Download or read book Partial Differential Equations in Mechanics 2 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Download or read book Biharmonic Problem in the Theory of Elasticity written by Lurie and published by CRC Press. This book was released on 1995-11-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference work offers a method of deriving exact solutions to the biharmonic equation in the context of elasticity problems. A general mathematical model is presented and specific applications outlined.
Download or read book Ill Posed Internal Boundary Value Problems for the Biharmonic Equation written by M. A. Atakhodzhaev and published by VSP. This book was released on 2002-01-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: An internal boundary value problem deals with the problem of determining the solution of an equation, if data are given on two manifolds. One manifold is the domain boundary and the other manifold is situated inside the domain. This monograph in the Inverse and Ill-Posed Problems Series studies three essentially ill-posed internally boundary value problems for the biharmonic equation and the Cauchy problem for the abstract biharmonic equation, both qualitatively and quantitatively. In addition, some variants of these problems and the Cauchy problem, as well as the m-dimensional case are considered.This monograph, in which the author introduces some new notions, such as the notion of complete solvability, will be of interest to specialists in mathematical physics.
Download or read book Boundary Integral Equation Analyses of Singular Potential and Biharmonic Problems written by D. B. Ingham and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.
Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Download or read book Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry written by Ye-lin Ou and published by World Scientific. This book was released on 2020-04-04 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.
Download or read book Partial Differential Equations and Functional Analysis written by Erik Koelink and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.
Download or read book Formulation of Problems of Finding Stress Functions with the Aid of Biharmonic Potentials written by Yu. D. Kopeykin and published by . This book was released on 1966 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Fast Finite Difference Method for Biharmonic Equations on Irregular Domains written by and published by . This book was released on 2004 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary conditions. The irregular domain is embedded into a rectangular region and the biharmonic equation is decoupled to two Poisson equations. An auxiliary unknown quantity deltau along the boundary is introduced so that fast Poisson solvers on irregular domains can be used. Non-trivial numerical example show the efficiency of the proposed method. The number of iterations of the method is independent of the mesh size. Another key to the method is a new interpolation scheme to evaluate the residual of the Schur complement system. The new biharmonic solver has been applied to solve the incompressible Stokes flow on an irregular domain.
Download or read book Immersed Interface Method for Biharmonic Equations on Irregular Domain and Its Applications written by Guo Chen and published by . This book was released on 2003 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: immersed interface method, biharmonic equation, GMRES.
Download or read book Biharmonic Functions and Applications written by David Fremont Brauch and published by . This book was released on 1961 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Numerical Solutions of Harmonic Biharmonic and Similar Equations by the Difference Method Not Through Successive Approximations written by Hatsuo Ishizaki and published by . This book was released on 1957 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reflection of Biharmonic Functions Across Analytic Boundary Conditions written by James M. Sloss and published by . This book was released on 1962 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The reflection of solutions of a biharmonic equation across an analytic arc satisfies two analytic boundary conditions. More specifically but without stating all hypotheses, if a biharmonic function is given on a simply connected open set, partially bounded by an analytic arc (without end points), and satisfies two analytic boundary conditions, then there exists a simply connected region containing the analytic arc in its interior, and a unique function biharmonic on this region, which agrees with the biharmonic function. There are two cases treated. In the first case, linear boundary conditions with analytic coefficients are given and a condition on the coefficients is stated. In the second case, nonlinear boundary conditions are given, and a condition is stated, which when satisfied, permits reflection locally. The conditions in the linear case will cover, among other things, the boundary conditions of the first and second fundamental boundary value problems of elasticity as well as the fundamental mixed boundary value problems in elasticity. (Author).
Download or read book Boundary Element Analysis of Nonhomogeneous Biharmonic Phenomena written by Charles V. Camp and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the date of this writing, there is no question that the boundary element method has emerged as one of the major revolutions on the engineering science of computational mechanics. The emergence of the technique from relative obscurity to a cutting edge engineering analysis tool in the short space of basically a ten to fifteen year time span is unparalleled since the advent of the finite element method. At the recent international conference BEM XI, well over one hundred papers were presented and many were pub lished in three hard-bound volumes. The exponential increase in interest in the subject is comparable to that shown in the early days of finite elements. The diversity of appli cations of BEM, the broad base of interested parties, and the ever-increasing presence of the computer as an engineering tool are probably the reasons for the upsurge in pop ularity of BEM among researchers and industrial practitioners. Only in the past few years has the BEM audience become large enough that we have seen the development of specialty books on specific applications of the boundary element method. The present text is one such book. In this work, we have attempted to present a self-contained treatment of the analysis of physical phenomena governed by equations containing biharmonic operators. The biharmonic operator defines a very important class of fourth-order PDE problems which includes deflections of beams and thin plates, and creeping flow of viscous fluids.
Download or read book Nonlinear Evolution Equations and Dynamical Systems written by Yi Cheng and published by World Scientific. This book was released on 2003 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast-paced economic growth in Southeast Asia from the late 1960s until the mid-1990s brought increased attention to the overseas Chinese as an economically successful diaspora and their role in this economic growth. Events that followed, such as the transfer of Hong Kong and Macau to the People's Republic of China, the election of a non-KMT government in Taiwan, the Asian economic crisis and the plight of overseas Chinese in Indonesia as a result, and the durability of the Singapore economy during this same crisis, have helped to sustain this attention. The study of the overseas Chinese has by now become a global enterprise, raising new theoretical problems and empirical challenges. New case studies of overseas Chinese, such as those on communities in North America, Cuba, India, and South Africa, continually unveil different perspectives. New kinds of transnational connectivities linking Chinese communities are also being identified. It is now possible to make broader generalizations of a Chinese diaspora, on a global basis. Further, the intensifying study of the overseas Chinese has stimulated renewed intellectual vigor in other areas of research. The transnational and transregional activities of overseas Chinese, for example, pose serious challenges to analytical concepts of regional divides such as that between East and Southeast Asia. Despite the increased attention, new data, and the changing theoretical paradigms, basic questions concerning the overseas Chinese remain. The papers in this volume seek to understand the overseas Chinese migrants not just in terms of the overall Chinese diaspora per se, but also local Chinese migrants adapting to local societies, in different national contexts.
Download or read book Efficient Solution of the Biharmonic Equation written by Stanford University. Computer Science Department. Numerical Analysis Project and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.
