A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates

Kutlu, Akif; Dördüncü, Mehmet; Rabczuk, Timon

doi:10.1016/j.compstruct.2021.113886

Cited by 40 publications

(6 citation statements)

References 78 publications

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“…Ozutok and Madenci [25] combined mixed finite element method (MFEM) and HSDT to perform static analysis of laminated composite beams. Kutlu et al [26][27][28] and Aribas et al [29][30][31] revealed some advantages of MFEM based formulations on the prediction of accurate stress resultants and stress components of various beam, helix and plate type structures. Shao et al [32] proposed a new HSDT for the free vibration analysis of laminated composite beams.…”

Section: Introductionmentioning

confidence: 99%

Stress Analysis of Laminated HSDT Beams Considering Bending Extension Coupling

BAB

Kutlu

2023

Turkish Journal of Civil Engineering

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This study demonstrates a mixed finite element formulation procedure for the bending and stress analyses of laminated composite beams. The finite element method is based on the Hellinger-Reissner variational principle, while the beam assumptions are based on the Higher Order Shear Deformation Theory (HSDT). Reddy’s shear function is employed for the beam theory where the beam is discretized by two-noded linear elements. The displacements and stress resultants are obtained directly at the nodes according to the proposed mixed formulation. The validation of current study is performed by comparison and convergence analyzes for various lamination cases under different boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Stress Analysis of Laminated HSDT Beams Considering Bending Extension Coupling

BAB

Kutlu

2023

Turkish Journal of Civil Engineering

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“…Dorduncu [41] analyzed functionally graded sandwich plates by incorporating a peridynamic differential operator [42] with the RZT. Recently, Kutlu et al [43] developed a novel MFE approach to examine the static behavior of laminated composite plates by applying the RZT. Sahoo and Singh [44] implemented a new trigonometric zigzag theory for the analysis of composite and sandwich plates and demonstrated its application under various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Obtaining stress resultants directly from the FE solution paves the way for calculating the strain measures from compliance relations instead of error-prone numerical derivatives of kinematic variables. In recent studies [43,50], it is shown that this approach performs superior on the prediction of stress components in laminated structures modeled by RZT [39,46,56]. The details of the proposed numerical procedure, namely the Mixed Higher-Order Plate Theory (MHPT), are introduced in Section 2.…”

Section: Introductionmentioning

confidence: 99%

A C0 continuous mixed FE formulation for bending of laminated composite plates based on unified HSDT

Bab,

Kutlu

2023

Z Angew Math Mech

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This study proposes a unified C0 continuous mixed finite element (MFE) formulation for the accurate and efficient prediction of stress components in laminated composite plates relying on Higher Order Shear Deformation Theory (HSDT). This unified form of the MFE accepts any convenient function for the representation of transverse shear deformation. The Hellinger–Reissner variational principle is employed for the derivation of MFE equations within a two‐field formulation involving stress resultants along with kinematical variables. Thus, the displacement and stress resultant fields are obtained directly from the global solution of the system of equations. In this manner, the in‐plane stress components are calculated over constitutive relations at the nodes without any need for error‐prone spatial derivatives. Furthermore, the independent interpolation of kinematic and stress resultant type variables allows the numerical solution to overcome the shear‐locking problem and ensure C0 continuity requirement. Numerical examples include convergence and comparison tests of predicted displacements and stress components under various boundary conditions and material configurations. Various test cases are considered for both the thin and thick plates subjected to sinusoidal and uniformly distributed loads. It is demonstrated that the proposed MFE formulation can capture stress components with high accuracy while being computationally efficient.

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“…Kefal et al [17] demonstrated how to use peridynamics for topology optimisation of cracked structures. There have also been many studies presenting peridynamic formulations for beams and plates to model isotropic materials [18–22], functionally graded materials [23–28], and composite materials [29,30]. Peridynamics has also been extended to model other physical fields.…”

Section: Introductionmentioning

confidence: 99%

Double horizon peridynamics

Yang

Öterkuş

Oterkus

et al. 2023

Mathematics and Mechanics of Solids

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In this study, a new double horizon peridynamics formulation was introduced by utilising two horizons instead of one as in traditional peridynamics. The new approach allows utilisation of large horizon sizes by controlling the size of the inner horizon size. To demonstrate the capability of the current approach, four different numerical cases were examined by considering static and dynamic conditions, different boundary and initial conditions, and different outer and inner horizon size values. For both static and dynamic cases, it was observed that as the inner horizon decreases, peridynamic solutions converge to classical continuum mechanics solutions even by using a larger horizon size value. Therefore, the proposed approach can serve as an alternative approach to improve computational efficiency of peridynamic simulations by obtaining accurate results with larger horizon sizes.

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A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates

Cited by 40 publications

References 78 publications

Stress Analysis of Laminated HSDT Beams Considering Bending Extension Coupling

Stress Analysis of Laminated HSDT Beams Considering Bending Extension Coupling

A C0 continuous mixed FE formulation for bending of laminated composite plates based on unified HSDT

Double horizon peridynamics

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