A Finite Element Approach for Wave Propagation in Elastic Solids
Author: Arkadiusz Żak
Publisher: Springer Nature
Published:
Total Pages: 332
ISBN-13: 3031568362
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The Wave Finite Element Method
Author: Boris F. Shorr
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 358
ISBN-13: 354044579X
DOWNLOAD EBOOKComputational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.
Ultrasonic Guided Waves in Solid Media
Author: Joseph L. Rose
Publisher: Cambridge University Press
Published: 2014-08-11
Total Pages: 551
ISBN-13: 113991698X
DOWNLOAD EBOOKUltrasonic guided waves in solid media have become a critically important subject in nondestructive testing and structural health monitoring, as new faster, more sensitive, and more economical ways of looking at materials and structures have become possible. This book will lead to fresh creative ideas for use in new inspection procedures. Although the mathematics is sometimes sophisticated, the book can also be read by managers without detailed understanding of the concepts as it can be read from a 'black box' point of view. Overall, the material presented on wave mechanics - in particular, guided wave mechanics - establishes a framework for the creative data collection and signal processing needed to solve many problems using ultrasonic nondestructive evaluation and structural health monitoring. The book can be used as a reference in ultrasonic nondestructive evaluation by professionals and as a textbook for seniors and graduate students. This work extends the coverage of Rose's earlier book Ultrasonic Waves in Solid Media.
The Scaled Boundary Finite Element Method
Author: John P. Wolf
Publisher: John Wiley & Sons
Published: 2003-03-14
Total Pages: 398
ISBN-13: 9780471486824
DOWNLOAD EBOOKA 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.
Elastic Waves in Anisotropic Laminates
Author: G.R. Liu
Publisher: CRC Press
Published: 2001-11-13
Total Pages: 472
ISBN-13: 9780849310706
DOWNLOAD EBOOKUltrasonic non-destructive evaluation (NDE) plays an increasingly important role in determining properties and detecting defects in composite materials, and the analysis of wave behavior is crucial to effectively using NDE techniques. The complexity of elastic wave propagation in anisotropic media has led to a reliance on numerical methods of analysis-methods that are often quite time-consuming and whose results yield even further difficulties in extracting explicit phenomena and characteristics. Innovative and insightful, Elastic Waves in Anisotropic Laminates establishes a set of high-performance, analytical-numerical methods for elastic wave analysis of anisotropic layered structures. The treatment furnishes a comprehensive introduction, sound theoretical development, and applications to smart materials, plates, and shells. The techniques, detailed in both the time and frequency domains, include methods that combine the finite element method (FEM) with the Fourier transform approach and the strip element method (SEM). These -methods can also be used for expediently finding the Green's function for anisotropic laminates useful for inverse problems related to wave propagation, and methods for inverse analyses, including conjugate gradient methods, and genetic algorithms are also introduced. The text is complemented by many examples generated using software codes based on the techniques developed. Filled with charts and illustrations, Elastic Waves in Anisotropic Laminates is accessible even to readers from non-engineering backgrounds and offers a unique opportunity to discover methods that can lead to an understanding of the dynamic characteristics and wave motion behaviors of advanced composite materials.
The Finite Element Method: Theory, Implementation, and Applications
Author: Mats G. Larson
Publisher: Springer Science & Business Media
Published: 2013-01-13
Total Pages: 403
ISBN-13: 3642332870
DOWNLOAD EBOOKThis book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Spectral Finite Element Method
Author: Srinivasan Gopalakrishnan
Publisher: Springer Science & Business Media
Published: 2007-12-05
Total Pages: 449
ISBN-13: 1846283566
DOWNLOAD EBOOKThis book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. Readers will gain understanding of how to formulate Spectral Finite Element; learn about wave behaviour in inhomogeneous and anisotropic media; and, be able to design some diagnostic tools for monitoring the health of a structure. Tables, figures and graphs support the theory and case studies are included.
Waves in Layered Media
Author: L Brekhovskikh
Publisher: Elsevier
Published: 2012-12-02
Total Pages: 520
ISBN-13: 0323161626
DOWNLOAD EBOOKWaves in Layered Media discusses different theories about the relationship between waves and media. The book specifically covers several factors that can affect the behavior and formation of various kinds of waves in different types of media. Comprised of nine chapters, the book establishes the fundamentals by first tackling simplest concepts, such as the behavior plane wave and discretely layered media. The succeeding chapters cover much more complex ideas, such as the refraction and reflection of waves, spherical wave, and wave in inhomogeneous media. The book will be a great asset to researchers whose work involves acoustics, or to professionals whose line of work involves sound waves.
Dynamics of Lattice Materials
Author: A. Srikantha Phani
Publisher: John Wiley & Sons
Published: 2017-09-25
Total Pages: 312
ISBN-13: 1118729595
DOWNLOAD EBOOKProvides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
Elastic Wave Propagation and Generation in Seismology
Author: Jose Pujol
Publisher: Cambridge University Press
Published: 2003-05-01
Total Pages: 462
ISBN-13: 9780521817301
DOWNLOAD EBOOKBridging the gap between introductory textbooks and advanced monographs, this book provides the necessary mathematical tools to tackle seismological problems and demonstrates how to apply them. Including student exercises, for which solutions are available on a dedicated website, it appeals to advanced undergraduate and graduate students. It is also a useful reference volume for researchers wishing to "brush up" on fundamentals before they study more advanced topics in seismology.
