This book presents various questions of continuum mechanical modeling in the context of experimental and numerical methods, in particular, multi-field problems that go beyond the standard models of continuum mechanics. In addition, it discusses dynamic problems and practical solutions in the field of numerical methods. It focuses on continuum mechanics, which is often overlooked in the traditional division of mechanics into statics, strength of materials and kinetics. The book is dedicated to Prof. Volker Ulbricht, who passed away on April 9, 2021.

Review(s) ...recommend this book to the applied community as a valuable source of practical examples of parametric excitations, treated in a modern fashion. - "Mathematical Reviews"; [Cartmell] has successfully presented the usually complicated and difficult subjects of parametric and nonlinear vibrations in a concise, clear and easy-to-understand manner - "Choice".

This book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts. The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal-semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods. The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions. The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.

This volume emphazises the most early 1990s advances in fracture mechanics as specifically applied to steel bar reinforced concrete. Fracture mechanics has been applied to plain and fibre reinforced concrete with increasing success over recent years. This workshop extended these concepts to steel bar reinforced and pre-stressed concrete design. Particularly for high strength concrete, which is a very brittle material, and in the case of large structural members, the application of fracture mechanics appears to be very useful for improving the present design rules. The participants at the Turin workshop contributed expert opinions in four selected areas for which a rational approach, using fracture mechanics, could introduce variations into the concrete design codes: size effects; anchorage and bond; minimum reinforcement for elements in flexure; and shear resistance. The 23 chapters logically address these themes and demonstrate the unique ability of fracture mechanics to capture all the experimentally observed characteristics.

Vortex flow is one of the fundamental types of fluid and gas motion. These flows are the most spectacular in the form of concentrated vortices, characterized by the localization of vorticity (curl of velocity) in bounded regions of a space, beyond which the vorticity is either absent or rapidly falls down to zero. Concentrated vortices are often observed in nature, exemplified by atmospheric cyclones, whirlwinds and tornados, oceanic vortices, whirlpools on a water s- face, and ring vortices caused by explosive outburst of volcanoes. In technical - vices concentrated vortices form when flow separates from sharp edges of flying vehicles and ships. Among these are vortices flowing off the ends of airplane wings, and intentionally generated vortices for intensification of burning in c- bustion chambers, vortices in cyclonic devices used for mixing or separation of impurities in fluids and gases. One such remarkable and frequent type of conc- trated vortices is a vortex ring which constitutes a vortex tube closed into a t- oidal ring moving in a surrounding fluid like an isolated body out of contact with solid boundaries of the flow region if such boundaries exist. Formation and motion of vortex rings are important part of the dynamics of a continuum medium and have been studied for more than a century.

This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.

This book addresses the hydrostatics and stability of ships and other floating marine structures - a fundamental aspect of naval architecture and offshore engineering for naval architects and marine engineers. It starts from the most basic concepts, assuming that the reader has no prior knowledge of the subject. By presenting the topic in a methodical and step-by-step manner, the book helps students to enhance their understanding, while also providing valuable guidelines for lecturers teaching related courses.

Undeservedly little attention is paid in the vast literature on the theories of vibration and plasticity to the problem of steady-state vibrations in elastoplastic bodies. This problem, however, is of considerable interest and has many important applications. The problem of low-cyclic fatigue of metals, which is now in a well de veloped state is one such application. The investigations within this area are actually directed to collecting experimental facts about repeated cyclic loadings, cf. 47J. Theoretical investigations within this area usually con sider the hysteretic loops and the construction of models of plasticity theory which are applicable to the analysis of repeated loadings and the study of the simplest dynamic problems. Another area of application of the theory of the vibration of elastoplas tic bodies is the applied theory of amplitude-dependent internal damping. Another name for this theory is the theory of energy dissipation in vibrat ing bodies. In accordance with the point of view of Davidenkov "internal damping" in many metals, alloys and structural materials under consider able stress presents exactly the effect of micro plastic deformations. There fore, it may be described by the methods of plasticity theory. This point of view is no doubt fruitful for the theory of energy dissipation in vibrating bodies, as it allows one to write down the constitutive equations appropri ate both for vibrational analysis of three-dimensional stress states and an investigation of nonharmonic deformation. These problems are known to be important for the theory of internal damping."

