Bi-Linear Shear Deformable ANCF Shell Element Using Continuum Mechanics Approach

2014 ◽  
Author(s):  
Hiroki Yamashita ◽  
Antti I. Valkeapää ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Shell Element ◽  
Material Point ◽  
Deformation Analysis ◽  
Position Vector ◽  
Normal Strain ◽  
Assumed Strain ◽  
Linear Shear ◽  
Shear Deformable

In this investigation, a bi-linear shear deformable shell element is developed using the absolute nodal coordinate formulation for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the mid-plane and the position vector gradient at a material point in the element are interpolated by bi-linear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element locking exhibited in this type of element can be eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the bi-linear shear deformable ANCF shell element proposed in this investigation.

Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Hiroki Yamashita ◽  
Antti I. Valkeapää ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Absolute Nodal Coordinate Formulation ◽  
Shell Element ◽  
Deformation Analysis ◽  
Normal Strain ◽  
Absolute Nodal Coordinate ◽  
Assumed Strain ◽  
Shear Deformable ◽  
The Continuum

In this investigation, a continuum mechanics based bilinear shear deformable shell element is developed using the absolute nodal coordinate formulation (ANCF) for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the transverse gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the middle surface and the position vector gradient at a material point in the element are interpolated by bilinear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element lockings exhibited in the element are eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the continuum mechanics based bilinear shear deformable ANCF shell element proposed in this investigation.

scholarly journals Numerical Modeling and Digital Image Correlation Strain Measurements of Coated Metal Sheets Submitted to Large Bending Deformation

2013 ◽  
Vol 554-557 ◽  
pp. 2424-2431
Author(s):  
Laurent Duchêne ◽  
Amine Ben Bettaieb ◽  
Victor Tuninetti ◽  
Anne Marie Habraken
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Shell Element ◽  
Numerical Results ◽  
Image Correlation ◽  
Integration Scheme ◽  
Forming Process ◽  
Coated Metal ◽  
Assumed Strain ◽  
Assumed Natural Strain

The recently developed SSH3D solid-shell element [1], which is based on the Enhanced Assumed Strain (EAS) and the Assumed Natural Strain (ANS) techniques, is utilized for the modeling of a severe bending sheet forming process. To improve the element's ability to capture the through thickness gradients, a specific integration scheme was developed. In this paper, the performances of this element for the modeling of the T-bent process were assessed thanks to comparison between experimental and numerical results in terms of the strain field at the outer surface of the sheet. The experimental results were obtained by Digital Image Correlation. It is shown that a qualitative agreement between experimental and numerical results is obtained but some numerical parameters should be optimized to improve the accuracy of the simulation predictions. In this respect, the influence of the penalty coefficient of the contact modeling was analyzed.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

An improved assumed strain solid shell element formulation with bubble function displacements

1997 ◽  
Author(s):  
Chahngmin Cho ◽  
Brian Kemp ◽  
Sung Lee ◽  
Chahngmin Cho ◽  
Brian Kemp ◽  
...  
Keyword(s):  
Shell Element ◽  
Element Formulation ◽  
Solid Shell ◽  
Assumed Strain ◽  
Bubble Function

scholarly journals Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
G. M. Kulikov ◽  
A. A. Mamontov ◽  
S. V. Plotnikova ◽  
S. A. Mamontov
Keyword(s):  
Stress Analysis ◽  
Numerical Solutions ◽  
Variational Equation ◽  
Shell Element ◽  
Middle Surface ◽  
Superior Performance ◽  
Lagrange Polynomials ◽  
Shell Formulation ◽  
Coarse Meshes ◽  
Doubly Curved

AbstractA hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

scholarly journals Analysis of Sangihe Islands Movements derived from Recent GPS Observation

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Krishna Fitranto Nugroho
Keyword(s):  
The Philippines ◽  
Border Region ◽  
Movement Speed ◽  
Deformation Analysis ◽  
Normal Strain ◽  
Vertical Deformation ◽  
Horizontal Deformation ◽  
Tectonic Plate ◽  
Monitoring Point ◽  
Plate Movement

Sangihe Islands is one of the districts located in the border region of the Republic of Indonesia precisely located in North Sulawesi Province which borders with the Philippines. Sangihe subduction zone is a subduction between the Sangihe plate and the Maluku sea plate. (Di Leo, et al., 2012). This situation causes the Sangihe Islands region to be very prone to earthquake and others disasters, so mitigation efforts are needed to minimize casualties and losses in other material forms. One of these efforts is mapping the potential of earthquakes through Geodynamic studies which are represented at the point of deformation control. This study is using four times GNSS observations epoch 2015, 2016, 2017 and 2018 tied to ITRF 2014. The data used for 3D deformation analysis with the multiepoch method to calculate the movement speed of the Sangihe plate and simultaneous tectonic plate strain observation. The results of this study are the coordinates and accuracy values of monitoring point also the plate movement speed and annual tectonic plate strain values. The movement speed of the Sangihe plate is SGH1 point is having horizontal deformation of 9.88 mm / year to the southeast and vertical deformation descend by 58.66 mm/year. SGH3 point is having horizontal deformation of 12.74 mm/year to the southeast and vertical deformation descend by 18.51 mm/year. SGH4 point is having horizontal deformation of 19.04 mm/year to the southeast and vertical deformation descend by 5.27 mm/ year. This research also proves the hypothesis of a change in the volume of the Sangihe Islands tectonic plate based on the values of normal strain parameters and shear strain in the fraction of 10-6 to 10-4 strains.

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