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 draws together the most interesting recent results to emerge in mechanical engineering in Russia, providing a fascinating overview of the state of the art in the field in that country which will be of interest to a wide readership. A broad range of topics and issues in modern engineering are discussed, including dynamics of machines, materials engineering, structural strength, transport technologies, machinery quality and innovations. The book comprises selected papers presented at the 9th conference "Modern Engineering: Science and Education", held at the Peter the Great Saint Petersburg Polytechnic University in June 2020 with the support of the Russian Engineering Union. The authors are experts in various fields of engineering, and all of the papers have been carefully reviewed. The book will be of interest to mechanical engineers, lecturers in engineering disciplines and engineering graduates.

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

This volume comprises the latest developments in both fundamental science and patient-specific applications, discussing topics such as: cellular mechanics, injury biomechanics, biomechanics of the heart and vascular system, algorithms of computational biomechanics for medical image analysis, and both patient-specific fluid dynamics and solid mechanics simulations. With contributions from researchers world-wide, Computational Biomechanics for Medicine: Measurments, Models, and Predictions provides an opportunity for specialists in the field to present their latest methodologies and advancements.

ICTAEM_1 treated all aspects of theoretical, applied and experimental mechanics including biomechanics, composite materials, computational mechanics, constitutive modeling of materials, dynamics, elasticity, experimental mechanics, fracture, mechanical properties of materials, micromechanics, nanomechanics, plasticity, stress analysis, structures, wave propagation. During the conference special symposia covering major areas of research activity organized by members of the Scientific Advisory Board took place. ICTAEM_1 brought together the most outstanding world leaders and gave attendees the opportunity to get acquainted with the latest developments in the area of mechanics. ICTAEM_1 is a forum of university, industry and government interaction and serves in the exchange of ideas in an area of utmost scientific and technological importance.

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 is intended for mechanicians, engineering mathematicians, and, generally for theoretically inclined mechanical engineers. It has its origin in my Master's Thesis (J 957), which I wrote under the supervision of Professor Dr. R. Timman of the Delft TH and Dr. Ir. A. D. de Pater of Netherlands Railways. I did not think that the surface of the problem had even been scratched, so I joined de Pater, who had by then become Professor in the Engineering Mechanics Lab. of the Delft TH, to write my Ph. D. Thesis on it. This thesis (1967) was weil received in railway circles, which is due more to de Pater's untiring promotion than to its merits. Still not satisfied, I feit that I needed more mathe matics, and I joined Professor Timman's group as an Associate Professor. This led to the present work. Many thanks are due to G. M. L. Gladwell, who thoroughly polished style and contents of the manuscript. Thanks are also due to my wife, herself an engineering mathematician, who read the manuscript through critically, and made many helpful comments, to G. F. M. Braat, who also read an criticised, and, in addition, drew the figures together with J. Schonewille, to Ms. A. V. M. de Wit, Ms. M. den Boef, and Ms. P. c. Wilting, who typed the manuscript, and to the Publishers, who waited patiently. Delft-Rotterdam, 17 July 1990. J. J."

This book covers most of the damage mechanism in the scope of mechanical engineering and civil engineering. The failure pattern of various materials and structures is mainly discussed. The sub-topics covers fatigue damage, fatigue crack initiation and propagation, life prediction techniques, computational fracture mechanics, dynamic fracture, damage mechanics and assessment, non-destructive test (NDT), concrete failure assessment, failure on soil structures, structural durability and reliability, structural health monitoring, construction damage recovery, and any relevant topics related to failure analysis.

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.