This work reviews methods for the experimental determination of concrete toughness and presents theories and models suitable for describing cracking and fracturing phenomena in plain and reinforced concrete. Test methods based on classsical linear fracture mechanics cannot be applied to laboratory sized concrete specimens. The book compares the currently used methods and presents recommended test procedures for mode I fracture/toughness using notched beam and other specimens. Crack propagation under mixed-mode loading (Mode II) is discussed and current test methods are extensively reviewed. Effects of loading rate, temperature and humidity effects are treated in a separate chapter. The book concludes with descriptions and recommendations of techniques for detecting the fracture process zone in concrete, in particular, pulse velocity and laser interferometry techniques. The introduction of the concepts of fracture toughness and fracture energy into structural concrete design codes means that the experimental determination of fracture porperties is ceasing to be an academic exercise and is becoming a technical need. This book has been prepared by RILEM Technical committee 89-FMT and

This volume sets out to present recent research findings on the applications of fracture mechanics to concrete structures. Papers from international contributors describe existing and new modelling techniques in the analysis of concrete materials and structures. Topics discussed include structural modelling, bending, shear, bond and anchorage. The book forms the proceedings of a RILEM workshop held in Sweden in 1989. It is dedicated to Professor Arne Hillerborg, whose contribution to fracture mechanics is also reviewed.

This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.

Cooperative Control Design: A Systematic, Passivity-Based Approach discusses multi-agent coordination problems, including formation control, attitude coordination, and synchronization. The goal of the book is to introduce passivity as a design tool for multi-agent systems, to provide exemplary work using this tool, and to illustrate its advantages in designing robust cooperative control algorithms. The discussion begins with an introduction to passivity and demonstrates how passivity can be used as a design tool for motion coordination. Followed by the case of adaptive redesigns for reference velocity recovery while describing a basic design, a modified design and the parameter convergence problem. Formation control is presented as it relates to relative distance control and relative position control. The coverage is concluded with a comprehensive discussion of agreement and the synchronization problem with an example using attitude coordination.

This is the first complete overview of the present state of the art of flexible barrier materials such as textile, paper and leather, including methods for barrier evaluation. It will be of interest to readers in industries, consumers, and members of the scientific community. The scope of the field is clearly delineated here for the first time, and it deals with a number of specific topics such as barrier to fire and antibacterial properties.

Micro Electro Mechanical Systems (MEMS) is already about a billion dollars a year industry and is growing rapidly. So far major emphasis has been placed on the fabrication processes for various devices. There are serious issues related to tribology, mechanics, surfacechemistry and materials science in the operationand manufacturingof many MEMS devices and these issues are preventing an even faster commercialization. Very little is understood about tribology and mechanical properties on micro- to nanoscales of the materials used in the construction of MEMS devices. The MEMS community needs to be exposed to the state-of-the-artoftribology and vice versa. Fundamental understanding of friction/stiction, wear and the role of surface contamination and environmental debris in micro devices is required. There are significantadhesion, friction and wear issues in manufacturing and actual use, facing the MEMS industry. Very little is understood about the tribology of bulk silicon and polysilicon films used in the construction ofthese microdevices. These issues are based on surface phenomenaand cannotbe scaled down linearly and these become increasingly important with the small size of the devices. Continuum theory breaks down in the analyses, e. g. in fluid flow of micro-scale devices. Mechanical properties ofpolysilicon and other films are not well characterized. Roughness optimization can help in tribological improvements. Monolayers of lubricants and other materials need to be developed for ultra-low friction and near zero wear. Hard coatings and ion implantation techniques hold promise.

"Control of Complex Systems: Structural Constraints and Uncertainty" focuses on control design under information structure constraints, with a particular emphasis on large-scale systems. The complexity of such systems poses serious computational challenges and severely restricts the types of feedback laws that can be used in practice. This book systematically addresses the main issues, and provides a number of applications that illustrate potential design methods, most which use Linear Matrix Inequalities (LMIs), which have become a popular design tool over the past two decades. Authors Aleksandar I. Zecevic and Dragoslav D. Siljak use their years of experience in the control field to also:

• Address the issues of large-scale systems as they relate to robust control and linear matrix inequalities
• Discuss a new approach to applying standard LMI techniques to large-scale systems, combining graphic-theoretic decomposition techniques with appropriate low-rank numerical approximations and dramatically reducing the computational effort
• Providing numerous examples and a wide variety of applications, ranging from electric power systems and nonlinear circuits to mechanical problems and dynamic Boolean networks

"Control of Complex Systems: Structural Constraints and Uncertainty" will appeal to practicing engineers, researchers and students working in control design and other related areas.

