Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Sá, J. M. A. César de; Jorge, R.M. Natal; Valente, R. A. F.; Areias, P.

doi:10.1002/nme.360

Cited by 77 publications

(62 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this purpose, an analysis of the efficiency of the EAS method using the framework of the subspace analysis is now underway and will be reported in future publications. This method was initially developed by César de Sà and Owen [54] for 2D elements and successfully applied later for 2D plane strain quadrilateral in [55,56], shell elements [43,48], 3D solid-shell elements by Alves de Sousa et al [25] and Caseiro et al [40].…”

Section: Discussionmentioning

confidence: 99%

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

Bettaieb

Sena

Sousa

et al. 2015

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

In the present paper, a detailed description of the formulation of the new SSH3D solid-shell element is presented. This formulation is compared with the previously proposed RESS solid-shell element [1,2]. Both elements were recently implemented within the LAGAMINE in-house research finite element code. These solid-shell elements possess eight nodes with only displacement nodal degrees of freedom (DOF). In order to overcome various locking pathologies, the SSH3D formulation employs the well known Enhanced Assumed Strain (EAS) concept originally introduced by Simo and Rifai [3] and based on the Hu-Veubeke-Washizu variational principle combined with the Assumed Natural Strain (ANS) technique based on the work of Dvorkin and Bathe [4]. For the RESS solid-shell element, on the other hand, only the EAS technique is used with a Reduced Integration (RI) Scheme. A particular characteristic of these elements is their special integration schemes, with an arbitrary number of integration points along the thickness direction, dedicated to analyze problems involving non-linear through-thickness distribution (i.e. metal forming applications) without requiring many element layers. The formulation of the SSH3D element is also particular, with regard to the solid-shell elements proposed in the literature, in the sense that it is characterized by an in-plane full integration and a large variety in terms of (i) enhancing parameters, (ii) the ANS version choice and (iii) the number of integration points through the thickness direction. The choice for these three parameters should be adapted to each problem so as to obtain accurate results and to keep the calculation time low. Numerous numerical examples are performed to investigate the performance of these elements. These examples illustrate the reliability and the efficiency of the proposed formulations in various cases including linear and non-linear problems. SSH3D element is more robust thanks to the various options proposed and its full in-plane integration scheme, while RESS element in more efficient from a computational point of view.

show abstract

Section: Discussionmentioning

confidence: 99%

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

Bettaieb

Sena

Sousa

et al. 2015

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

show abstract

“…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].…”

Section: Introductionmentioning

confidence: 93%

“…The enhanced terms are judiciously chosen and directly included into the convective transverse shear strain field, in order to enlarge the subspace of null (transverse shear strain) energy modes and, consequently, retain the Kirchhoff-Koiter conditions in situations where a pure displacement-based formulation would fail. In this sense, the following analysis relies on the linear shell formulation presented in detail by the authors in Reference [29], although the finite element formulated here is more simple than those introduced in the last reference.…”

Section: General Aspectsmentioning

confidence: 99%

“…For the specific case of shell elements, the likelihood of transverse shear locking to happen was related to the ability (or not) of a given formulation to successfully reproduce the correct solution by naturally providing enough components to the subspace basis [29]. The main advantage of this subspace analysis was that its validity remains unaltered irrespective of the loading and boundary conditions applied to a given element, thus being a characteristic of a given formulation.…”

Section: Introductionmentioning

confidence: 99%

“…Instead of performing a replacement of transverse shear strain terms to correct the element formulation, the EAS method was then used to additively improve the transverse shear strain field coming from the displacement-based formulation. This has led to a set of shell elements with distinct number of internal variables and with no transverse shear locking for a variety of linear test cases [29]. A preliminary study on large rotation problems, while keeping elastic strains, was performed by the authors in Reference [32] with encouraging results.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Valente

Parente

Jorge

et al. 2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn this work, a previously proposed Enhanced Assumed Strain (EAS) finite element formulation for thin shells is revised and extended to account for isotropic and anisotropic material non-linearities. Transverse shear and membrane-locking patterns are successfully removed from the displacement-based formulation. The resultant EAS shell finite element does not rely on any other mixed formulation, since the enhanced strain field is designed to fulfil the null transverse shear strain subspace coming from the classical degenerated formulation. At the same time, a minimum number of enhanced variables is achieved, when compared with previous works in the field. Non-linear effects are treated within a local reference frame affected by the rigid-body part of the total deformation. Additive and multiplicative update procedures for the finite rotation degrees-of-freedom are implemented to correctly reproduce mid-point configurations along the incremental deformation path, improving the overall convergence rate. The stress and strain tensors update in the local frame, together with an additive treatment of the EAS terms, lead to a straightforward implementation of non-linear geometric and material relations. Accuracy of the implemented algorithms is shown in isotropic and anisotropic elasto-plastic problems.

show abstract

Non‐linear analysis of shells with arbitrary evolving cracks using XFEM

Areias

Belytschko

2004

Numerical Meth Engineering

158

View full text Add to dashboard Cite

SUMMARYA new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method. The method is valid for completely non-linear problems. Through-the-thickness cracks in sandwich shells are considered. An exact shell kinematics is presented, and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition. To avoid locking, an enhanced strain formulation is proposed for the 4-node cracked shell element. A finite strain plane stress constitutive model based on the logarithmic corotational rate is employed. A cohesive zone model is introduced which embodies the special characteristics of the shell kinematics. Stress intensity factors are calculated for selected problems and crack propagation problems are solved.

show abstract

Development of shear locking‐free shell elements using an enhanced assumed strain formulation

Cited by 77 publications

References 32 publications

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

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

Non‐linear analysis of shells with arbitrary evolving cracks using XFEM

Contact Info

Product

Resources

About