Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient…

By G. Engel, Krishna C. Garikipati, Thomas J. R. Hughes, Mats G. Larson, Luca Mazzei, Robert Taylor. 2002

509 citations recorded by the source corpus.

Subfields: Computational Mechanics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4c338d6a772207d56432dacda08c3a46bf033cfd

How researchers see this paper

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

In Computational Mechanics

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A new finite element method for strain gradient theories and applications to fracture analyses (2006, background): “…1996; Wei and Hutchinson, 1997; Zhang et al., 1998; Huang et al., 1999; Shi et al., 2000), as well as the plate (or beam) bending problem (Engel et al., 2002), it is still important and a tough challenge to develop an effective finite element methods for the strain gradient theories…”
Poincaré–Friedrichs Inequalities for Piecewise H 2 Functions (2004, methodology): “Fourth order problems can also be solved by the C0 interior penalty method (Brenner and Sung, 2003; Engel et al., 2002).”
A new discontinuous Galerkin method for Kirchhoff–Love shells (2008, background): “In the resulting one-field formulations, the jump discontinuities can be related to the unknown fields and to their derivatives [6], or to the derivatives alone [5, 7].”
A hybridizable discontinuous Galerkin method for linear elasticity (2009, methodology): “In particular, the development of the DG methods for elliptic problems includes the unifying analysis of DG methods for second-order problems [7], the introduction of DG methods for linear elasticity [8], for incompressible and near incompressible elastic materials [9, 10], for Timoshenko beams [11]”
Discontinuous Galerkin methods for non‐linear elasticity (2006, background): “, [19, 27, 26, 39, 1, 30, 16, 3, 40, 12]) can be found in [2], which provides a common framework for most proposed methods.”
C0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains (2005, methodology): “Our work is motivated by the recent paper [ 20 ], where consistent”
Computational homogenization for the multi-scale analysis of multi-phase materials (2002, methodology): “A more sophisticated method is the effective medium approximation, as established by Eshelby (1957) and further developed by a number of authors, see, e.g. Hashin (1962); Budiansky (1965); Mori and Tanaka (1973).”