The Finite Element Method: Its Basis and Fundamentals

By O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. 2005

3,310 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2b5e14c64308e78cd6d5187af7d1a90a3a9a19d8

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Citations in the corpus

Overview of modelling and simulation of metal powder bed fusion process at Lawrence Livermore National Laboratory (2015, methodology): “Interested readers can find more information in Hughes(51) and Zienkiewicz et al.(52) The coupling of the thermal and mechanical problems was achieved using a staggered operator split algorithm.”
Comparison of the absolute nodal coordinate and geometrically exact formulations for beams (2014, unknown): “Note that textbooks detailing the fundamentals of the finite element method [10, 11, 36] recommend to use the lowest possible order of derivative in the strain-displacement relationships of structural mechanics elements; higher-order derivatives lead to lower accuracy and higher continuity requireme”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, unknown): “, [16–19]), have been extended to FPDEs.”
FEAP - - A Finite Element Analysis Program (2011, background): “10a) and introducing Voigt notation yields(1) Details on shape functions and basic finite element schemes uses may be found in References [2] and [3].”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, background): “In this case, it is well-known that general constant strain states have to be reproduced so that the optimal convergence rate can be achieved [77].”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, background): “The inability to represent arbitrary bivariate functions on general quadrilateral meshes, stiffening due to element distortion, and its poor performance for constrained media problems are some of the deficiencies of the serendipity element [60].”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “The penalty method, see for instance [23] or [24], enjoys great popularity in practice because of its simple implementation, and in that, the size of the equation system remains unaltered.”
A domain decomposition approach to implementing fault slip in finite‐element models of quasi‐static and dynamic crustal deformation (2013, methodology): “Solid Earth, 118, 3059–3079, doi:10.1002/jgrb.50217.”