Download or read book Finite element approximations of a class of highly nonlinear boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1978 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite element approximations of a class of nonlinear two point boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1974 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A theory of finite element approximations for a class of nonlinear two point boundary value problems in finite elasticity written by John Tinsley Oden and published by . This book was released on 1977 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On finite element approximation of general boundary value problems in nonlinear elasticity written by Rolf Rannacher and published by . This book was released on 1978 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Contact Problems in Elasticity written by N. Kikuchi and published by SIAM. This book was released on 1988-01-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.
Download or read book Finite Elements of Nonlinear Continua written by J. T. Oden and published by Courier Corporation. This book was released on 2013-04-15 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view. The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined. Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua
Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
Download or read book The Finite Element Method for Boundary Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2016-11-17 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.
Download or read book Finite Element Solution of Boundary Value Problems written by O. Axelsson and published by Academic Press. This book was released on 2014-05-10 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.
Download or read book Finite Element Approximation of Contact and Friction in Elasticity written by Franz Chouly and published by Springer Nature. This book was released on 2023-06-23 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematics behind the formulation, approximation, and numerical analysis of contact and friction problems. It also provides a survey of recent developments in the numerical approximation of such problems as well as several remaining unsolved issues. Particular focus is placed on the Signorini problem and on frictionless unilateral contact in small strain. The final chapters cover more complex, applications-oriented problems, such as frictional contact, multi-body contact, and large strain. Finite Element Approximation of Contact and Friction in Elasticity will be a valuable resource for researchers in the area. It may also be of interest to those studying scientific computing and computational mechanics.
Download or read book The Scaled Boundary Finite Element Method written by John P. Wolf and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
Download or read book Mechanics Today written by S. Nemat-Nasser and published by Elsevier. This book was released on 2013-10-22 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics Today, Volume 2 consists of four articles considering applied mechanics. Each article starts with a discussion of fundamentals and continues with a presentation of analytical and experimental results. Topics discussed in the first three articles include theory of creep and shrinkage in concrete structures; nonequilibrium thermodynamics of continua; and mathematical aspects of finite-element approximations in continuum mechanics. The last article shows the utilization of exact simple wave solutions for the construction of uniform approximations for waves in nonlinear dissipative or bounded media. This book is useful to specialists and accessible to non-experts but with sufficient background of the subject matter.
Download or read book An analysis of finite element approximations in some simple nonlinear elasticity problems written by Ricardo Garcia de Castro Nicolau del Roure and published by . This book was released on 1977 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1993 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Accuracy of Finite Element Approximations to Structural Problems written by Langley Research Center and published by . This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1988 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Approximations for Fluid Flows Governed by Nonlinear Slip Boundary Conditions of Friction Type written by Mbehou Mohamed and published by . This book was released on 2014 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is divided in three main chapters devoted to the study of finite element approximations of fluid flows with special nonlinearities coming from boundary con- ditions. In Chapter 1, we consider the finite element approximations of steady Navier-Stokes and Stokes equations driven by threshold slip boundary conditions. After re-writing the problems in the form of variational inequalities, a fixed point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge respectively to the solutions of each continuous problem. Finally, Uzawa’s algorithm is formulated and convergence of the procedure is shown, and numerical validation tests are achieved. Chapter 2 is concerned with the finite element approximation for the stationary power law Stokes equations driven by slip boundary conditions of “friction type”. It is shown that by applying a variant of Babuska-Brezzi’s theory for mixed problems, convergence of the finite element approximation formulated is achieved with classi- cal assumptions on the regularity of the weak solution. Solution algorithm for the mixed variational problem is presented and analyzed in details. Finally, numerical simulations that validate the theoretical findings are exhibited. In Chapter 3, we are dealing with the study of the stability for all positive time of Crank-Nicolson scheme for the two-dimensional Navier-Stokes equation driven by slip boundary conditions of “friction type”. We discretize these equations in time using the Crank-Nicolson scheme and in space using finite element approximation. We prove that the numerical scheme is stable in L2 and H1-norms with the aid of different versions of discrete Grownwall lemmas, under a CFL-type condition.
