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

The variational multiscale method—a paradigm for computational mechanics

A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations

We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian–Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-α time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.

Isogeometric fluid-structure interaction: theory, algorithms, and computations

A new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces. In the deforming-spatial-domain/space-time (DSD/ST) procedure the variational formulation of a problem is written over its space-time domain, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. Because the space-time mesh is generated over the space-time domain of the problem, within each time step, the boundary (or interface) nodes move with the boundary (or interface). Whether the motion of the boundary is specified or not, the strategy is nearly the same. If the motion of the boundary is unknown, then the boundary nodes move as defined by the other unknowns at the boundary (such as the velocity or the displacement). At the end of each time step a new spatial mesh covers the new spatial domain. For computational feasibility, the finite element interpolation functions are chosen to be discontinuous in time, and the fully discretized equations are solved one space-time slab at a time.

A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests

Space-time finite element methods are developed for classical elastodynamics. The approach employs the discontinuous Galerkin method in time and incorporates stabilizing terms of least-squares type. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Optimal error estimates are predicted, and confirmed numerically, for arbitrary combinations of displacement and velocity interpolations. The procedures developed are easily generalized to structural dynamics and a wide class of second-order hyperbolic problems.

Space-time finite element methods for elastodynamics: formulations and error estimates

Galerkin/least-squares finite-element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of streamline-upwind Petrov-Galerkin methods, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. Some numerical results for compressible Navier-Stokes flows are presented.

The Galerkin/least-squares method for advective-diffusive equations

Les algorithmes d'integration pas a pas dans le temps pour la dynamique des structures requierent un vecteur acceleration initial, en addition aux vecteurs deplacement et vitesse. Ce vecteur acceleration peut etre calcule en resolvant les equations du mouvement a un temps initial, tandis qu'un vecteur acceleration initial, tronque est obtenu en prenant les valeurs des accelerations a zero

An error analysis of truncated starting conditions in step‐by‐step time integration: Consequences for structural dynamics

Two unconditionally stable implicit methods with controllable numerical dissipation are compared, namely the improved version of the Hilber-Hughes-Taylorα-method and the recently developed Θ 1 - method . The accuracy, spectral properties and implementational aspects in nonlinear problems are discussed. Both methods maintain second order accuracy in the presence of viscous physical damping and numerical dissipation. They are overshooting-free and theer spurious roots vanish for small time steps. Applied to nonlinear problems, two alternative implementation can be employed. Both methods are similar in the first implementation, whereas differences occur in the second.

G. M. Hulbert

Papers

Space-time finite element methods for elastodynamics: formulations and error estimates

The Galerkin/least-squares method for advective-diffusive equations

An error analysis of truncated starting conditions in step‐by‐step time integration: Consequences for structural dynamics

Extended comparison of the Hilber-Hughes-Taylor α-method and the φ 1 -method