Extension of Vlasov’s Semi-membrane Theory to Reinforced Composite Shells

1992 ◽  
Vol 59 (2) ◽  
pp. 462-464 ◽  
Author(s):  
V. Birman
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Membrane Theory ◽  
Composite Shells ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Membrane Shell ◽  
Reinforced Composite ◽  
Statics And Dynamics ◽  
Vibration Problems

Governing equations for the statics and dynamics of reinforced composite shells are developed based on Vlasov’s semi-membrane shell theory. These equations have closed-form solutions illustrated for buckling and free vibration problems. The buckling solution converges to the known result for unstiffened isotropic shells.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

Membrane Theory for Layered Ellipsoidal Shells

1983 ◽  
Vol 105 (4) ◽  
pp. 356-362 ◽  
Author(s):  
D. L. Logan ◽  
M. Hourani
Keyword(s):  
Elastic Behavior ◽  
Pressure Loading ◽  
Membrane Theory ◽  
Shells Of Revolution ◽  
Ellipsoidal Shell ◽  
Closed Form Solutions ◽  
Membrane Shell ◽  
Epoxy Material ◽  
Specific Geometry ◽  
Membrane Shells

The stress analysis of a laminated anisotropic ellipsoidal membrane shell of revolution is considered. A system of equations which is appropriate to the elastic behavior of anisotropic membrane shells of revolution is used as a basis. These equations are applied to the specific geometry of an ellipsoidal shell to develop the particular equations used in the analysis. Closed-form solutions are derived for the stresses and displacements. Methods for determining the extremely cumbersome integrals in the equations for the displacements are discussed as well. To illustrate the equations, solutions are presented for an ellipsoidal shell simply supported on one edge and subjected to internal pressure loading. Numerical results are presented for glass-epoxy and boron-epoxy material systems.

DISCRETE SINGULAR CONVOLUTION (DSC) FOR FREE VIBRATION ANALYSIS OF CONICAL SHELLS WITH VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (01) ◽  
pp. 81-108 ◽  
Author(s):  
ÖMER CIVALEK
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Shell Theory ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Conical Shells ◽  
Various Boundary Conditions ◽  
Discrete Singular Convolution ◽  
Thin Shell Theory

This paper gives a relatively novel computational approach, the discrete singular convolution (DSC) algorithm, for the free vibration analysis of isotropic and orthotropic conical shells with different boundary conditions. The governing differential equations of vibration of the shell are formulated using Love's first approximation classical thin shell theory. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. Typical numerical results are presented illustrating the effect of various geometric and material parameters. The influence of boundary conditions on the frequency characteristics is also discussed. The obtained results are in excellent agreement with those in the literature.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

2019 ◽  
Vol 17 (03) ◽  
pp. 1850133 ◽  
Author(s):  
T. Truong-Thi ◽  
T. Vo-Duy ◽  
V. Ho-Huu ◽  
T. Nguyen-Thoi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Numerical Solutions ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Discrete Shear Gap

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

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