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This book is devoted to the static and dynamic analysis of structures on elastic foundation. Through comprehensive analysis, the book shows analytical and mechanical relationships among classic and modern methods of solving boundary value problems. The book provides a wide spectrum of applications of modern techniques and methods of calculation of static and dynamic problems of engineering design. It pursues both methodological and practical purposes, and the accounting of all methods is accompanied by solutions of the specific problems, which are not merely illustrative in nature but may represent an independent interest in the study of various technical issues. Two special features of the book are the extensive use of the generalized functions for describing the impacts on structures and the substantiations of the methods of the apparatus of the generalized functions. The book illustrates modern methods for solving boundary-value problems of structural mechanics and soil mechanics based on the application of boundary equations. The book presents the philosophy of boundary equations and boundary element methods. A number of examples of solving different problems of static and dynamic calculation of structures on an elastic foundation are given according to the methods presented in the book. Introduces a general approach to the method of integral transforms based on the spectral theory of the linear differential operators. The Spectral Method of Boundary Element (SMBE) is developed based on using integral transforms with an orthogonal kernel in the extended domain. Presents a new, versatile foundation model with a number of advantages over the ground-based models currently used in practical calculations. Provides new transforms which will aid in solving various problems relevant to bars, beams, plates, and shells in particular for the structures on elastic foundation. Examines the methods of solving boundary-value problems typical for structural mechanics and related fields.

Effectively Construct Integral Formulations Suitable for Numerical ImplementationFinite Element and Boundary Methods in Structural Acoustics and Vibration provides a unique and in-depth presentation of the finite element method (FEM) and the boundary element method (BEM) in structural acoustics and vibrations. It illustrates the principles using a

Most texts on computational methods are borne out of research activities at postgraduate study programs, and this is no exception. After being introduced to the boundary element method (BEM) (then referred to as the boundary integral equation method (BIEM)) in 1981 by Prof. Jim Liggett of Cornell University, a number of graduate students and myself under his supervision took active interest in the development of the theory and its application to a wide range of engineering problems. We certainly achieved some amount of success. A personal desire to have a deeper understanding and appreciation of computational methods prompted one to take related courses in fmite deference method, and to undertake a self-instructed study of variational and fmite element methods. These exposures were not only quite instructive but fruitful, and may have provided the motivation for the current research on the Green element method (GEM) - a name coined by Prof. Liggett in 1987 during my visit as Professor to the School of Civil & Environmental Engineering, Cornell University. The main objectives of this text are to serve as an instructional material to senior undergraduate and first year graduate students undertaking a course in computational methods, and as a resource material for research scientists, applied mathematicians, numerical analysts, and engineers who may wish to take these ideas to other frontiers and applications.

1. 1 Historical Background Thin plates and shells are widely used structural elements in numerous civil, mechanical, aeronautical and marine engineering design applications. Floor slabs, bridge decks, concrete pavements, sheet pile retaining walls are all, under normal lateral loading circumstances, instances of plate bending in civil engineering. The problem of elastic instability of plates occurs when load is applied in a direction parallel to the plane of the plate. The deck of a bridge subjected to a strong wind loading, the web of a girder under the action of shear forces transmitted by the flanges, the turbine blade of a machinery undergoing longitudinal temperature differentials, would all eventually buckle when the applied load, or its temperature equivalent in the last case, exceeds a certain limit, that is the buckling load. Although the plate may exhibit a considerable post-buckling strength, the buckling load is considered in many design instances, especially in aeronautical and marine engineering, as a serviceability limit because of the abrupt and substantial change in the dimensions and shape of the buckled plate. Nevertheless, the post-buckling region retains its importance either as an essential safety margin or as a stage of loading actually reached under normal loading conditions. The design engineer will therefore need rigorous tools of analysis to predict, in addition to the buckling load, the deflections and stresses at both buckling and initial post-buckling stages.

