This detailed guide to the fundamentals of non-linear finite element analysis provides an engineering rather than a mathematical bias. Aimed at those who wish to use non-linear techniques to solve practical problems, it discusses the main ideas of geometric non-linearity and explores continuum mechanics, plasticity, element technology, and stability theory and solution procedures. The author also gives an introduction to recent research in this developing field. Many of the ideas considered are illustrated with a simple non-linear finite element computer program for which FORTRAN listings, data and subroutines are included. The logic can also be followed without this finer detail since these computer programs and subroutines are also represented by examples and flowcharts. The practical approach will appeal to professional engineers, researchers and senior undergraduate and graduate students in civil, structural, aeronautical and mechanical engineering.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Gewicht
ISBN-13
978-0-471-92996-3 (9780471929963)
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Schweitzer Klassifikation
Part 1 General introduction, brief history and introduction to geometric non-linearity: general introduction and a brief history; a simple example for geometric non-linearity with one degree-of-freedom; a simple example with two degres-of-freedom; special notation; list of books on (or related to) non-linear finite elements; references to early work on non-linear finite elements. part 2 A shallow truss element with fortran computer program: a shallow truss element; a set of fortran subroutines; a flow-chart and computer program for an incremental (euler) solution; a flow-chart and computer program for an iterative solution using the Newton-Raphson method; a flow-chart and computer program for an incremental/iterative solution using full or modified New-Raphson iterations; problems for analysis; special notation; references. Part 3 Truss-elements and solutions for different strain-measures: a simple example with one degree-of-freedom; solutions for a bar under unizxial tension or compression; a truss-element based on Green's strain; an alternative formulation using a rotated "engineering strain"; an alternative formulation using a rotated log-strain; an alternative "co-rotational formulation" using "engineering strain"; space-truss elements; mid-point incremental strain up-dates; fortran subroutines for deep truss elements; problems for analysis; special notation; references. Part 4 Basic continuum mechanics: stress and strain; stress-strain relationships; transformations and rotations; Green's strain; Almansi's strain; the true or Cauchy stress; summarizing the different stress and strain measures; the polar-decomposition theorem; Green and Almansi strains in terms of the principal stretches; a simple description of the 2nd Piola-Kirchhoff stress; co-rotational stresses and strains; more on constitutive laws; special notation; references. Part 5 Basic finite element analysis continua: introduction and the total Lagrangian formulation; implementation of the total Lagrangian method; the up-dated lagrangian formulation; implementation of the up-dated Lagrangian method; special notation; references. Part 6 Basic plasticity: stress up-dating - incremental or iterative strains?; the standard elasto-plastic modular matrix for an elastic/perfectly-plastic von Mises material under plan-stress; introducing hardening; von Mises plasticity in three-dimensions; integrating the "rate equations"; the consistent tangent modular matrix (or tensor); special two-dimensional situations; numerical examples; plasticity and mathematical programming; special notation; references. Part 7 Two-dimensional formulations for beams and rods: a shallow-arch formulation; a simple co-rotational element using Kirchhoff theory; a simple co-rotational element using Timoshenko beam theory; an alternative co-rotational element using Reissner's beam theory; an isoparametric degenerate-continuum approach using the total-Lagrangian formulation; special notation; references.
