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

http://gfem.cee.illinois.edu/papers/cmame_published.pdf

An h-p adaptive method using clouds

Isogeometric shell analysis with Kirchhoff–Love elements

1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

Computational aspects of a linear stress resultant (classical) shell theory, obtained by systematic linearization of the geometrically exact nonlinear theory, considered in Part I of this work, are examined in detail. In particular, finite element interpolations for the reference director field and the linearized rotation field are constructed such that the underlying geometric structure of the continuum theory is preserved exactly by the discrete approximation. A discrete canonical, singularity-free mapping between the five and the six degree of freedom formulation is constructed by exploiting the geometric connection between the orthogonal group (SO(3)) and the unit sphere (S2). The proposed numerical treatment of the membrane and bending fields, based on a mixed Hellinger-Reissner formulation,provides excellent results for the 4-node bilinear isoparametric element. As an example, convergent results are obtained for rather coarse meshes in fairly demanding, singularity-dominated, problems such as the classical rhombic plate test. The proposed theory and finite element implementation are evaluated through an extensive set of benchmark problems. The results obtained with the present approach exactly match previous solutions obtained with state-of-the-art implementations based on the so-called degenerated solid approach.

Richard H. MacNeal

Papers

A proposed standard set of problems to test finite element accuracy

The evolution of lower order plate and shell elements in MSC/NASTRAN

Toward a defect-free four-noded membrane element