This book presents a new formulation of the boundary element method for two-dimensional and axisymmetric contact problems. The solution procedure includes the effects of non-frictional as well as frictional contact between elastic bodies. Following a literature survey of various experimental and analytical approaches for solving elastic contact problems, a comprehensive review of numerical techniques used for analyses of contact problems is presented. The boundary element formulations for two-, three-dimensional and axisymmetric problems in elasticity are derived and numerical implementation using constant and linear elements is described. For analysis of contact problems, boundary elements are employed to compute flexibility matrices representing the relationship between tractions and displacements only at nodes coming into contact. The contact analysis is performed using the flexibility matrices in conjunction with contact boundary conditions. In this approach, only equations corresponding to the node coming into contact are required and consequently very efficient computation is achieved. Furthermore, the boundary element analysis and the contact analysis are performed separately, which makes it easy to implement the contact analysis procedure into boundary element codes. A new contact criterion for nodes coming into contact is proposed. Load incremental and iterative schemes are used to obtain accurate solutions. Some classical Hertz and non-Hertz contact problems are studied and results are found to be in good agreement with analytical and other numerical solutions.

The Boundary Element Method is a simple, efficient and cost effective computational technique which provides numerical solutions - for objects of any shap- for a wide range of scientific and engineering problems. In dealing with the development of the mathematics of the Boundary Element Method the aim has been at every stage, only to present new material when sufficient experience and practice of simpler material has been gained. Since the usual background of many readers will be of differential equations, the connection of differential equations with integral equations is explained in Chapter 1, together with analytical and numerical methods of solution. This information on integral equations provides a base for the work of subsequent chapters. The mathematical formulation of boundary integral equations for potential problems - derived from the more familiar Laplace partial differential equation which governs many important physical problems - is set out in Chapter 2. It should be noted here that this initial formulation of the boundary integral equations reduces the dimensionality of the problem. In the key Chapter 3, the essentials of the Boundary Element Method are presented. This first presentation of the Boundary Element Method is in its simplest and most approachable form - two dimensional, with the shape of the boundary approximated by straight lines and the functions approximated by constants over each of the straight lines.

This volume, dedicated to Professor Dimitri Beskos, contains contributions from leading researchers in Europe, the USA, Japan and elsewhere, and addresses the needs of the computational mechanics research community in terms of timely information on boundary integral equation-based methods and techniques applied to a variety of fields. The contributors are well-known scientists, who also happen to be friends, collaborators as past students of Dimitri Beskos. Dimitri is one the BEM pioneers who started his career at the University of Minnesota in Minneapolis, USA, in the 1970s and is now with the University of Patras in Patras, Greece. The book is essentially a collection of both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the newer Mesh Reduction Methods (MRM), covering a variety of research topics. Close to forty contributions compose an over-500 page volume that is rich in detail and wide in terms of breadth of coverage of the subject of integral equation formulations and solutions in both solid and fluid mechanics.

Boundary Methods: Elements, Contours, and Nodes presents the results of cutting-edge research in boundary-based mesh-free methods. These methods combine the dimensionality advantage of the boundary element method with the ease of discretization of mesh-free methods, both of which, for some problems, hold distinct advantages over the finite element

The Boundary Element Method, or BEM, is a powerful numerical analysis tool with particular advantages over other analytical methods. With research in this area increasing rapidly and more uses for the method appearing, this timely book provides a full chronological review of all techniques that have been proposed so far, covering not only the funda

This book is addressed mainly to younger geoscientists and students of geologically related subjects. It discusses: (1) the concepts, definitions and experience of strength, particularly rock strength, with application of experimental techniques; (2) the physical-chemical aspects of the strength of pure phases; (3) strengthening of grain packings by “intermolecular forces”; (4) the behaviour of Buntersandstone samples underwater and lessons for understanding weathering processes; (5) deductions concerning the distribution of substances and forces in Buntersandstone samples from observing the response of samples underwater.The urgency of environmental studies has been the main driving force for this book. The discussion of single problems is wide-ranging, particularly for chemical and physical topics, so as to enhance the reader's understanding. The book is more a research account than a textbook. Thus, no “completed”, well-defined subject area is presented; on the contrary, many questions are raised which should form the basis for future research. The book has been written to stimulate lively debate.

The interest in finite element method as a solution technique of the computer age is reflected in the availability of many general and special purpose software based on this technique. This work aims to provide a complete and detailed explanation of the basics of the application areas.

The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations. Also included are developments made by the authors in the boundary integral formulation of thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is formulated for the first time as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-differential equations.

This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.