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# J. Tinsley OdenAssociate Vice President for ResearchDirector, Institute for Computational Engineering and SciencesCockrell Family Regents' Chair in Engineering No. 2Peter O'Donnell Jr. Centennial Chair in Computing SystemsProfessor of Aerospace Engineering and Engineering MechanicsProfessor of Computer ScienceProfessor of Mathematics

### Books

Cover | Title | Author | Abstract |
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Contact Problems in Elasticity : A Study of Variational Inequalities and Finite Element Methods (SIAM Studies in Applied and Numerical Methematics) (Siam Studies in Applied Mathematics) | Oden, J. Tinsley | The contact of one deformable body with another lies at the heart of almost every | |

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. |
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Finite Elements: An Introduction. Volume I | Oden, J. Tinsley | This book provides an introduction to the finite element method presented as a general approach | |

This book provides an introduction to the finite element method presented as a general approach to the approximation of solutions to boundary- and initial -value problems involving linear partial differential equations. The discussion beginning with the notion of weak forms of two-point boundary -value problems, trial and test function spaces, with an introduction to elementary properties of H1 and L2 spaces, the direct stiffness method of matrix assembly, finite element families, and extensions to two-dimensional elliptic problems. A chapter on the development of computer programs to implement the method , together with a code for one-dimensional problems is provided. A brief account of applications to time -dependent parabolic problems is included. Extensive examples and exercises are presented. |
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A Posterori Error Estimation in Finite Element Analysis | Oden, J. Tinsley | An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on | |

An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on a posteriori error estimation for finite element approximation in mechanics and mathematics. It emphasizes methods for elliptic boundary value problems and includes applications to incompressible flow and nonlinear problems. Recent years have seen an explosion in the study of a posteriori error estimators due to their remarkable influence on improving both accuracy and reliability in scientific computing. In an effort to provide an accessible source, the authors have sought to present key ideas and common principles on a sound mathematical footing. Topics covered in this timely reference include: - Implicit and explicit a posteriori error estimators
- Recovery-based error estimators
- Estimators, indicators, and hierarchic bases
- The equilibrated residual method
- Methodology for the comparison of estimators
- Estimation of errors in quantities of interest
A Posteriori Error Estimation in Finite Element Analysis is a lucid and convenient resource for researchers in almost any field of finite element methods, and for applied mathematicians and engineers who have an interest in error estimation and/or finite elements. |
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An Introduction to the Mathematical Theory of Finite Elements | Oden, J. Tinsley | This introduction to the basic mathematical theory of the finite element method is geared toward | |

This introduction to the basic mathematical theory of the finite element method is geared toward readers with limited mathematical backgrounds. Its coherent demonstrations explain the use of these techniques in developing the theory of finite elements, with detailed proofs of the major theorems and numerous examples. 1976 edition. |
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Finite Elements of Nonlinear Continua | Oden, J. Tinsley | This text extends applications of the finite element method from linear problems in elastic structures | |

This text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. Its general and unified treatment of theory and applications emphasizes nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. 1972 edition. |
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Applied Functional Analysis, Second Edition | Oden, J. Tinsley | Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of | |

Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources. |
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An Introduction to Mathematical Modeling: A Course in Mechanics | Oden, J. Tinsley | A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An | |

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: -
Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations -
Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles -
Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics
Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics. |
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Applied Functional Analysis (Computational Mechanics and Applied Mathematics) | Oden, J. Tinsley | Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated | |

Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated functional analysis. This text has few mathematical prerequisites and provides the fundamental concepts and therorems essential to mathematical analysis and modeling |