Non-Linear Finite Element Analysis of Solids and Structures: Basics: Disk Vol 1

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.