The Finite Element Method: Linear Static and Dynamic Finite Element Analysis

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This text is geared toward assisting engineering and physical science students in cultivating comprehensive skills in linear static and dynamic finite element methodology. Based on courses taught at Stanford University and the California Institute of Technology, it ranges from fundamental concepts to practical computer implementations. Additional sections touch upon the frontiers of research, making the book of potential interest to more experienced analysts and researchers working in the finite element field. In addition to its examination of numerous standard aspects of the finite element method, the volume includes many unique components, including a comprehensive presentation and analysis of algorithms of time-dependent phenomena, plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. It also contains a systematic treatment of "weak," or variational, formulations for diverse classes of initial/boundary-value problems. Directed toward students without in-depth mathematical training, the text incorporates introductory material on the mathematical theory of finite elements and many important mathematical results, making it an ideal primer for more advanced works on this subject. Advanced undergraduate or graduate physics and engineering students with at least a working knowledge of calculus and basic physics will profit immensely from studying this outstanding volume. Table of Contents Preface A brief Glossary of Notations Part One: Linear Static Analysis Fundamental concepts; A simple one-dimensional boundary-value problem Formulation of two-and three-dimensional boundary-value problems Isoprametric elements and elementary programming concepts Mixed and penalty methods, reduced and selective integration, and sundry variational crimes The C0-Approach to plates and beams The C0-Approach to curved structural elements Part Two: Linear Dynamic Analysis Formulation of Parabolic, Hyperbolic, and Elliptic eigenvalue problems Algorithms for parabolic problems Algorithms for hyperbolic and parabolic-hyperbolic problems Solution techniques for eigenvalue problems Dlearn—A linear static and dynamic finite element analysis program References Index.