Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory
01 Jun 1978-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 45, Iss: 2, pp 371-374
About: This article is published in Journal of Applied Mechanics.The article was published on 1978-06-01. It has received 343 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.
Citations
More filters
17 Aug 2012
TL;DR: De Borst et al. as mentioned in this paper present a condensed version of the original book with a focus on non-linear finite element technology, including nonlinear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.
Abstract: 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.
2,568 citations
TL;DR: This is a tutorial article that reviews the use of partitioned analysis procedures for the analysis of coupled dynamical systems using the partitioned solution approach for multilevel decomposition aimed at massively parallel computation.
806 citations
TL;DR: Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods.
Abstract: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.
794 citations
TL;DR: Numerical solution methods surveyed here will be of much use to practicing computational/finite element/structural engineers working in the area of dynamics of structures.
427 citations
TL;DR: In this paper, a Petrov-Galerkin finite element formulation for first-order hyperbolic systems of conservation laws with particular emphasis on the compressible Euler equations is presented.
410 citations