Hybrid and Incompatible Finite Element Methods

By T. Pian, Chang-chun Wu. 2005

148 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/4a453c55651d73275dfa134a1fd4abc537478836

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In Control and Systems Engineering

In Mechanical Engineering

Citations in the corpus

A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS (2008, background): “Many efforts have been made in resolving this issue, especially in the area of hybrid FEM formulations (see, e.g. [Pian and Wu (2006)]).”
A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements (2008, methodology): “To this end, we start with the modified Hellinger–Reissner variational principle [28] with the assumed strain vector ~e and displacements u as independent field variables in which note that ~e 1⁄4 e for NeY-shaped areas XðaÞ e of elements: Uðu;~eÞ 1⁄4 Z”
A novel FEM by scaling the gradient of strains with factor α (αFEM) (2009, methodology): “For the first drawback, many assumed strain or mixed models have been proposed in the past decades to reduce the stiffness of the standard FEM model [2,8,22,24,28,29,31,32,34,35,37,40,42].”
A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, unknown): “To this end, we start with the modified Hellinger–Reissner variational principle with the assumed strain vector ẽ and displacements u as independent field variables [28] U (u, ẽ)=− ∫ 1 2 ẽDẽd + ∫ (Dẽ)(∇su)d − ∫ uTbd − ∫”
An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells (2018, unknown): “ε(ξ, η) = T(ξ, η) ⎢⎢⎢⎣ ē Ēζζ ?̄? ?̄? ⎥⎥⎥⎦ , (32)”
Theoretical aspects of the smoothed finite element method (SFEM) (2007, unknown): “VARIATIONAL PRINCIPLE FOR SFEM In this section, the Galerkin weak form for SFEM is established from the Hu–Washizu three-field variational principle [12]: U (u, ẽ, r)= ∫ 1 2 ẽDẽ d − ∫ rTẽ d + ∫ r(∇Su) d − ∫ uTb d − ∫”
EDGE-BASED SMOOTHED POINT INTERPOLATION METHODS (2008, background): “Many efforts have been made to solve the overly-stiff problem of a compatible FEM model, such as the development of hybrid FEM formulations [Pian and Wu (2006)].”
An unsymmetric 4‐node, 8‐DOF plane membrane element perfectly breaking through MacNeal's theorem (2015, background): “N B Q E 4 [1 9] 21 .”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “To this end, we start with the modified Hellinger–Reissner variational principle with the assumed strain vector ~e and displacements u as independent field variables [24]:”
Advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements (2017, methodology): “For the contravariant stress components, we use the ‘optimal’ interpolation proposed by Pian and Tong [13, 49] defined as N Œ D N Œ ˇe (14d) where ˇe collects the 18 stress parameters, and the interpolation functions N Œ are given in [13, 49].”