Non-Linear Finite Element Analysis of Solids and Structures, by Rene de Borst, Mike A. Crisfield, Joris J. C. Remmers,

By Rene de Borst, Mike A. Crisfield, Joris J. C. Remmers, Clemens V. Verhoosel(auth.)

Built upon the 2 unique books by means of Mike Crisfield and their very own lecture notes, popular scientist Rene de Borst and his group supply a completely up to date but condensed variation that keeps and builds upon the superb popularity and attraction among scholars and engineers alike for which Crisfield's first version is acclaimed.

Together with various additions and updates, the recent authors have retained the center content material of the unique booklet, whereas bringing a higher specialise in new advancements and ideas. This variation deals the most recent insights in non-linear finite aspect expertise, together with non-linear resolution options, computational plasticity, harm mechanics, time-dependent results, hyperelasticity and large-strain elasto-plasticity.

The authors' built-in and constant variety and unrivalled engineering strategy assures this book's particular place in the computational mechanics literature.

Key features:

  • Combines the 2 earlier volumes into one seriously revised textual content with out of date fabric got rid of, a better format and up to date references and notations
  • Extensive new fabric on newer advancements in computational mechanics
  • Easily readable, engineering orientated, without extra info ordinarily textual content than essential to comprehend the concepts.
  • Pseudo-code all through makes the hyperlink among concept and algorithms, and the particular implementation.
  • Accompanied via an internet site (www.wiley.com/go/deborst) with a Python code, in response to the pseudo-code in the ebook and appropriate for fixing small-size difficulties.

Non-linear Finite point research of Solids and buildings, second variation is a vital reference for practicing engineers and researchers that could even be used as a textual content for undergraduate and graduate scholars inside of computational mechanics.

Content:
Chapter 1 Preliminaries (pages 1–29):
Chapter 2 Non?linear Finite aspect research (pages 31–62):
Chapter three Geometrically Non?linear research (pages 63–111):
Chapter four answer options in Quasi?Static research (pages 113–141):
Chapter five answer thoughts for Non?linear Dynamics (pages 143–166):
Chapter 6 harm Mechanics (pages 67–218):
Chapter 7 Plasticity (pages 219–280):
Chapter eight Time?dependent fabric versions (pages 281–304):
Chapter nine Beams and Arches (pages 305–342):
Chapter 10 Plates and Shells (pages 343–362):
Chapter eleven Hyperelasticity (pages 363–399):
Chapter 12 Large?strain Elasto?plasticity (pages 401–424):
Chapter thirteen Interfaces and Discontinuities (pages 425–440):
Chapter 14 Meshless and Partition?of?unity tools (pages 441–472):
Chapter 15 Isogeometric Finite aspect research (pages 473–507):

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Non-Linear Finite Element Analysis of Solids and Structures, Second Edition

Equipped upon the 2 unique books through Mike Crisfield and their very own lecture notes, popular scientist Rene de Borst and his workforce supply a completely up-to-date but condensed variation that keeps and builds upon the wonderful acceptance and charm among scholars and engineers alike for which Crisfield's first variation is acclaimed.

Additional info for Non-Linear Finite Element Analysis of Solids and Structures, Second Edition

Example text

3 Vectors and Tensors So far, vectors have been introduced and treated as mere mathematical tools, arrays which contain a number of scalar quantities in an ordered fashion. Nonetheless, vectors can be given a physical interpretation. Take for instance the concept of force. A force not only has a magnitude, but also has a direction. It is often of interest to know how the components of a force change if the force is represented in a different coordinate system. A translation only adds the same number to all force components.

Golub GH and van Loan CF 1983 Matrix Computations. The Johns Hopkins University Press. Noble B and Daniel JW 1969 Applied Linear Algebra. Prentice-Hall. Ortega JM 1987 Matrix Theory – A Second Course. Plenum Press. Ramsey N 1994 Literate programming simplified. IEEE Software 11, 97–105. Saad Y 1996 Iterative Methods for Sparse Linear Systems. International Thomson Publishing. 2 Non-linear Finite Element Analysis The pure displacement version of the finite element method is the most convenient spatial discretisation method for the majority of the applications of non-linear constitutive relations.

Verhoosel. © 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd. 2) 32 Non-linear Finite Element Analysis of Solids and Structures where n is the outward unit vector at the boundary of the body. 1). 1 Symmetry of the stress tensor We start the proof by considering rotational equilibrium of a body B. If tk are the components of the surface traction and if gk are the components of the gravity acceleration, we have: S eijk xj tk dS + V ρeijk xj gk dV = 0 We insert the relation between the stress vector and the stress tensor to obtain: S eijk xj σlk nl dS + V ρeijk xj gk dV = 0 with nl the components of the unit normal vector on the given plane.

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