A Parametric Study for Four Node Bilinear EAS Shell Elements

2010 ◽  
Vol 26 (4) ◽  
pp. 431-438
Author(s):  
Cengiz Polat
Keyword(s):  
Variational Principle ◽  
Transverse Shear ◽  
Strain Field ◽  
Shell Element ◽  
Shell Structures ◽  
Shear Locking ◽  
Shell Elements ◽  
Assumed Strain ◽  
Dependent Strain ◽  
Transverse Shear Locking

ABSTRACTA locking free formulation of 4-node bilinear shell element and its application to shell structures is demonstrated. The Enhanced Assumed Strain (EAS) method based on three-field variational principle of Hu-Washizu is used in the formulation. Transverse shear locking and membrane locking are circumvented by means of enhancing the displacement-dependent strain field with extra assumed strain field. Several benchmark shell problems are analyzed.

scholarly journals A Family of C0 Quadrilateral Plate Elements Based on the Refined Zigzag Theory for the Analysis of Thin and Thick Laminated Composite and Sandwich Plates

2019 ◽  
Vol 3 (4) ◽  
pp. 100 ◽  
Author(s):  
Di Sciuva ◽  
Sorrenti
Keyword(s):  
Transverse Shear ◽  
Laminated Composite ◽  
Thin Plates ◽  
Sandwich Plates ◽  
Shear Locking ◽  
Reduced Integration ◽  
Quadrilateral Plate ◽  
Plate Elements ◽  
Transverse Shear Locking ◽  
Zigzag Theory

The present work focuses on the formulation and numerical assessment of a family of C0 quadrilateral plate elements based on the refined zigzag theory (RZT). Specifically, four quadrilateral plate elements are developed and numerically tested: The classical bi-linear 4-node element (RZT4), the serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c). To assess the relative merits and drawbacks, numerical tests on bending (maximum deflection and stresses) and free vibration analysis of laminated composite and sandwich plates under different boundary conditions and transverse load distributions are performed. Convergences studies with regular and distorted meshes, transverse shear-locking effect for thin and very thin plates are carried out. It is concluded that the bi-linear 4-node element (RZT4) has performances comparable to the other elements in the range of thin plates when reduced integration is adopted but presents extra zero strain energy modes. The serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c) show remarkable performance and predictive capabilities for various problems, and transverse shear-locking is greatly relieved, at least for aspect ratio equal to 5 × 102, without using any reduced integration scheme. Moreover, RZT4c has well-conditioned element stiffness matrix, contrary to RZT4 using reduced integration strategy, and has the same computational cost of the RZT4 element.

Locking Behavior of Isoparametric Curved Beam Finite Elements

1995 ◽  
Vol 48 (11S) ◽  
pp. S25-S29 ◽  
Author(s):  
Miguel Luiz Bucalem ◽  
Klaus-Ju¨rgen Bathe
Keyword(s):  
Shell Element ◽  
Beam Element ◽  
Curved Beam ◽  
Shear Locking ◽  
Shell Elements ◽  
One Dimensional ◽  
Curved Beam Element ◽  
The One ◽  
Insight Into ◽  
The Continuum

We present a study of the membrane and shear locking behavior in an isoparametric curved beam element. The objective is to gain insight into the locking phenomenon, specially membrane locking, of continuum based degenerated shell elements. This is possible since the isobeam element is the one-dimensional analogue of the continuum based shell element. In this context, reduced integration and mixed interpolation schemes are briefly examined. Such a study can be a valuable aid when developing new shell elements.

A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains

1986 ◽  
Vol 53 (2) ◽  
pp. 278-290 ◽  
Author(s):  
K. C. Park ◽  
G. M. Stanley
Keyword(s):  
Shell Element ◽  
Benchmark Problems ◽  
Integration Rule ◽  
Shell Elements ◽  
Curvature Effects ◽  
Point Integration ◽  
Membrane Bending ◽  
Transverse Shear Locking ◽  
Natural Coordinate ◽  
Membrane Strain

A curved C0 shell element is presented, which corrects several deficiencies in existing quadratic shell elements. The improvements realized in the present element include rank sufficiency without transverse shear locking, consistent membrane strain interpolation that admits inextensional bending without reduced integration, and adequate representation of curvature effects to capture the important membrane-bending coupling. The element can be constructed either by a nine-point integration rule or by a four-point integration rule with the proper rank compensating terms. Numerical experiments with the present element on several benchmark problems indicate that the element yields accurate and reliable solutions without any ostensible deficiency. The element is recommended for production analysis of shell structures.