The edited book comprises invited book chapter contributions from global experts in the field of sustainable materials and resilient infrastructure. The book covers the most critical and emerging topics for creating sustainable solutions for the construction industry, promoting the technologies and monitoring methods for resilient infrastructure. It focuses on sustainable solutions and offers techniques and methodologies to deliver high-quality end solutions in civil engineering. In addition, the content provides knowledge-based information for the readers to assess, monitor, measure, and practice sustainability for resilient infrastructure. The contents of the volume are a blend of academic research work and industrial case studies. It covers the use of sustainable materials like Lime-Pozzolona Binders, biopolymers, lignosulphonate, lightweight aggregates made from fly ash, calcinated clay, paper ash, and limestone as amendments/ameliorators for soil remediation, development of neo-construction materials and composites for civil engineering applications. Design of innovative pavements using alkali activation and pervious concrete for sustainable infrastructure is also discussed. The chapters also highlight the role of civil engineers in achieving UN Sustainable Development Goals, promoting climate change design for urban landscapes, and modelling building energy demand. This book is framed to address the principles and practice from the corners of geoenvironment, sustainable construction materials, low carbon materials, energy efficiency, and waste management. It is a valuable reference for faculty, researchers, field experts, scientists, and practicing engineers.

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.

This augmented and updated fourth edition introduces a new complement of computational tools and examples for each chapter and continues to provide a grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical and biomedical engineering and materials and earth science. Professor Gould's proven approach allows faculty to introduce this subject early on in an educational program, where students are able to understand and apply the basic notions of mechanics to stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials and finite element mechanics. With the introductory material on the use of MATLAB, students can apply this modern computational tool to solve classic elasticity problems. The detailed solutions of example problems using both analytical derivations and computational tools helps student to grasp the essence of elasticity and practical skills of applying the basic mechanics theorem.

This thesis presents experimental research on the interaction between the optical field and the mechanical oscillator in whispering-gallery mode microcavities. It demonstrates how optomechanical interactions in a microresonator can be used to achieve non-magnetic non-reciprocity and develop all-optically controlled non-reciprocal multifunctional photonic devices. The thesis also discusses the interaction between the travelling optical and mechanical whispering-gallery modes, paving the way for non-reciprocal light storage as a coherent, circulating acoustic wave with a lifetime of up to tens of microseconds. Lastly, the thesis presents a high-frequency phase-sensitive heterodyne vibrometer, operating up to 10 GHz, which can be used for the high-resolution, non-invasive mapping of the vibration patterns of acoustic devices. The results presented here show that optomechanical devices hold great potential in the field of information processing.

This pioneering book presents new models for the thermomechanical behavior of composite materials, taking into account internal physico-chemical transformations such as thermodecomposition, sublimation, and melting at high temperatures. It collects unique experimental results on mechanical and thermal properties of composites at temperatures up to 2000 C. "

The idea that materials can be designed to satisfy specific performance requirements is relatively new. With high-performance composites, however, the entire process of designing and fabricating a part can be worked out before manufacturing. The purpose of this book is to present an integrated approach to the design and manufacturing of products from advanced composites. It shows how the basic behavior of composites and their constitutive relationships can be used during the design stage, which minimizes the complexity of manufacturing composite parts and reduces the repetitive "design-build-test" cycle. Designing it right the first time is going to determine the competitiveness of a company, the reliability of the part, the robustness of fabrication processes, and ultimately, the cost and development time of composite parts. Most of all, it should expand the use of advanced composite parts in fields that use composites only to a limited extent at this time. To achieve these goals, this book presents the design and fabrication of novel composite parts made for machine tools and other applications like robots and automobiles.
This book is suitable as a textbook for graduate courses in the design and fabrication of composites. It will also be of interest to practicing engineers learning about composites and axiomatic design.
A CD-ROM is included in every copy of the book, containing Axiomatic CLPT software. This program, developed by the authors, will assist readers in calculating material properties from the microstructure of the composite.
This book is part of the Oxford Series on Advanced Manufacturing.

