First-order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels

Cho, Y.B.; Averill, Ronald C.

doi:10.1016/s0263-8223(99)00063-x

Cited by 92 publications

(42 citation statements)

References 27 publications

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“…Examples of these approaches can be found in Reddy [27]. Similar techniques, denoted as 'sub-laminate approaches', have recently been developed in the already mentioned Cho and Averill article [81], in the framework of zig-zagtype theories. The so-called 'hierarchy' ÿnite elements for laminated plates were discussed by Babuska et al [88] for similar reasons.…”

Section: Finite Element Implementationsmentioning

confidence: 99%

Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

Carrera

Demasi

2002

Numerical Meth Engineering

215

119

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SUMMARYThis paper deals with the formulation of ÿnite plate elements for an accurate description of stress and strain ÿelds in multilayered, thick plates subjected to static loadings in the linear, elastic cases. The so-called zig-zag form and interlaminar continuity are addressed in the considered formulations. Two variational statements, the principle of virtual displacements (PVD) and the Reissner mixed variational theorem (RMVT ) are employed to derive ÿnite element matrices. Transverse stress assumptions are made in the framework of RMVT and the resulting ÿnite elements describe a priori interlaminar continuous transverse shear and normal stresses. Both modellings which preserve the number of variables independent of the number of layers (equivalent single-layer models, ESLM) and layer-wise models (LWM) in which the same variables are independent in each layer, have been treated. The order N of the expansions assumed for both displacement and transverse stress ÿelds in the plate thickness direction z as well as the number of element nodes Nn have been taken as free parameters of the considered formulations. By varying N , Nn, variable treatment (LW or ESL) as well as variational statements (PVD and RMVT), a large number of newly ÿnite elements have been presented. Finite elements that are based on PVD and RMVT have been called classical and advanced, respectively.In order to write the matrices related to the considered plate elements in a concise form and to implement them in a computer code (see Part 2), extensive indicial notations have been set out. As a result, all the ÿnite element matrices have been built from only ÿve arrays that were called fundamental nuclei (four are related to RMVT applications and one to PVD cases). These arrays have 3 × 3 dimensions and are therefore constituted of only nine terms each. The di erent formulations are then obtained by expanding the indices that were introduced for the N -order expansion, for the number of nodes Nn and for the constitutive layers N l . Compliances and=or sti ness are accumulated from layer to multilayered level according to the corresponding variable treatment (ESLM or LWM). The numerical evaluations and assessment for the presented plate elements have been provided in the companion paper (Part 2), where it has been concluded that it is convenient to refer to RMVT as a variational tool to formulate multilayered plate elements that are able to give a quasi-three-dimensional description of stress=strain ÿelds in multilayered thick structures.

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Section: Finite Element Implementationsmentioning

confidence: 99%

Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

Carrera

Demasi

2002

Numerical Meth Engineering

215

119

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“…Extensions of the kinematics of the Di Sciuva's First-order zigzag theory (linear zigzag model) include, among other: (i) extension to the linear [41] and nonlinear [48] multilayered shell theory; (ii) general lamination lay-up [42,47,49]; (iii) satisfaction of the shear stress-free boundary conditions on the top and bottom surfaces [44,46,50]; (iv) polynomial expansion of the global part to any degree [47,49]; (v) extension to the dynamics, buckling [16,47,49,48]; (vi) thermal effects [68], [69]; (vii) sublaminates approach [68,69,70,71,72,73,74]; (viii) inclusion of von Kármán geometrically nonlinear effects [16,48,49]; (ix) extension to the nonlinear theory of laminated composites with damaged interfaces [49,68,69,74,75,76]; (x) inclusion of the transverse normal strain and stress [74,77,78]; (xi) visco-elastic effects [79]; (xii) active control of beams, plates and shells [80].…”

Section: Introductionmentioning

confidence: 99%

First-Order Displacement-Based Zigzag Theories for Composite Laminates and Sandwich Structures: A Review

Sciuva¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…An enormous amount of research effort has therefore been made in the establishment of plate theory-based lamination models for a close estimation of the structural behaviour at reduced computational demands. Layer-wise models (LWMs) [1][2][3][4] and zigzag models (ZZMs) [5][6][7][8][9] achieve the reproduction of piecewise continuous displacement fields in the thickness direction by employing the first-order shear deformation theory (FSDT) or higher-order shear deformation theories (HSDTs) at each constitutive layer and imposing C 0 continuity constraints at laminar interfaces. The Equivalent Single Layer Models (ESLMs) [10], which follow the idea of Murakami [11] with further developments, obtain piecewise displacements by simply adding Murakami's zigzag function [11] to a classical Taylor type expansion defined along the whole plate thickness.…”

Section: Introductionmentioning

confidence: 99%

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

Liang

Izzuddin

2015

Composite Structures

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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.

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First-order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels

Cited by 92 publications

References 27 publications

Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

First-Order Displacement-Based Zigzag Theories for Composite Laminates and Sandwich Structures: A Review

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

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