Thin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.

model. They conclude that the models using three fitting parameters provide the best fit over a wide range of suctions. Models for soil-water characteristic curves are only useful if we have experimental data on which to base them. Agus, Leong and Rahardjo (Singapore) present a large number of experimental soil-water characteristic curves determined for two types of residual soil from Sigapore. They present data for eight different sites. This data set allows them to relate the parameters of the soil-water characteristic curves to index properties. They conclude that the relationships derived are suitable to pro vide a quick preliminary estimate of a soil-water characteristic curve. The importance of soil-water characteristic curves is emphasized by another con tribution dealing with this topic. Aung, Rahardjo, Leong and Toll (Singapore) inves tigate the relationship between mercury intrusion porosimetry measurements and soil-water characteristic curves. The porosimetry measurements are presented as soil-air characteristic curves. The slopes of the soil-air characteristic curves are found to be similar to the slopes of the soil-water characteristic curves. The equiv alent pore diameters calculated from the mercury entry value and the air entry value appear to be related. Therefore, it is suggested that porosimetry data can be used to construct an estimate of the soil-water characteristic curve."

This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.

This book presents a novel continuum finite deformation framework addressing the complex interactions among electrostatics, species transport, and mechanics in solid networks immersed in a fluid phase of solvent and ions. Grounded on cutting-edge multiphysics theories for soft active materials, the proposed model is primarily applied to ionic polymer metal composites (IPMCs). First, the influence of shear deformation on the IPMC response is analyzed through semi-analytical solutions obtained via the method of matched asymptotic expansions. Second, the novel electrochemo-poromechanical theory is used to predict the curvature relaxation and electric discharge that are observed in IPMC actuation and sensing, respectively, under a sustained stimulus. This newly formulated theory is, in turn, applied to biological cell clusters. Here, important mechanical considerations are integrated into classical bioelectrical models, thus offering novel insights into the interplay of mechanical and electrical signaling in the coordination of developmental processes.

Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first - a solid foundation for the later study of the free-body formulation of the dynamics problem.

A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids.

Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics.

This book presents interdisciplinary, cutting-edge and creative applications of graph theory and modeling in science, technology, architecture and art. Topics are divided into three parts: the first one examines mechanical problems related to gears, planetary gears and engineering installations; the second one explores graph-based methods applied to medical analyses as well as biological and chemical modeling; and the third part includes various topics e.g. drama analysis, aiding of design activities and network visualisation. The authors represent several countries in Europe and America, and their contributions show how different, useful and fruitful the utilization of graphs in modelling of engineering systems can be. The book has been designed to serve readers interested in the subject of graph modelling and those with expertise in related areas, as well as members of the worldwide community of graph modelers.

The book covers a wide range of applied research compactly presented in one volume, and shows innovative engineering solutions for automotive, marine and aviation industries, as well as power generation. While targeting primarily the audience of professional scientists and engineers, the book can also be useful for graduate students, and also for all those who are relatively new to the area and are looking for a single source with a good overview of the state-of-the-art as well as an up-to-date information on theories, numerical methods, and their application in design, simulation, testing, and manufacturing. The readers will find here a rich mixture of approaches, software tools and case studies used to investigate and optimize diverse powertrains, their functional units and separate machine parts based on different physical phenomena, their mathematical representation, solution algorithms, and experimental validation.

The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.

This book includes keynote presentations, invited speeches, and general session papers presented at the 7th International Symposium on Environmental Vibration and Transportation Geodynamics (formerly the International Symposium on Environmental Vibration), held from October 28 to 30, 2016 at Zhejiang University, Hangzhou, China. It discusses topics such as the dynamic and cyclic behaviors of soils, dynamic interaction of vehicle and transportation infrastructure; traffic-induced structure and soil vibrations and wave propagation; soil-structure dynamic interaction problems in transportation; environmental vibration analysis and testing; vehicle, machine and human-induced vibrations; monitoring, evaluation and control of traffic induced vibrations; transportation foundation deformation and deterioration induced by vibration; structural safety and serviceability of railways, metros, roadways and bridges; and application of geosynthetics in transportation infrastructure. It is a valuable resource for government managers, scientific researchers, and engineering professionals engaged in the field of geotechnical and transportation engineering.