New enhanced strain elements for incompressible problems

Abstract

A new enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four-node finite element, is initially presented. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analysing at the element level the deformation modes which form a basis for the incompressible subspace the extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently another new element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and non-linear situations.

An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

“…Unfortunately, the reduced integration often causes the instability due to rank deficiency and results in zero-energy modes. It is therefore many various improvements of formulations as well as numerical techniques have been developed to overcome the shear locking phenomenon and to increase the accuracy and stability of the solution such as mixed formulation/hybrid elements [13][14][15][16][17][18][19][20][21][22][23], Enhanced Assumed Strain (EAS) methods [24][25][26][27][28] and Assumed Natural Strain (ANS) methods [29][30][31][32][33][34][35][36][37][38]. Recently, the discrete shear gap (DSG) method [39] which avoids shear locking was proposed.…”

On the Equivalent of Mixed Element Formulations and the Concept of Reduced Integration in Large Deformation Problems

“…Departing from Simo & Rifai [67], many new element formulations were derived, refer in the small deformation case to Andelfinger et al [2], Andelfinger & Ramm [1], Hueck h Wriggers [28], Piltner & Taylor [55], Korelc & Wriggers [37,39], Bischoff et al [13], Cesar de Sa & Natal Jorge [16], Kasper & Taylor [32], Perego [51], Taylor [75] [41].…”

Enhanced transverse shear strain shell formulation applied to large elasto‐plastic deformation problems

“…Departing from the conventional degenerated approach applied to bilinear (four-node) fully integrated shell elements, a complete analysis of the null transverse shear strain subspace was performed in Reference [29]. Along with the present work, this reference points to previous developments by the authors in EASbased two dimension, shell and solid-shell finite elements technology [30][31][32][33][34][35][36].…”