Non-linear wrinkling of a sandwich panel with functionally graded core – Extended high-order approach

2018 ◽  
Vol 148-149 ◽  
pp. 122-139 ◽  
Author(s):  
Y. Frostig ◽  
V. Birman ◽  
G.A. Kardomateas
Keyword(s):  
Sandwich Panel ◽  
Functionally Graded ◽  
High Order ◽  
Non Linear

Free vibration analysis of sandwich beams with carbon nanotube reinforced face sheets based on extended high-order sandwich panel theory

2016 ◽  
Vol 20 (2) ◽  
pp. 219-248 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Sandwich Panel ◽  
Sandwich Beam ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
High Order ◽  
Reinforced Composite ◽  
The Face ◽  
Composite Face

Free vibration analysis of a sandwich beam with soft core and carbon nanotube reinforced composite face sheets, hitherto not reported in the literature, based on extended high-order sandwich panel theory is presented. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded. In this theory, the face sheets follow the first-order shear deformation theory. Besides, the two-dimensional elasticity is used for the core. The field equations are derived via the Ritz-based solution which is suitable for any essential boundary conditions. Chebyshev polynomials multiplying boundary R-functions are used as admissible functions and evidence of their good performance is given. A detailed parametric study is conducted to study the effects of nanotube volume fraction and their distribution pattern, core-to-face sheet thickness ratio, and boundary conditions on the natural frequencies and mode shapes of sandwich beams with functionally graded carbon nanotube reinforced composite face sheets and soft cores. Since the extended high-order sandwich panel theory can be used with any combinations of core and face sheets and not only the soft cores that the other theories demand, the results for the same beam with functionally graded carbon nanotube reinforced composite face sheets and stiff core are also provided for comparison. It is concluded that the sandwich beam with X and V distribution figures of face sheets, no matter what the boundary conditions, has higher vibration performance than the beam with UD-CNTRC face sheets.

Free vibration analysis of micro-magneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube–reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory

2017 ◽  
Vol 29 (5) ◽  
pp. 863-882 ◽  
Author(s):  
M Mohammadimehr ◽  
SM Akhavan Alavi ◽  
SV Okhravi ◽  
SH Edjtahed
Keyword(s):  
Boundary Conditions ◽  
Sandwich Panel ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
High Order ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Temperature Dependent ◽  
Modified Strain Gradient Theory ◽  
The Face

In this article, based on high-order sandwich panel theory and modified strain gradient theory, free vibration analysis of a micro-magneto-electro-elastic sandwich panel with a transversely flexible core and functionally graded carbon nanotube–reinforced nanocomposite face sheets is investigated. Also, the influences of temperature-dependent material properties and various circuit boundary conditions such as open and closed are considered in this study. Carbon nanotubes are arranged in longitudinal direction inside polyvinylidene fluoride matrix with various functionally graded (FG) distributions such as uniform, FG-V, FG-A, FG-X, and FG-O in the face sheets. The generalized rule of mixture is employed to predict mechanical, electrical, magnetic, and thermal properties of micro-sandwich composite panel. The classical shell theory and an elasticity high-order theory are used for the face sheets and the core, respectively. Then, the governing equations of motion are derived using Hamilton’s principle. In this article, the influences of the volume fraction, the various distributions of carbon nanotubes, the multi-physical fields, open- and closed-circuit boundary conditions, the material length scale parameters, different face sheet and core thicknesses, and temperature changes on the natural frequency are investigated, and the obtained results show that these influences play an important role in the natural frequencies and can be used in order to prevent the resonance phenomenon and also for manufacturing process design and optimization of micro-magneto-electro-elastic composite sandwich cylindrical panels.

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

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