While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.

This book describes the various Smoothed Point Interpolation Method (S-PIM) models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail.

Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations — one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.

This book contains selected, extended papers presented at the thematic ECCOMAS conference on Computational Modelling and Advanced Simulations (CMAS2009) held in Bratislava, Slovakia, June 30 – July 3, 2009. Modelling and simulation of engineering problems play a very important role in the classic and new composite material sciences, and in design and computational prototyping of modern and advanced technologic parts and systems. According to this, the existing numerical methods have been improved and new numerical methods have been established for modelling and simulation of more and more complex and complicated engineering problems. The present book should contribute to the effort to make modelling and simulation more effective and accurate.

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.

Edited by and featuring contributions from world-class researchers, Ophthalmological Imaging and Applications offers a unified work of the latest human eye imaging and modeling techniques that have been proposed and applied to the diagnosis of ophthalmologic problems, including inflammation, cataracts, diabetic retinopathy, and glaucoma. With a foc

Advances and Trends in Structural Engineering, Mechanics and Computation features over 300 papers classified into 21 sections, which were presented at the Fourth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2010, Cape Town, South Africa, 6-8 September 2010). The SEMC conferences have been held every 3 years in

Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.