Large Strain Finite Element Method
Large Strain Finite Element Method

Author: Antonio A. Munjiza

Publisher: John Wiley & Sons

Published: 2015-02-16

Total Pages: 486

ISBN-13: 1118405307

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An introductory approach to the subject of large strains and large displacements in finite elements. Large Strain Finite Element Method: A Practical Course, takes an introductory approach to the subject of large strains and large displacements in finite elements and starts from the basic concepts of finite strain deformability, including finite rotations and finite displacements. The necessary elements of vector analysis and tensorial calculus on the lines of modern understanding of the concept of tensor will also be introduced. This book explains how tensors and vectors can be described using matrices and also introduces different stress and strain tensors. Building on these, step by step finite element techniques for both hyper and hypo-elastic approach will be considered. Material models including isotropic, unisotropic, plastic and viscoplastic materials will be independently discussed to facilitate clarity and ease of learning. Elements of transient dynamics will also be covered and key explicit and iterative solvers including the direct numerical integration, relaxation techniques and conjugate gradient method will also be explored. This book contains a large number of easy to follow illustrations, examples and source code details that facilitate both reading and understanding. Takes an introductory approach to the subject of large strains and large displacements in finite elements. No prior knowledge of the subject is required. Discusses computational methods and algorithms to tackle large strains and teaches the basic knowledge required to be able to critically gauge the results of computational models. Contains a large number of easy to follow illustrations, examples and source code details. Accompanied by a website hosting code examples.

A Finite Element Formulation for Problems of Large Strain and Large Displacement
A Finite Element Formulation for Problems of Large Strain and Large Displacement

Author: Hugh D. Hibbitt

Publisher:

Published: 1969

Total Pages: 36

ISBN-13:

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An incremental and piecewise linear finite element theory is developed for the large displacement, large strain regime with particular reference to elastic-plastic behavior in metals. The resulting equations, though more complex, are in a similar form to those previously developed for large displacement, small strain problems, the only additional term being an initial load stiffness matrix which is dependent on current loads. This similarity in form means that existing nonlinear general purpose programs may easily be extended to include finite strains. A large displacement, small strain formulation (as applicable to problems of structural stability) is obtained from this theory by assuming that changes in length of line elements and relative rotation of orthogonal line elements are negligible compared to unity. The simplified equations are in essential agreement with previous formulations in the literature. The only difference which is observed is the persistence of the initial load stiffness matrix, which may be significant in some cases. (Author).

Nonlinear Finite Element Analysis of Solids and Structures
Nonlinear Finite Element Analysis of Solids and Structures

Author: René de Borst

Publisher: John Wiley & Sons

Published: 2012-07-25

Total Pages: 481

ISBN-13: 1118376013

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Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations Extensive new material on more recent developments in computational mechanics Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.