Smooth, second order, non‐negative meshfree approximants selected by maximum entropy

By C. J. Cyron, Marino Arroyo, Magdalena Ortiz. 2009

86 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/32fd750d0143287aab1349e5518f478c6c214cbc

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A generalized approximation for the meshfree analysis of solids (2011, methodology): “[32] introduced a gap function to allow errors in the second-order constraint while maintaining the convex condition and weak Kronecker-delta property at the boundaries.”
Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment (2013, background): “[31] extended these schemes to second-order maximum-entropy approximation schemes.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “Recently, higher order versions of maximum entropy approximations have been developed (Cyron et al. 2009; González et al. 2010; Rosolen et al. 2013; Sukumar 2013).”
Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory (2013, background): “Thanks to advanced numerical approaches such as finite elements (FEM) [7], smoothed finite elements (SFEM) [16, 17], extended finite elements [18, 19], meshfree methods [20, 21, 22] and extended meshfree methods [23, 24], we can solve effectively more complicated problems in practice.”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, methodology): “The shape functions are also very smooth (C∞), which results in an accurate numerical integration with a relatively low number of integration points, especially for Gauss-Legendre quadrature [5, 8, 10].”
On the optimum support size in meshfree methods: A variational adaptivity approach with maximum‐entropy approximants (2010, background): “Recently, the informationtheoretic concept of maximum-entropy (max-ent) has been put forth to develop meshfree first-order and second-order approximants [6, 7], and polygonal approximants [8].”