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The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: • Weighted residual methods and Galerkin approximations, • A model problem for one-dimensional linear elastostatics, • Weak formulations in one dimension, • Minimum principles in one dimension, • Error estimation in one dimension, • Construction of Finite Element basis functions in one dimension, • Gaussian Quadrature, • Iterative solvers and element by element data structures, • A model problem for three-dimensional linear elastostatics, • Weak formulations in three dimensions, • Basic rules for element construction in three-dimensions, • Assembly of the system and solution schemes, • An introduction to time-dependent problems and • An introduction to rapid computation based on domain decomposition and basic parallel processing. The approach is to introduce the basic concepts first in one-dimension, then move on to three-dimensions. A relatively informal style is adopted. This primer is intended to be a “starting point”, which can be later augmented by the large array of rigorous, detailed, books in the area of Finite Element analysis. In addition to overall improvements to the first edition, this second edition also adds several carefully selected in-class exam problems from exams given over the last 15 years at UC Berkeley, as well as a large number of take-home computer projects. These problems and projects are designed to be aligned to the theory provided in the main text of this primer.
A thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its facets. A Primer for Finite Elements in Elastic Structures disassembles the entire finite element method for civil engineering students and professionals, detailing its supportive theory and its mathematical and structural underpinnings, in the context of elastic structures and the principle of virtual work. The book opens with a discussion of matrix algebra and algebraic equation systems to foster the basic skills required to successfully understand and use the finite element method. Key mathematical concepts outlined here are joined to pertinent concepts from mechanics and structural theory, with the method constructed in terms of one-dimensional truss and framework finite elements. The use of these one-dimensional elements in the early chapters promotes better understanding of the fundamentals. Subsequent chapters describe many two-dimensional structural finite elements in depth, including the geometry, mechanics, transformations, and mapping needed for them. Most chapters end with questions and problems which review the text material. Answers for many of these are at the end of the book. An appendix describes how to use MATLAB(r), a popular matrix-manipulation software platform necessary to perform the many matrix operations required for the finite element method, such as matrix addition, multiplication, inversion, partitioning, rearrangement, and assembly. As an added extra, the m-files discussed can be downloaded from the Wiley FTP server.
Nonlinear Optimization of Vehicle Safety Structures: Modeling of Structures Subjected to Large Deformations provides a cutting-edge overview of the latest optimization methods for vehicle structural design. The book focuses on large deformation structural optimization algorithms and applications, covering the basic principles of modern day topology optimization and comparing the benefits and flaws of different algorithms in use. The complications of non-linear optimization are highlighted, along with the shortcomings of recently proposed algorithms. Using industry relevant case studies, users will how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given. The authors draw on research work with the likes of MIRA, Jaguar Land Rover and Tata Motors European Technology Centre as part of multi-million pound European funded research projects, emphasizing the industry applications of recent advances. The book is intended for crash engineers, restraints system engineers and vehicle dynamics engineers, as well as other mechanical, automotive and aerospace engineers, researchers and students with a structural focus. - Focuses on non-linear, large deformation structural optimization problems relating to vehicle safety - Discusses the limitations of different algorithms in use and offers guidance on best practice approaches through the use of relevant case studies - Author's present research from the cutting-edge of the industry, including research from leading European automotive companies and organizations - Uses industry relevant case studies, allowing users to understand how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.
Multifunctional Metallic Hollow Sphere Structures are an emerging new material category, belonging like metal foams to the class cellular metals. Thanks to their advantageous mechanical and sound absorbing properties, Multifunctional Metallic Hollow Sphere Structures are very promising for various applications and our technological knowledge makes them ready for industrial usage. This reference gives a complete overview on this new materials class, the fundamentals, the applications and the perspective for future use. It provides the foundations for a profound understanding (production and processing), their physical properties (surface properties and stalility) and applicaltion (in particular for sound absorption and chemical adsorption in structural parts). The book is written for material scientists, product designers and developers as well as academic researches and scientists.
The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background, and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formally but also to think intuitively about what is going on and to describe that process clearly and cogently in ordinary English. Ash tries to aid intuition by keeping proofs short and as informal as possible, and using concrete examples as illustration. Thus it is an ideal textbook for an audience with limited experience in formalism and abstraction. A number of expository innovations are included, for example, an informal development of set theory which teaches students all the basic results for algebra in one chapter.
The second edition of this well-received textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the reader is led through the derivation of definitions, concepts, and methods for solving typical problems. Theorems then are formulated, proved, and illustrated by more problems of increasing difficulty.