This book includes a collection of state-of-the-art contributions addressing both theoretical developments in, and successful applications of, seismic structural health monitoring (S2HM). Over the past few decades, Seismic SHM has expanded considerably, due to the growing demand among various stakeholders (owners, managers and engineering professionals) and researchers. The discipline has matured in the process, as can be seen by the number of S2HM systems currently installed worldwide. Furthermore, the responses recorded by S2HM systems hold great potential, both with regard to the management of emergency situations and to ordinary maintenance needs. The book's 17 chapters, prepared by leading international experts, are divided into four major sections. The first comprises six chapters describing the specific requirements of S2HM systems for different types of civil structures and infrastructures (buildings, bridges, cultural heritage, dams, structures with base isolation devices) and for monitoring different phenomena (e.g. soil-structure interaction and excessive drift). The second section describes available methods and computational tools for data processing, while the third is dedicated to hardware and software tools for S2HM. In the book's closing section, five chapters report on state-of-the-art applications of S2HM around the world.

This book provides a critical review of the equilibrium elastic properties of rubber, together with the kinetic-theory background. It is suitable for the non-specialist and the emphasis is on the physical reality embodied in the mathematical formulations. Polymer science had developed greatly since the second edition of this text in 1958, and the two main advances - the refinements of the network theory and associated thermodynamic analysis, and the development of the phenomenological or non-molecular approach to the subject - are both reflected in the structure of this third edition.

This collection of classic papers in shock compression science makes available not only some of the most important classic papers on shock waves by Poisson, Rankine, Earnshaw, Riemann, and Hugoniot, which remain important references, but also some pathbreaking papers from the 1940s and 1950s on shocks in solids and fluids by such theorists as Bethe, and Weyl. Although their ideas and results remain of current interest, many of these papers have been hard to find, since the journals in which they were published are not available in many libraries. The editors have also translated papers written in French to make them accessible to a wider audience. This collection is thus not only a valuable historical resource but also a vital reference for those working in the field.

Finite Element, Boundary Element, Finite Volume, and Finite Difference Analysis are all commonly used in nearly all engineering disciplines to simplify complex problems of geometry and change. But they all tend to oversimplify. The Cell Method is a more recent computational approach developed initially for problems in solid mechanics and electro-magnetic field analysis. It is a more algebraic approach, and it offers a more accurate representation of geometric and topological features. This will be perhaps the first book-length work in the world that explicates the Cell Method and that shows how useful it can be for practical problem solving, especially in problems in solid mechanics.

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 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 evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works.

This book describes the main concepts of and recent advances in the base forces element method (BFEM). It combines theories, methods, models, numerical results, and an analysis of the BFEM. Each chapter starts with an introduction and derivation of a new mathematical model for the proposed method. Subsequently, the methods are described and numerical examples demonstrating the significance of the proposed method are presented. The closing chapter summarizes the performance and features of the BFEM and describes the prospects for its application. The book is intended for engineers, scientists and graduate students in applied mechanics and applied mathematics, and for all readers interested in numerical computations and simulations.

This text closes the gap between traditional textbooks on structural dynamics and how structural dynamics is practiced in a world driven by commercial software, where performance-based design is increasingly important. The book emphasizes numerical methods, nonlinear response of structures, and the analysis of continuous systems (e.g., wave propagation). Fundamentals of Structural Dynamics: Theory and Computation builds the theory of structural dynamics from simple single-degree-of-freedom systems through complex nonlinear beams and frames in a consistent theoretical context supported by an extensive set of MATLAB codes that not only illustrate and support the principles, but provide powerful tools for exploration. The book is designed for students learning structural dynamics for the first time but also serves as a reference for professionals throughout their careers.

This book offers a comprehensive and timely overview of the latest developments in the field of biomechanics and extensive knowledge of tissue structure, function, and modeling. Gathering chapters written by authoritative scientists, it reports on a range of continuum and computational models of solids, and related experimental works, for biomechanical applications. It discusses cutting-edge advances such as constitutive modeling and computational simulation of biological tissues and organs under physiological and pathological conditions, and their mechanical characterization. It covers innovative studies on arteries, heart, valvular tissue, and thrombus, brain tumor, muscle, liver, kidney, and stomach, among others. Written in honor of Professor Gerhard A. Holzapfel, the book provides specialized readers with a thorough and timely overview of different types of modeling in biomechanics, and current knowledge about biological structures and function.