Model Validation and Uncertainty Quantification, Volume 3.  Proceedings of the 33rd IMAC, A Conference and Exposition on Balancing Simulation and Testing, 2015, the third volume of ten from the Conference brings together contributions to this important area of research and engineering.  The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Uncertainty Quantification & Model Validation Uncertainty Propagation in Structural Dynamics Bayesian & Markov Chain Monte Carlo Methods Practical Applications of MVUQ Advances in MVUQ & Model Updating

This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute�. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

The book is focused on constitutive description of mechanical behaviour of engineering materials: both conventional (polycrystalline homogeneous isotropic or anisotropic metallic materials) and non-conventional (heterogeneous multicomponent anisotropic composite materials). Effective material properties at the macro-level depend on both the material microstructure (originally isotropic or anisotropic) as well as dissipative phenomena occurred on fabrication and consecutive loading phase (hardening) resulting in irreversible microstructure changes (acquired anisotropy). The material symmetry is a background and anisotropy is a core around which the book is formed. In this way a revision of classical rules of enhanced constitutive description of materials is required.

This volume presents a collection of contributions on materials modeling, which were written to celebrate the 65th birthday of Prof. Nobutada Ohno. The book follows Prof. Ohno’s scientific topics, starting with creep damage problems and ending with homogenization methods.

This book summarizes the main methods of experimental stress analysis and examines their application to various states of stress of major technical interest, highlighting aspects not always covered in the classic literature. It is explained how experimental stress analysis assists in the verification and completion of analytical and numerical models, the development of phenomenological theories, the measurement and control of system parameters under operating conditions, and identification of causes of failure or malfunction. Cases addressed include measurement of the state of stress in models, measurement of actual loads on structures, verification of stress states in circumstances of complex numerical modeling, assessment of stress-related material damage, and reliability analysis of artifacts (e.g. prostheses) that interact with biological systems. The book will serve graduate students and professionals as a valuable tool for finding solutions when analytical solutions do not exist.

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.

This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers and Chapter 9, which addresses various perturbational aspects in contact problems and introduces the sensitivity of articular contact mechanics. This book is intended for advanced undergraduate and graduate students, researchers in the area of biomechanics, and engineers interested and involved in the analysis and design of thin-layer structures.

This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green’s functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail and 2D and 3D elastodynamic problems are treated in full. This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green’s function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.

The book presents interesting examples of recent developments in this area. Among the studied materials are bulk metallic glasses, metamaterials, special composites, piezoelectric smart structures, nonwovens, etc. The last decades have seen a large extension of types of materials employed in various applications. In many cases these materials demonstrate mechanical properties and performance that vary significantly from those of their traditional counterparts. Such uniqueness is sought – or even specially manufactured – to meet increased requirements on modern components and structures related to their specific use. As a result, mechanical behaviors of these materials under different loading and environmental conditions are outside the boundaries of traditional mechanics of materials, presupposing development of new characterization techniques, theoretical descriptions and numerical tools. The book presents interesting examples of recent developments in this area. Among the studied materials are bulk metallic glasses, metamaterials, special composites, piezoelectric smart structures, nonwovens, etc.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.

This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches�, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

In this book, we shall consider the kinematics and dynamics of the flows of fluids exhibiting a yield stress. To highlight the principal characteristics of such fluids, the first chapter emphasizes the role played by the yield stress. Next, a careful description of the continuum mechanics behind the constitutive equations for incompressible and compressible viscoplastic fluids is given in Chapters 2-4. In Chapters 5 and 6 analytical solutions to several steady and unsteady flows of Bingham fluids are presented. The subsequent Chapters 7-10 are concerned with the development of variational principles and their numerical solutions, along with perturbation methods which play a significant role in numerical simulations.

Fracture, Fatigue, Failure and Damage Evolution, Volume 5: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, the fifth volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on a wide range of areas, including: Mixed Mode Fracture I: Emphasis on Modeling Mixed Mode Fracture II: Emphasis on Experimental Measurements Full-Field Measurements of Fracture Microscale & Microstructural Effects on Mechanical Behavior I: Nanoscale Effects Microscale & Microstructural Effects on Mechanical Behavior II: MEMS Microscale & Microstructural Effects on Mechanical Behavior III: Microstructure Microscale & Microstructural Effects on Mechanical Behavior IV: Shape Memory Alloys Fracture & Fatigue of Composites Fracture & Fatigue for Engineering Applications Wave-Based Techniques in Fracture & Fatigue I Wave-Based Techniques in Fracture & Fatigue II: Acoustic Emissions

Engineering Viscoelasticity covers all aspects of the thermo- mechanical response of viscoelastic substances that a practitioner in the field of viscoelasticity would need to design experiments, interpret test data, develop stress-strain models, perform stress analyses, design structural components, and carry out research work. The material in each chapter is developed from the elementary to the esoteric, providing the background in mathematics and mechanics that are central to understanding the subject matter being presented. This book also examines how viscoelastic materials respond to the application of loads, and provides practical guidelines to use them in the design of commercial, military and industrial applications.

This book lays down the foundation on the mechanics and design of auxetic solids and structures, solids that possess negative Poisson's ratio. It will benefit two groups of readers: (a) industry practitioners, such as product and structural designers, who need to control mechanical stress distributions using auxetic materials, and (b) academic researchers and students who intend to produce unique mechanical and other physical properties of structures using auxetic materials.

Dynamic Behavior of Materials, Volume 1: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, the first volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Experimental Mechanics, including papers on:  ·        General Dynamic Materials Response ·        Novel Dynamic Testing Techniques ·        Dynamic Fracture and Failure ·        Dynamic Behavior of Geo-materials ·        Dynamic Behavior of Composites and Multifunctional materials ·        Dynamic Behavior of Low-Impedance materials ·        Dynamic Modeling and Simulation of Dynamic Behavior of Materials ·        Quantitative Visualization of Dynamic Behavior of Materials ·        Shock/Blast Loading of Materials ·        Interface and Structural Dynamics ·        Material Response

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. Please visit the author's website for supplemental material, including PowerPoint presentations and MATLAB codes, at http://www2.mae.ufl.edu/nkim/INFEM/

This revised third edition of Rheology of Fluid, Semisolid, and Solid Foods includes the following important additions: * A section on microstructure * Discussion of the quantitative characterization of nanometer-scale milk protein fibrils in terms of persistence and contour length. * A phase diagram of a colloidal glass of hard spheres and its relationship to milk protein dispersions * Microrheology, including detailed descriptions of single particle and multi-particle microrheological measurements * Diffusive Wave Spectroscopy * Correlation of Bostwick consistometer data with property-based dimensionless groups * A section on the effect of calcium on the morphology and functionality of whey protein nanometer-scale fibrils * Discussion of how tribology and rheology can be used for the sensory perception of foods

This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.

This comprehensive book offers a clear account of the theory and applications of advanced metal forming. It provides a detailed discussion of specific forming processes, such as deep drawing, rolling, bending extrusion and stamping. The author highlights recent developments of metal forming technologies and explains sound, new and powerful expert system techniques for solving advanced engineering problems in metal forming. In addition, the basics of expert systems, their importance and applications to metal forming processes, computer-aided analysis of metalworking processes, formability analysis, mathematical modeling and case studies of individual processes are presented.