An Exact 3d Solution for Free Vibrations of Multilayered Cross-Ply Composite and Sandwich Plates and Shells

Brischetto, Salvatore

doi:10.1142/s1758825114500768

Cited by 74 publications

(75 citation statements)

References 45 publications

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“…The proposed exact 3D solution was developed by Brischetto in [5][6][7][8][9][10] where the differential equations of equilibrium written in general orthogonal curvilinear coordinates were exactly solved by means of the exponential matrix method. The 2D and 3D FE results were obtained by means of the commercial finite element code Straus7 [11].…”

Section: Introductionmentioning

confidence: 99%

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

Tornabene

Brischetto

Fantuzzi

et al. 2015

Composites Part B: Engineering

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The present paper shows a comparison between classical two-dimensional (2D) and three-dimensional (3D) finite elements (FEs), classical and refined 2D generalized differential quadrature (GDQ) methods and an exact three-dimensional solution. A free vibration analysis of one-layered and multilayered isotropic, composite and sandwich cylindrical and spherical shell panels is made. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the FE and GDQ methods (numerical solutions) and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 3D and 2D finite element results are obtained by means of a well-known commercial FE code. Classical and refined 2D GDQ models are based on a generalized unified approach which considers both equivalent single layer and layer-wise theories. The differences between 2D and 3D FE solutions, classical and refined 2D GDQ models and 3D exact solutions depend on several parameters. These include the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

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Section: Introductionmentioning

confidence: 99%

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

Tornabene

Brischetto

Fantuzzi

et al. 2015

Composites Part B: Engineering

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“…A simple method of reducing its order to the first one is described in [3,31] and it may be summarized as a redoubling of the involved variables. In the first author's past works [20,21], a detailed description of this approach can be found. The compact form of the reduced system of first order partial differential equations is:…”

Section: Use Of the Exponential Matrix And Mathematical Layers In Thementioning

confidence: 99%

“…Details about their determination can be found in the first author's past works [20][21][22][23][24][25][26].…”

Section: Use Of the Exponential Matrix And Mathematical Layers In Thementioning

confidence: 99%

“…In the present 3D solution, the equilibrium equations are written in orthogonal mixed curvilinear coordinates. The first author's past works extensively described all the details of the proposed 3D formulation used for the free vibration analysis of one-layered and multilayered spherical, cylindrical and flat one-layered panels [20,21]. The same idea was extended to the static problem of shells subjected to harmonic loads on the top and bottom surfaces in [22].…”

Section: Introductionmentioning

confidence: 99%

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Convergence Investigation for the Exponential Matrix and Mathematical Layers in the Static Analysis of Multilayered Composite Structures

Brischetto

Torre

2017

J. Compos. Sci.

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Abstract:The exact three-dimensional analysis of a large group of geometries is accomplished here using the same formulation written in orthogonal mixed curvilinear coordinates. This solution is valid for plates, cylindrical shells, cylinders and spherical shells. It does not need specialized equations for each proposed geometry. It makes use of a formulation that is valid for spherical shells and automatically degenerates in the simpler geometries. Second order differential equations are reduced of an order redoubling the number of variables, and then they are solved via the exponential matrix method. Coefficients of equations vary through the thickness when shells are considered. M mathematical layers must be introduced into each physical layer to approximate the curvature. The correlation between M and the order of expansion N for the exponential matrix is analyzed in this paper in order to find their opportune combined values to obtain the exact results. As their effects may depend on different parameters, several geometries, lamination sequences, thickness ratios and imposed half-wave numbers are taken into consideration.

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“…Their interest in this subject is mainly due to the fact that the use of advanced materials has shown inadequacy of the classical or first-order theories to capture the effective mechanical behavior of this class of materials, such as laminated composites or functionally graded materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In these particular circumstances, the fundamental hypotheses of a lower-order model could lead to inaccurate results since some effects are neglected or not even considered.…”

Section: Introductionmentioning

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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An Exact 3d Solution for Free Vibrations of Multilayered Cross-Ply Composite and Sandwich Plates and Shells

Cited by 74 publications

References 45 publications

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels

Convergence Investigation for the Exponential Matrix and Mathematical Layers in the Static Analysis of Multilayered Composite Structures

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

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