The Use of 9-Parameter Shell Theory for Development of Exact Geometry 12-Node Quadrilateral Piezoelectric Laminated Solid-Shell Elements

2015 ◽  
Vol 22 (6) ◽  
pp. 490-502 ◽  
Author(s):  
G. M. Kulikov ◽  
S. V. Plotnikova
Keyword(s):  
Shell Theory ◽  
Solid Shell ◽  
Shell Elements ◽  
Exact Geometry

scholarly journals Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements

2019 ◽  
Vol 31 (1) ◽  
pp. 53-70
Author(s):  
GM Kulikov ◽  
SV Plotnikova ◽  
E Carrera
Keyword(s):  
Shell Element ◽  
Middle Surface ◽  
Solid Shell ◽  
Modeling And Analysis ◽  
Lagrange Polynomials ◽  
Shell Elements ◽  
Exact Geometry ◽  
Piezoelectric Solid ◽  
Assumed Natural Strain ◽  
Shell Formulation

An exact geometry four-node piezoelectric solid-shell element through the sampling surfaces formulation is proposed. The sampling surfaces formulation is based on choosing inside the shell N – 2 sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The bottom and top surfaces are also included into a set of sampling surfaces. Such choice of unknowns with the use of Lagrange polynomials of degree N – 1 in the through-the-thickness interpolations of displacements, strains, electric potential, and electric field yields a robust piezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed. The developed hybrid-mixed four-node piezoelectric solid-shell element is based on the Hu-Washizu variational principle and shows the excellent performance for coarse mesh configurations. It can be useful for the 3D stress analysis of piezoelectric shells with variable curvatures, in particular for the modeling and analysis of spiral actuators.

Some new results and current challenges in the finite element analysis of shells

Acta Numerica ◽  
2001 ◽  
Vol 10 ◽  
pp. 215-250 ◽  
Author(s):  
Dominique Chapelle
Keyword(s):  
Finite Element ◽  
Shell Theory ◽  
Shell Structures ◽  
Engineering Practice ◽  
Element Analysis ◽  
Shell Elements ◽  
Shell Models ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Mathematical Analyses

This article, a companion to the article by Philippe G. Ciarlet on the mathematical modelling of shells also in this issue of Acta Numerica, focuses on numerical issues raised by the analysis of shells.Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of ‘shell finite element’ is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements – such as the general shell elements – derived from 3D formulations using some kinematic assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and treatment of the deficiencies associated with the analysis of thin shells (among which is the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behaviour of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements when faced with these pathological phenomena, which is essential for the design of improved procedures.

scholarly journals Application of P1-Nonconforming Element for Shell Structure of Incompressible Materiel

2011 ◽  
Vol 2-3 ◽  
pp. 1051-1056
Author(s):  
Lei Chen ◽  
Gang Won Jang ◽  
Tae Jin Chung ◽  
Tae Hyun Baek
Keyword(s):  
Topology Optimization ◽  
Shell Structure ◽  
Optimization Design ◽  
Incompressible Material ◽  
High Order ◽  
Solid Shell ◽  
Shell Elements ◽  
Volumetric Locking ◽  
Nonconforming Element ◽  
Nonconforming Elements

This research focused on solving volumetric locking problem of shell structure of incompressible material. Degenerated solid-shell elements are widely applied on curved structure. But, volumetric locking will take place when the structure is made of incompressible material, such as rubber. Due to Poisson’s locking free property of P1-nonconforming element, it is employed to solve volumetric locking problem of shell structure. Furthermore, the study on shell structure is extended to topology optimization design. To verify the volumetric locking free of P1-nonconforming element on shell structure of incompressible material, some structures are studied by different elements. Comparing with the utilization of high order elements to solve volumetric locking problems, P1-nonconforming elements can save calculation time and reduce the numerical cost.

scholarly journals Single point incremental forming simulation with adaptive remeshing technique using solid-shell elements

2016 ◽  
Vol 33 (5) ◽  
pp. 1388-1421 ◽  
Author(s):  
José I.V. Sena ◽  
Cedric Lequesne ◽  
L Duchene ◽  
Anne-Marie Habraken ◽  
Robertt A.F. Valente ◽  
...  
Keyword(s):  
Finite Element ◽  
Incremental Forming ◽  
Single Point ◽  
Nonlinear Material ◽  
Single Point Incremental Forming ◽  
Solid Shell ◽  
Contact Conditions ◽  
Adaptive Remeshing ◽  
Content Type ◽  
Shell Elements

Purpose – Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced. Design/methodology/approach – SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years. Findings – In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results. Originality/value – It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

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