Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons

78 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A scaled boundary polygon formulation for elasto-plastic analyses (2014, methodology): “The shape functions of the polygon elements reported in [1, 2, 3, 4, 11, 12] are rational polynomials and require special integration techniques e.”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, background): “, concave ones), harmonic shape functions [15, 16, 17] and max-entropy shape functions [18, 19, 20] need to be computed numerically at the quadrature points element by element.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “On a different path, discrete bonded particle methods have been developed and coupled with FEM for similar applications (Beissel et al. 2006; Johnson 1994; Johnson et al. 1986, 2000, 2002, 2013) [for a review, see (Johnson 2011)].”
Consistent element‐free Galerkin method (2014, background): “For example, the maximum entropy approximation introduced by Sukumar [17] satisfies a weak Kronecker delta property on boundaries, and thus, the essential boundary conditions can be directly enforced [18, 19].”