Non‐Linear Finite Element Analysis of Solids and Structures, Volume 1

Abstract

The finite element method has emerged as the primary tool in computational solid mechanics and with it has come an increased demand for modern texts dealing with delicate issues, such as the numerical implementation of non-linear analysis. Recently, the extension of M. Crisfield's book Volume I: Non-¸inear finite element analysis of solids and structures, Volume II: Non-linear finite element analysis of solids and structures; advanced topics, has appeared in the market. This book fills an important gap in pedagogic treatment of the application of FEM to non-linear hyperelastic and plastic solids undergoing finite deformations. As with the earlier volume, an engineering approach is adopted in contrast to a strict mathematical development. The emphasis is on numerical implementation of large deformation theories in the analysis of a solid continua. A main feature of the book is its concise coverage of both the necessary back-

On the unimportance of constitutive models in computing brain deformation for image-guided surgery

“…We used the explicit (central difference) time integration (Crisfield 1998) as it requires no iterations and its effectiveness in brain deformation computation was demonstrated by Wittek et al (2007).…”

Analysis of Snap Behaviour of Shallow Cylindrical Shells Using the Finite Strip Method

“…Snap-through is observed when structure reaches load limit point, and snap-back when the structure reaches displacement limit point. Although not common in practice, this behaviour is experimentally proved [1].…”

Computational Assessment of the Progressive Collapse of a Five Storey Structure Considering Two Different Building Codes

“…A corotational formulation, as presented in Crisfield [4] and Batini [18], is a reinterpretation of the deformation of a beam element or, in the most general case, a tridimensional body. This reinterpretation consists in not using the same global reference system in which the structure is inserted for the calculation of strain and displacements of each element but to assume individual local reference systems for these elements instead (Fig.…”

“…Technical information on how the internal force vector and the stiffness matrix of the finite element are derived can be found in [4] and [18].…”

“…strain rate dependent elastic-plastic behavior, under dynamic loading. Geometrically nonlinear effects (allowing for the representation of catenary effects) are here included in the multiscale framework and investigated by means of a corotational formulation [4]. The resulting numerical tool is presented in Section 3.…”