The Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method
Author: Chongmin Song
Publisher: John Wiley & Sons
Total Pages: 500
Release: 2018-09-04
Genre: Science
ISBN: 1119388155

An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.

Methods of the Classical Theory of Elastodynamics

Methods of the Classical Theory of Elastodynamics
Author: Vladimir B. Poruchikov
Publisher: Springer Science & Business Media
Total Pages: 329
Release: 2012-12-06
Genre: Science
ISBN: 3642770991

"Methods of the Classical Theory of Elastodynamics" deals not only with classical methods as developed in the past decades, but presents also very recent approaches. Applications and solutions to specific problems serve to illustrate the theoretical presentation. Keywords: Smirnov-Sobolev method with further developments; integral transforms; Wiener-Hopf technique; mixed boundary-value problems; time-dependent boundaries; solutions for unisotropic media (Willis method); 3-d dynamical problems for mixed boundary conditions.

Numerical Solution of Partial Differential Equations—III, SYNSPADE 1975

Numerical Solution of Partial Differential Equations—III, SYNSPADE 1975
Author: Bert Hubbard
Publisher: Academic Press
Total Pages: 510
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483262367

Numerical Solution of Partial Differential Equations—III: Synspade 1975 provides information pertinent to those difficult problems in partial differential equations exhibiting some type of singular behavior. This book covers a variety of topics, including the mathematical models and their relation to experiment as well as the behavior of solutions of the partial differential equations involved. Organized into 16 chapters, this book begins with an overview of elastodynamic results for stress intensity factors of a bifurcating crack. This text then discusses the effects of nonlinearities, such as bifurcation, which occur in problems of nonlinear mechanics. Other chapters consider the equations of changing type and those with rapidly oscillating coefficients. This book discusses as well the effective computational methods for numerical solutions. The final chapter deals with the principal results on G-convergence, such as the convergence of the Green's operators for Dirichlet's and other boundary problems. This book is a valuable resource for engineers and mathematicians.

Fracture Mechanics

Fracture Mechanics
Author: National Symposium on Fracture Mechanics
Publisher: ASTM International
Total Pages: 608
Release: 1980
Genre: Fracture mechanics
ISBN: 9780803103634

Dynamic Fracture Mechanics

Dynamic Fracture Mechanics
Author: L. B. Freund
Publisher: Cambridge University Press
Total Pages: 592
Release: 1998-03-28
Genre: Mathematics
ISBN: 9780521629225

This volume focuses on the development and analysis of mathematical models of fracture phenomena.

Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Mathematical Theory of Elasticity of Quasicrystals and Its Applications
Author: Tian-You Fan
Publisher: Springer
Total Pages: 462
Release: 2016-09-20
Genre: Science
ISBN: 9811019843

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.

Fracture Mechanics

Fracture Mechanics
Author: George A. Papadopoulos
Publisher: Springer Science & Business Media
Total Pages: 291
Release: 2012-12-06
Genre: Science
ISBN: 1447119924

Fracture and Mechanics is concerned with the experimental method of static and dynamic caustics and the Distribution of Determinant (Det.)-criterion of fracture. The Det.-criterion determines the conditions causing a crack and gives information on the expected angle of crack propagation. The object of this publication is to present the latest results to the re.earch and development community and to assist the teaching of experimental fracture mechanics and stress analysis in undergraduate and postgraduate courses. After discussing the basic theoretical considerations on the subject, experimental techniques and applications are introduced. Most of the results presented are based on the author's own investigations in the field of experimental mechanics since 1973 at the National Technical University of Athens.