Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene 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.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.

Computational methods in Lagrangian and Eulerian hydrocodes

The variational formulation and computational aspects of a three-dimensional finite-strain rod model, considered in Part I, are presented. A particular parametrization is employed that bypasses the singularity typically associated with the use of Euler angles. As in the classical Kirchhoff-Love model, rotations have the standard interpretation of orthogonal, generally noncommutative, transformations. This is in contrast with alternative formulations proposed by Argyris et al. [5–8], based on the notion of semitangential rotation. Emphasis is placed on a geometric approach, which proves essential in the formulation of algorithms. In particular, the configuration update procedure becomes the algorithmic counterpart of the exponential map. The computational implementation relies on the formula for the exponential of a skew-symmetric matrix. Consistent linearization procedures are employed to obtain linearized weak forms of the balance equations. The geometric stiffness then becomes generally nonsymmetric as a result of the non-Euclidean character of the configuration space. However, complete symmetry is recovered at an equilibrium configuration, provided that the loading is conservative. An explicit condition for this to be the case is obtained. Numerical simulations including postbuckling behavior and nonconservative loading are also presented. Details pertaining to the implementation of the present formulation are also discussed.

A three-dimensional finite-strain rod model. Part II: Computational aspects

A three-dimensional finitestrain rod model. part II. Computational aspects

An improved algorithm is presented for integrating rate constitutive equations in large-deformation analysis. The algorithm is shown to be ‘objective’ with respect to large rotation increments.

Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis

An element-by-element solution algorithm for problems of structural and solid mechanics

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

A new type of element-by-element implicit algorithm is proposed for heat conduction analysis. The algorithm is shown to be unconditionally stable, but does not involve a global coefficient matrix. Consequently, there are considerable operation count advantages over typical implicit schemes. Numerical test examples indicate the good behavior of the method. It is believed that the new approach will enable large heat conduction calculations to be performed much more economically than heretofore and is suggestive of related developments in other areas of engineering and the physical sciences.

James Winget

Papers

Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis

An element-by-element solution algorithm for problems of structural and solid mechanics

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

Element-by-Element Implicit Algorithms for Heat Conduction

A profile solver for specially structured symmetric-unsymmetric equation systems