Improved Bilinear Degenerated Shell Element

2015 ◽  
Vol 12 (02) ◽  
pp. 1550004 ◽  
Author(s):  
N. V. Swamy Naidu ◽  
B. Sateesh
Keyword(s):  
Shell Element ◽  
Shell Structures ◽  
Thin Plates ◽  
Element Formulation ◽  
Rigid Body Modes ◽  
Test Requirements ◽  
Degenerated Shell Element ◽  
Deformation Modes ◽  
Torsional Rotation ◽  
Transverse Shear Strains

The development of a new four node 24 degree of freedom bilinear degenerated shell element is presented for the analysis of shell structures. The present finite element formulation considers the assumed covariant transverse shear strains to avoid the shear locking problem and the assumed covariant membrane strains, which are separated from covariant in-plane strains, to overcome the membrane locking problem. The formulation also includes the deviation of the normal torsional rotation of the mid surface in the governing equation. This element is free from serious shear and membrane locking problems and undesirable spurious kinematic deformation modes. The element is tested for rigid body modes and distorted edges to meet the patch test requirements. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples for thick and thin plates.

Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain

2019 ◽  
Vol 37 (3) ◽  
pp. 823-849 ◽  
Author(s):  
Abdessalem Hajlaoui ◽  
Elouni Chebbi ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Shell Element ◽  
Functionally Graded ◽  
Shell Structures ◽  
Element Formulation ◽  
Transverse Shear Strain ◽  
Solid Shell ◽  
Static Behavior ◽  
Content Type

Purpose This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered. Design/methodology/approach Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions. Findings The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed. Originality/value The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. This formulation guarantees a zero transverse shear stress on the top and bottom surfaces of the shell and the shear correction factors is no longer needed.

Advanced Finite Element Formulation for Piezoelectric Smart Shell Structures Under Consideration of Geometrical Nonlinearity

2008 ◽  
Author(s):  
Katrin Schulz ◽  
Sven Klinkel ◽  
Werner Wagner
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Degrees Of Freedom ◽  
Geometrical Nonlinearity ◽  
Shell Element ◽  
Shell Structures ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Displacement Fields ◽  
Piezoelectric Structures

A geometrically nonlinear highly accurate finite element formulation to analyze piezoelectric shell problems is presented. The formulation is based on the mixed field variational principle of Hu-Washizu including the independent fields displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The normal zero stress condition and the normal zero dielectric displacement condition for shells are enforced by the independent resultant stress and resultant dielectric displacement fields. The arbitrary reference surface of the shell is modeled with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed shell element fulfills the patchtests and is able to model arbitrary curved shell structures. Some numerical examples demonstrate the applicability of the present shell element for piezoelectric systems and integrated piezoelectric structures.

Locking and Stability of 3D Woven Composite Reinforcements

2014 ◽  
Vol 611-612 ◽  
pp. 292-299 ◽  
Author(s):  
Sylvain Mathieu ◽  
Philippe Boisse ◽  
Nahiene Hamila ◽  
Florent Bouillon
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Constitutive Law ◽  
Element Formulation ◽  
Woven Composite ◽  
Anisotropic Behavior ◽  
Stabilization Procedure ◽  
Bias Extension ◽  
Deformation Modes ◽  
Composite Reinforcements

3D woven composite reinforcements preforming simulations are an unavoidable step of composite part processing. The present paper deals with thick composite fabric behavior modelling and issues arising during the numerical simulation of preforming. After the description of the independent deformation modes of initially orthotropic reinforcements, a physically motivated and invariant based hyperelastic strain energy density is introduced. This constitutive law is used to show the limitations of a classical finite element formulation in 3D fabric simulations. Tension locking is highlighted in bias extension tests and a reduced integration hexahedral finite element with specific physical hourglass stabilization is proposed. Instabilities due to the highly anisotropic behavior law, witnessed in bending dominated situations, are exposed and a stabilization procedure is initiated.

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 A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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