A formulation of general shell elements—the use of mixed interpolation of tensorial components

Bathe, Klaus‐Jürgen; Dvorkin, Eduardo N.

doi:10.1002/nme.1620220312

Cited by 725 publications

(348 citation statements)

References 21 publications

Supporting

Mentioning

313

Contrasting

Unclassified

Order By: Relevance

“…In this paper, the governing equations of the variable-kinematics plate element for the linear static coupled electro-mechanical analysis of composite structures are derived from the Principle of Virtual Displacement (PVD). Subsequently, FEM is adopted and the Mixed Interpolation of Tensorial Components (MITC) method [41][42][43][44] is used to contrast the shear locking. The developed methodology is, therefore, assessed and used for the analysis of composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations.…”

Section: Introductionmentioning

confidence: 99%

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Carrera

Valvano

Куликов

2017

International Journal of Smart and Nano Materials

View full text Add to dashboard Cite

In the present work, a new class of finite elements (FEs) for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modeling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories. Several numerical investigations, such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations, are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature. ARTICLE HISTORY

show abstract

Section: Introductionmentioning

confidence: 99%

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Carrera

Valvano

Куликов

2017

International Journal of Smart and Nano Materials

View full text Add to dashboard Cite

show abstract

“…Numerous locking-elimination methods have been developed, among which are reduced/selective integration methods [23][24], enhanced strain methods [25], and strain mapping methods [26][27][28]. Most of these methods can be equally applied to generalised strains at the level of overall cross-section or individual layers, where the latter is particularly advantageous for the present work, since the overall laminated shell response is obtained from contributions of layers that are processed individually as monolithic shells.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the additional zigzag displacement variables are defined in a 2D curvilinear shell system which follows the element local system according to a fixed relationship, thus avoiding the need for nonlinear co-rotational transformation of the additional zigzag variables. The Mixed Interpolation Tensorial Components (MITC) method [27,[31][32] is employed for each constitutive layer of the 9-noded shell element to overcome the locking phenomenon The paper proceeds with highlighting the principal characteristics of laminations with an alternating stiff/soft lay-up, which is followed by presenting the proposed laminated shell model. The application of the proposed laminated shell model is subsequently illustrated for a 9-noded co-rotational element, and several linear and nonlinear numerical examples are finally presented to demonstrate the accuracy and efficiency of the proposed approach.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of laminated shells with alternating stiff/soft lay-up

Liang

Izzuddin

2015

Composite Structures

View full text Add to dashboard Cite

This paper proposes a multi-layer formulation for the nonlinear analysis of laminated shells with an alternating stiff/soft lay-up. The zigzag variation of planar displacements is taken into account by adding to the Reissner-Mindlin formulation a specific set of zigzag function which is effective for the considered lay-up. Furthermore, a piecewise linear throughthickness distribution of the material transverse shear strain is assumed, which agrees well with the real distribution. The proposed lamination model with a low-order nonlinear straindisplacement relationship is incorporated within a co-rotational framework for geometric nonlinear analysis, thus upgrading the low-order local element formulation to large displacement analysis with relative ease. In addition, a local shell system is employed for direct definition of the additional zigzag displacement fields and associated parameters, which are thus excluded from the large displacement co-rotational transformations. The application of the proposed laminated shell modelling approach is illustrated in this paper for a 9-noded co-rotational shell element, which utilises the Mixed Interpolation of Tensorial Components (MITC) method in the local system for overcoming locking effects. Several linear and nonlinear numerical examples of multi-layer shell structures with alternating stiff/soft lay-ups are used to illustrate the effectiveness and efficiency of the proposed modelling approach.

show abstract

“…To a large extent, shell structures are now solved in practice using 4-node shell elements. Among those available, the MITC4 shell element is probably the most effective element, in particular when linear and nonlinear analyses are to be performed [1][2][3][4][5][6]. However, the other MITC shell elements can be more effective for specific analyses [5,[7][8][9].…”

Section: Introductionmentioning

confidence: 99%

A 4-node 3D-shell element to model shell surface tractions and incompressible behavior

Kim

Bathe

2008

Computers & Structures

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWe present in this paper a shell element that models the three-dimensional (3D) effects of surface tractions, like needed when a shell is confined between other solid media. The element is the widely used MITC4 shell element enriched by the use of a fully 3D stress-strain description, appropriate throughthe-thickness displacements to model surface tractions, and pressure degrees of freedom for incompressible analyses. The element formulation avoids instabilities and ill-conditioning. Various example solutions are presented to illustrate the capabilities of the element.

show abstract

A formulation of general shell elements—the use of mixed interpolation of tensorial components

Cited by 725 publications

References 21 publications

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

Nonlinear analysis of laminated shells with alternating stiff/soft lay-up

A 4-node 3D-shell element to model shell surface tractions and incompressible behavior

Contact Info

Product

Resources

About