New assumed natural strain formulation of the shallow shell element

1993 ◽  
Vol 9 (12) ◽  
pp. 989-1004 ◽  
Author(s):  
Rafi L. Muhanna
Keyword(s):  
Shallow Shell ◽  
Shell Element ◽  
Natural Strain ◽  
Strain Formulation ◽  
Assumed Natural Strain

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.

scholarly journals Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures

2018 ◽  
Vol 5 (1) ◽  
pp. 116-135 ◽  
Author(s):  
G. M. Kulikov ◽  
S. V. Plotnikova
Keyword(s):  
Stress Analysis ◽  
Shell Element ◽  
Middle Surface ◽  
Functionally Graded ◽  
Superior Performance ◽  
Solid Shell ◽  
Lagrange Polynomials ◽  
Graded Material ◽  
Assumed Natural Strain ◽  
Shell Formulation

Abstract A hybrid-mixed functionally graded material (FGM) piezoelectric four-node solid-shell element through the sampling surfaces (SaS) method is proposed. The SaS formulation is based on choosing inside the shell N SaS parallel to the middle surface in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. Such choice of unknowns with the use of Lagrange polynomials of degree N-1 in through-thickness interpolations of the displacements, strains, electric potential, electric field and material properties leads to a robust FGM piezoelectric shell formulation. The inner SaS are located at Chebyshev polynomial nodes that make it possible to minimize uniformly the error due to Lagrange interpolation. To implement the effective analytical integration throughout the element, the extended assumed natural strain (ANS) method is employed. As a result, the piezoelectric four-node solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the hybrid stress-strain solid-shell formulation via the Hu-Washizu variational principle is employed. The developed solid-shell element could be useful for the 3D stress analysis of FGMstructures because the SaS method allows obtaining the solutions with a prescribed accuracy, which asymptotically approach the exact solutions of electroelasticity as the number of SaS tends to infinity.

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