the project objectives were to predict the physical and mechanical performance of concrete with recycled aggregates; to understand the potential contribution of recycled fibers as a dispersed reinforcement in concrete matrices; and to demonstrate the feasibility and possible applications of natural fibers as a reinforcement in cementitious composites. All of these aspects are fully covered in the book. The opening chapters explain the material concept and design and discuss the experimental characterization of the physical, chemical, and mechanical properties of the recycled raw constituents, as well as of the cementitious composite incorporating them. The numerical models with potentialities for describing the behavior at material and structural level of constructions systems made by these composites are presented. Finally, engineering applications and guidelines for production and design are proposed.

This volume deals with topical problems concerning technology and design in construction of modern metamaterials. The authors construct the models of mechanical, electromechanical and acoustical behavior of the metamaterials, which are founded upon mechanisms existing on micro-level in interaction of elementary structures of the material. The empiric observations on the phenomenological level are used to test the created models. The book provides solutions, based on fundamental methods and models using the theory of wave propagation, nonlinear theories and composite mechanics for media with micro- and nanostructure. They include the models containing arrays of cracks, defects, with presence of micro- and nanosize piezoelectric elements and coupled physical-mechanical fields of different nature. The investigations show that the analytical, numerical and experimental methods permit evaluation of the qualitative and quantitative properties of the materials of this sort, with diagnosis of their effective characteristics, frequency intervals of effective energetic cutting and passing, as well as effective regimes of damage evaluation by the acoustic methods.

This book presents a collection of contributions on advanced approaches to the mechanics of materials and mechanics of structures for high-temperature applications, such as power plant components, engines and turbochargers. The contributions highlight advanced constitutive models for high-temperature materials, as well as new approaches to the efficient modeling and analysis of engineering structures operating in high-temperature environments.

The book summarizes the results of the European research project "Intelligent fixtures for the manufacturing of low rigidity components" (INTEFIX). The structure of the book follows the sub-projects which are dedicated to case studies within the scenarios "vibrations", "deformations" and "positioning". The INTEFIX project deals with the development and analysis of several exemplary types of intelligent, sensor and actuator integrated fixtures for the clamping of sensitive workpieces in cutting machine tools. Thus, the book gives a representative overview about this innovative field of technology. The demands of the case studies are described and the technological approaches and solutions are introduced. Furthermore, innovative methods for the design and optimization of intelligent fixtures are presented.

This book addresses theoretical and experimental methods for exploring microstructured metamaterials, with a special focus on wave dynamics, mechanics, and related physical properties. The authors use various mathematical and physical approaches to examine the mechanical properties inherent to particular types of metamaterials. These include: * Boundary value problems in reduced strain gradient elasticity for composite fiber-reinforced metamaterials * Self-organization of molecules in ferroelectric thin films * Combined models for surface layers of nanostructures * Computer simulation at the micro- and nanoscale * Surface effects with anisotropic properties and imperfect temperature contacts * Inhomogeneous anisotropic metamaterials with uncoupled and coupled surfaces or interfaces * Special interface finite elements and other numerical and analytical methods for composite structures