Vibration of Sandwich Plates with Random Material Properties using Improved Higher-Order Zig-Zag Theory

Pandit, Mihir Kumar; Singh, B.N.; Sheikh, Abdul Hamid

doi:10.1080/15376490903398698

Cited by 21 publications

(3 citation statements)

References 31 publications

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“…Recently researchers [63,52,4,55,66] adopted Zig Zag models to solve various problems involving bending analysis of functionally graded sandwich structures, laminated beams, and buckling calculations. The effectiveness of taking into account the displacements' slope discontinuity at the interfaces with Zig Zag models was proven.…”

Section: Reissner Multilayered Theory (Rmt)mentioning

confidence: 99%

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

Demasi

Ashenafi

Cavallaro

et al. 2015

Composite Structures

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Section: Reissner Multilayered Theory (Rmt)mentioning

confidence: 99%

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

Demasi

Ashenafi

Cavallaro

et al. 2015

Composite Structures

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“…By considering transverse normal strain, Pandit et al. [17] proposed an improved higher-order zig-zag model for vibration analysis of sandwich plates with random material properties. On the basis of the higher-order zig-zag model, Khandelwal et al.…”

Section: Introductionmentioning

confidence: 99%

A C⁰ three-node triangular element based on preprocessing approach for thick sandwich plates

Wanji

2017

Jnl of Sandwich Structures & Materials

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This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

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“…To avoid using the C 1 continuity displacement functions in zig-zag model's finite element implementation, Pandit et al [22] employed some artificial constraints in which the first derivatives of transverse displacement are replaced by the assumed variables. The same technique has been extended to analyze the vibration of sandwich plates with random material properties [23] and stochastic free vibration of soft-core sandwich plates [24]. By using the method of artificial constraints, Singh and Chakrabarti [25] proposed a C 0 finite element model based on the zig-zag theory to study the buckling of laminated composite plates.…”

Section: Introductionmentioning

confidence: 99%

A C0 zig-zag model for the analysis of angle-ply composite thick plates

Ren

2015

Composite Structures

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From a theoretical and practical viewpoint, the zigzag theory is well adopted in the analysis of laminated composite structures. Nevertheless, for the available zigzag models, artificial constraints in which the first derivatives of transverse displacement are replaced by the assumed variables have to be employed to avoid C 1 interpolation functions in the finite element implementation. Such artificial constraints violate continuity conditions of interlaminar transverse stresses at interfaces. To avoid using artificial constraints, a C 0-type zigzag model is proposed in this paper. C 0 interpolation functions are only required in the finite element formulation as first derivatives of transverse displacement have all been eliminated from the displacement field based on stress compatibility conditions between plies and on the top and bottom surfaces of the plate. Moreover, the number of variables involved in the proposed zigzag model is less than that of the existing zigzag models, yet accurate results are produced comparable to analytical solutions and three-dimensional finite element results. Effects of ply orientations, boundary conditions and length-to-thickness ratio on displacements and stresses of laminated composite plates have been studied.

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Vibration of Sandwich Plates with Random Material Properties using Improved Higher-Order Zig-Zag Theory

Cited by 21 publications

References 31 publications

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

A C⁰ three-node triangular element based on preprocessing approach for thick sandwich plates

A C0 zig-zag model for the analysis of angle-ply composite thick plates

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Vibration of Sandwich Plates with Random Material Properties using Improved Higher-Order Zig-Zag Theory

Cited by 21 publications

References 31 publications

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

A C0 zig-zag model for the analysis of angle-ply composite thick plates

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A C⁰ three-node triangular element based on preprocessing approach for thick sandwich plates