As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now, however, the limitations of FEM are becoming increasingly evident, and a new and more powerful class of techniques is emerging. For the first time in book form, Mesh Free Methods: Moving Beyond the Finite Element Method provides full, step-by-step details of techniques that can handle very effectively a variety of mechanics problems. The author systematically explores and establishes the theories, principles, and procedures that lead to mesh free methods. He shows that meshless methods not only accommodate complex problems in the mechanics of solids, structures, and fluids, but they do so with a significant reduction in pre-processing time. While they are not yet fully mature, mesh free methods promise to revolutionize engineering analysis. Filled with the new and unpublished results of the author's award-winning research team, this book is your key to unlocking the potential of these techniques, implementing them to solve real-world problems, and contributing to further advancements.

Mesh Free Methods: Moving Beyond the Finite Element Method

Science & Math

G.R. Liu

Mathematics

CRC-Press

Ill-posedness. Regularization. Stability. Uniqueness. To many engineers, the language of inverse analysis projects a mysterious and frightening image, an image made even more intimidating by the highly mathematical nature of most texts on the subject. But the truth is that given a sound experimental strategy, most inverse engineering problems can be well-posed and not difficult to deal with. Computational Inverse Techniques in Nondestructive Evaluation sets forth in clear, easy-to-understand terms the principles, computational methods, and algorithms of inverse analyses based on elastic waves or the dynamic responses of solids and structures. After describing the features of inverse problems, the authors discuss the regularization methods useful in handling ill-posed problems. The book also presents practical optimization algorithms, including some developed and successfully tested by his research group. Inverse analyses are fast becoming one of the engineer's most powerful tools in nondestructive evaluation and testing. With straightforward examples, a wealth of specific applications, and clear exposition written by engineers for engineers, this book offers an outstanding opportunity to overcome any trepidation and begin using inverse analysis in practice.

Computational Inverse Techniques in Nondestructive Evaluation

X. Han

Taylor&Francis

This book is a collection of the papers from the proceedings of the 1st Asian Workshop on Meshfree Methods held in conjunction with the 2nd International Conference on Structural Stability &amp; Dynamics (ICSSD02) on 16-18 December 2002 in Singapore. It contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported.

ADVANCES IN MESHFREE AND X-FEM METHODS (VOL 2) - WITH CD-ROM, PROCEEDINGS OF THE 1ST ASIAN WORKSHOP ON MESHFREE METHODS

World Scientific Publishing Company

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Books by G.R. Liu