Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Tornabene, Francesco; Fantuzzi, Nicholas; Bacciocchi, Michele; Viola, Erasmo

doi:10.1016/j.compositesb.2015.07.012

Cited by 113 publications

(33 citation statements)

References 157 publications

(150 reference statements)

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“…Once the governing equations are obtained, they are numerically solved by means of the Generalized Differential Quadrature (GDQ) method [90], whose main features are illustrated in detail by Tornabene et al in the review paper [91]. The accuracy, reliability and stability characteristic of this numerical tool can be checked considering the excellent results shown in the works [39][40][41][61][62][63][64][65][66][67][68][69][70][71][72][73][74][79][80][81][82][83][92][93][94][95][96][97][98][99][100][101][102], which have been obtained in different kinds of structural problems related to plates and shells.…”

Section: Definition Of the Geometrymentioning

confidence: 99%

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

et al. 2016

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Abstract:The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.

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Section: Definition Of the Geometrymentioning

confidence: 99%

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

et al. 2016

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“…Yazdani and Ribeiro [29] and Yazdani et al [30] recently published layerwise extensions of the earlier works by Akhavan and co-workers on the free vibration and bending behaviour of tow-steered laminates cited above. Finally, Tornabene et al [31] studied the free vibrations of doubly curved, variable-stiffness shells using a generalised higher-order model implemented via Carrera's Unified Formulation (CUF) using a local differential quadrature method. Due to the relative novelty of tow-steered laminates, there is little work in the literature on detailed analyses of full 3D stress fields in towsteered laminates and how these could be tailored to optimise structures for specific objectives.…”

Section: Variable-stiffness Laminated Compositesmentioning

confidence: 99%

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

Groh

2016

Composite Structures

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractThe higher-order, equivalent single-layer model developed in Part I is applied to the stretching and bending of exemplar multilayered flat plates, where the results are compared with different 3D models, and trends and insights are subsequently drawn. The present mixed displacement/stress-based model is derived from inherently equilibrated 3D stress fields that satisfy the interlaminar and surface traction equilibrium conditions. A new set of governing equations is derived from a contracted Hellinger-Reissner functional that only enforces the classical membrane and bending equations via Lagrange multipliers. Combined with the fact that the same set of stress resultants is used for all stress fields, the number of unknown variables of the theory reduces, while maintaining sufficient fidelity to capture higher-order transverse shearing and zig-zag effects. A wide range of stacking sequences are considered ranging from orthotropic straight-fibre laminates to sandwich panels with variable-stiffness face sheets, i.e. composite plies in which the reinforcing fibres describe curvilinear paths. Hence, the model is used to study laminated plates with 3D heterogeneity, that is laminates comprising layers with material properties that can differ by multiple orders of magnitude and that vary continuously in-plane. The governing equations are solved both analytically using trigonometric expansions and numerically using the pseudo-spectral differential quadrature method. The 3D stress fields predictions correlate closely with 3D elasticity and 3D finite element solutions and are accurate to within a few percent for thick plates with characteristic length to thickness ratios as small as 5:1. In fact, the results suggest that 3D stress fields from our model satisfy Cauchy's 3D equilibrium equations more accurately, and at a three-order degree of freedom reduction in computational cost, compared to high-fidelity 3D FEM models.

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“…The problem is approached numerically with the use of the GDQ method, as successfully applied in the literature for many applications, e.g., buckling problems and free vibrations of FG cantilever beams or shells reinforced with CNTs (see [29,[33][34][35][36][37] among others), the dynamics of undamaged and damaged arches with different shapes [38][39][40][41][42][43], as well as non-linear transient problems [44][45][46][47][48][49][50]. In the present work, we verify the ability of the GDQ method to capture the sensitivity of the structural response to the CNT pattern and volume fraction as well as to some geometry parameters.…”

Section: Among Others)mentioning

confidence: 99%

Thermal Buckling of Nanocomposite Stiffened Cylindrical Shells Reinforced by Functionally Graded Wavy Carbon Nanotubes with Temperature-Dependent Properties

et al. 2017

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Abstract:We study the thermal buckling behavior of cylindrical shells reinforced with Functionally Graded (FG) wavy Carbon NanoTubes (CNTs), stiffened by stringers and rings, and subjected to a thermal loading. The equilibrium equations of the problem are built according to the Third-order Shear Deformation Theory (TSDT), whereas the stiffeners are modeled as Euler Bernoulli beams. Different types of FG distributions of wavy CNTs along the radial direction of the cylinder are herein considered, and temperature-dependent material properties are estimated via a micromechanical model, under the assumption of uniform distribution within the shell and through the thickness. A parametric investigation based on the Generalized Differential Quadrature (GDQ) method aims at investigating the effects of the aspect ratio and waviness index of CNTs on the thermal buckling of FG nanocomposite stiffened cylinders, reinforced with wavy single-walled CNTs. Some numerical examples are here provided in order to verify the accuracy of the proposed formulation and to investigate the effects of several parameters-including the volume fraction, the distribution pattern of wavy CNTs, and the cylinder thickness-on the thermal buckling behavior of the stiffened cylinders made of CNT-reinforced composite (CNTRC) material.

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Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Cited by 113 publications

References 157 publications

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

Thermal Buckling of Nanocomposite Stiffened Cylindrical Shells Reinforced by Functionally Graded Wavy Carbon Nanotubes with Temperature-Dependent Properties

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