Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 64, Issue 15, Pages 2039-2071Publisher
WILEY
DOI: 10.1002/nme.1436
Keywords
generalized node; partition of unity; tetrahedron; triangle; generalized finite-element method; free mesh method
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The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright (c) 2005 John Wiley & Sons, Ltd.
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