Resolution of Defects in Degenerated Shell Elements Through Modification of Gauss Integration

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1877-1883 ◽  
Author(s):  
Y. D. Kwon ◽  
N. S. Goo ◽  
B. S. Lim
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Shell Element ◽  
Zero Energy ◽  
Integration Rule ◽  
Shell Elements ◽  
Reduced Integration ◽  
Stiffness Matrices ◽  
Assumed Strain ◽  
Degenerated Shell Element

In this paper, the modified Gauss integration method is developed to eliminate the shear and membrane locking phenomena of the degenerated shell element. The behavior of the element based on the Mindlin/Reissner theory in plates and shells sometimes causes a problem. In displacement-based shell elements, the full integration of stiffness matrices leads to a 'locking' or over-stiff behavior. The selective or reduced integration procedures may often overcome these difficulties, while overstiff solutions may still occur in the analysis with a highly constrained boundary. Except for the six zero-energy modes associated with shell rigid body movements, during the reduced integration of the stiffness matrices, many extra zero spurious energy modes are introduced due to reduced integration. This is a serious defect of degenerated shell element. In previous studies, several methods such as the addition of nonconforming displacement modes, an assumed strain method, and hybrid and mixed elements have been introduced in an attempt to overcome these difficulties. In this study a newly modified Gauss integration method combining both a selective and a weight-modified integration is suggested. Numerical experiments show that the new selective integration and weight-modified integration rule is very effective in eliminating the shear and membrane locking in static and modal analyses, and removes spurious zero-energy modes as well. Also, the effectiveness of proposed shell element is tested by applying it to some example problems. We solved post-buckling problem by the Riks arc-length method and dynamic problem by the Newmark's time integration method, as well as static problems.

scholarly journals EAS 3D triangular and quadrangular shell elements

2010 ◽  
pp. 205-215
Author(s):  
Philippe Jetteur ◽  
Philippe Pasquet
Keyword(s):  
Degrees Of Freedom ◽  
Shell Element ◽  
Element Formulation ◽  
Shell Elements ◽  
Assumed Strain ◽  
Definition Of ◽  
3D Solid ◽  
Assumed Strain Method ◽  
Internal Degrees Of Freedom

A new 3D solid shell element is developed in SAMCEF™ code. The purpose of this element is to make the meshing easier starting from a 3D definition of the structure, it is not necessary to extract the mean surface of the shell. Here, we are not concerned by the meshing; we only are concerned by the element formulation. In order to improve the quality of the results, we add internal degrees of freedom as suggested by Simo and co-authors. We use the Enhanced Assumed Strain method. A special handling of the transverse shear is performed in order to pass successfully the plate patch test (constant bending) and to avoid shear locking. The formulation is based on the work of Bathe and Dvorkin for classical shell. The element has been developed in linear and non-linear analysis; it can be a mono or multilayer element.

Consequences of Using the Plane Stress Assumption for Damage Calculations in Crash Analyses

2014 ◽  
Author(s):  
Carey L. Walters ◽  
Lars O. Voormeeren
Keyword(s):  
Plane Stress ◽  
Stress Triaxiality ◽  
Shell Element ◽  
Element Model ◽  
Offshore Structures ◽  
Two Dimensions ◽  
Shell Structures ◽  
Planar Case ◽  
Lode Parameter ◽  
Shell Elements

Simulation of failure in plate materials (represented as shell elements) is critical for the correct determination of crash performance of ships and offshore structures. This need has traditionally been filled with failure loci that give the failure strain in terms of stress triaxiality. In recent years, a third dimension (Lode parameter) has been introduced in the form of the Modified Mohr Coulomb failure criterion and Lode parameter adjusted Gurson-type models. This development introduces ambiguity for shell structures, in which only two dimensions are represented. The typical way of addressing this is to assume that shell structures fail in plane stress, thus reducing the problem back to 2-D. However, the assumption of plane stress is violated as soon as necking begins, causing different stress triaxialities and Lode parameters than would be expected from the planar case. More importantly, the inhomogenous necked region is then homogenized over the entire shell element. In this paper, the consequences of the through-thickness plane stress assumption are assessed through a finite element model of a plate that is subjected to a far-field stress.

scholarly journals Development of shear locking-free shell elements using an enhanced assumed strain formulation

2001 ◽  
Vol 53 (7) ◽  
pp. 1721-1750 ◽  
Author(s):  
José M. A. César de Sá ◽  
Renato M. Natal Jorge ◽  
Robertt A. Fontes Valente ◽  
Pedro M. Almeida Areias
Keyword(s):  
Shear Locking ◽  
Shell Elements ◽  
Enhanced Assumed Strain ◽  
Assumed Strain ◽  
Strain Formulation

Four-Node Quadrilateral Shell Element MITC4

2016 ◽  
Vol 825 ◽  
pp. 99-104 ◽  
Author(s):  
Edita Dvořáková ◽  
Bořek Patzák
Keyword(s):  
Three Dimensional ◽  
Shell Element ◽  
Thin Shells ◽  
Element Formulation ◽  
Finite Element Code ◽  
Shear Locking ◽  
Benchmark Problem ◽  
Quadrilateral Element ◽  
Shell Elements ◽  
Continuum Description

Four-node quadrilateral element MITC4 applicable to both thick and thin shells is presented. The element formulation starts from three-dimensional continuum description degenerated to shell behavior. Shear locking, which is common problem in analysis of thin shells, is overcome by the use of MITC (Mixed Interpolation of Tensorial Components) approach. Element has been implemented into finite element code OOFEM and its performance is demonstrated on Scordelis-Lo shell, a benchmark problem frequently used in the evaluation of shell elements.

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