Enhanced zigzag theory for static analysis of composite plates

Nath, Jayanta Kumar; Mishra, Bibhuti Bhusana

doi:10.1007/s00419-018-1390-x

Cited by 4 publications

(5 citation statements)

References 81 publications

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“…where W e denotes the work of external forces. The k xz and k yz are the assumed transverse shear stresses given by equation (24), and k…”

Section: Improved Transverse Shear Stressesmentioning

confidence: 99%

“…Recently, Wu et al 22,23 suggested a new global higher order zigzag model derived from the HW variational theorem for interlaminar stresses analysis of multilayered composite structures. By accounting for transverse normal deformation, Nath and Mishra 24 developed an enhanced zigzag theory to study bending behaviors of composite plates. Reviewing the abovementioned literature, [15][16][17][18][19][20][21][22][23][24] it is found that the first-order derivatives of transverse displacement are included in the displacement fields of the zigzag and global-local models.…”

Section: Introductionmentioning

confidence: 99%

“…By accounting for transverse normal deformation, Nath and Mishra 24 developed an enhanced zigzag theory to study bending behaviors of composite plates. Reviewing the abovementioned literature, [15][16][17][18][19][20][21][22][23][24] it is found that the first-order derivatives of transverse displacement are included in the displacement fields of the zigzag and global-local models. Therefore, C 1 -continuous interpolation functions are required to approximate the transverse displacement due to the presence of its second-order derivatives in the strain energy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

Jin

Yao

2020

Journal of Composite Materials

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An accurate and computationally attractive zigzag theory is developed for bending and buckling analysis of thick laminated soft core sandwich plates. The kinematic assumptions of the proposed zigzag theory are obtained by superimposing a nonlinear zigzag function on the first-order shear deformation theory. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional equilibrium equations and the Reissner mixed variational theorem is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stresses, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient four-node C0 quadrilateral plate element with linear interpolation function is proposed for bending and buckling analysis of soft core sandwich plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Moreover, the accurate transverse shear stresses can be involved in the strain energy which can actively improve the accuracy of critical loads. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model.

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“…where W e denotes the work of external forces. The k xz and k yz are the assumed transverse shear stresses given by equation (24), and k…”

Section: Improved Transverse Shear Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

Jin

Yao

2020

Journal of Composite Materials

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show abstract

“…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. Nath and Mishra [45] performed static analysis of composite plates based on enhanced zigzag theory. Dorduncu et al [46] extended the RZT theory by considering thickness stretching to investigate the dynamic response of laminated plates through a shear locking free finite element formulation.…”

Section: Introductionmentioning

confidence: 99%

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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A refined plate theory for functionally graded carbon nanotube-reinforced plates with piezoelectric actuator

Jin

Fu³

et al. 2021

European Journal of Mechanics - A/Solids

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Enhanced zigzag theory for static analysis of composite plates

Cited by 4 publications

References 81 publications

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

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

A refined plate theory for functionally graded carbon nanotube-reinforced plates with piezoelectric actuator

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