An assessment of refined hierarchical kinematic models for the bending and free vibration analyses of laminated and functionally graded sandwich cylindrical panels

Punera, Devesh; Kant, Tarun

doi:10.1177/1099636220909826

Cited by 13 publications

(4 citation statements)

References 58 publications

(75 reference statements)

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“…Further refinement on these models can be made by removing all the assumptions of classical theories. 196,197 These models become necessary as the material heterogeneity and thickness ratio of structure increases. In the framework of multi-layered composite analysis, these 2D theories are formulated with layer-dependent (layer-wise approach) or layer-independent (equivalent single-layer approach) kinematic parameters.…”

Section: Refined Analysis and Solution Approachesmentioning

confidence: 99%

Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites

Punera

Mukherjee

2022

Journal of Reinforced Plastics and Composites

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The functional advantages of tailored stiffness, often seen in nature, are also utilized in composite structures. Advancements in the multiaxis tow placement and automated fiber placement (AFP) machines led to the development of variable angle tow (VAT) composites, also referred further as variable stiffness composites (VSC). These composites are shown to effectively enhance the stress distribution and buckling load capacity of structures with greater flexibility on the design space. This review systematically presents the status of recent research on the topic of VSCs. Various manufacturing techniques of VSC are discussed; constraints and the defects associated with the manufacturing processes are enlisted. The review highlights the optimization studies based on the fiber profile and macro-scale stiffness invariants. Several studies existing in the domain of buckling, vibration, and aeroelastic tailoring of angle tow composites are summarized to connect the important aspects of analysis and present a holistic approach for future studies in this area.

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Section: Refined Analysis and Solution Approachesmentioning

confidence: 99%

Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites

Punera

Mukherjee

2022

Journal of Reinforced Plastics and Composites

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“…The HSDTs are further classified into polynomial and non-polynomial shear deformation theories based on the mathematical functions assumed along the thickness coordinate to reduce the 3D displacements to 2D variables. The polynomial HSDTs employ the Taylor series expansion [8][9][10][11] for the transverse shear and normal deformation. However, the non-polynomial models consider a warping function to accommodate the shear deformation through exponential [12][13][14], trigonometric [15][16][17], hyperbolic [18][19][20], inverse trigonometric [21], and inverse hyperbolic [22][23][24] approaches, and many more.…”

Section: Introductionmentioning

confidence: 99%

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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“…Trinh et al 40 presented the state-space Lévy solution for size-dependent static, free vibration and buckling behaviors of functionally graded sandwich panels. Punera and Kant 41 adopted the Navier’s method to carry out the bending and free vibration analyses of moderately thick laminated and functionally graded sandwich cylindrical shell panels. Zamani et al 42 utilized the Navier’s method to assess the excellent vibration performance of a novel angle graded auxetic honeycomb core designed for sandwich plates.…”

Section: Introductionmentioning

confidence: 99%

On new benchmark free vibration solutions of rectangular sandwich panels within the symplectic solution framework

Zhou

Zheng

et al. 2022

Jnl of Sandwich Structures & Materials

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In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.

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An assessment of refined hierarchical kinematic models for the bending and free vibration analyses of laminated and functionally graded sandwich cylindrical panels

Cited by 13 publications

References 58 publications

Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites

Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

On new benchmark free vibration solutions of rectangular sandwich panels within the symplectic solution framework

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