scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

scholarly journals Non-linear vibration of eccentrically stiffened laminated composite shells

2008 ◽  
Vol 30 (2) ◽  
pp. 67-70
Author(s):  
Dao Huy Bich ◽  
Vu Do Long
Keyword(s):  
Laminated Composite ◽  
Gauss Curvature ◽  
Dynamical Analysis ◽  
Linear Vibration ◽  
Shallow Shells ◽  
Non Linear ◽  
Internal Forces ◽  
Doubly Curved ◽  
Laminated Composite Shells ◽  
Thin Shell Theory

The present paper deals with a non-linear vibration of eccentrically stiffened laminated composite doubly curved shallow shells. The calculations of internal forces and displacements of the shell are based upon the thin shell theory considering the geometrical non-linearity and the Lekhnitsky's smeared stiffeners technique. From the deformation compatibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Bubnov-Galerkin's method and iterative procedure in conjunction with Newmark constant acceleration scheme are used for dynamical analysis of shells to give the frequency-amplitude relation of free nonlinear vibration and non-linear transient responses. Numerical results show the influence of boundary conditions and Gauss curvature on the non-linear vibration of shells.

scholarly journals Non-linear dynamical analysis of laminated reinforced composite doubly curved shallow shells

2007 ◽  
Vol 29 (3) ◽  
pp. 257-269
Author(s):  
Dao Huy Bich ◽  
Vu Do Long
Keyword(s):  
Laminated Composite ◽  
Dynamical Analysis ◽  
Motion Equations ◽  
Shallow Shells ◽  
Reinforced Composite ◽  
Non Linear ◽  
Doubly Curved ◽  
Laminated Composite Shells ◽  
Thin Shell Theory ◽  
Shell Geometry

The present paper deals with a non-linear dynamical analysis of laminated reinforced composite doubly curved shallow shells. The motion equations of shell based upon the thin shell theory considering the geometrical non-linearity and the Lekhnitsky's smeared stiffeners technique. Simultaneous ordinary differential equations are obtained by means of Bubnov-Galerkin's procedure. Non-linear responses are calculated by using an iterative procedure in conjunction with Newmark constant acceleration scheme. Obtained results allow to discover the influence of stiffeners, the shell geometry on the non-linear response of eccentrically stiffened laminated composite shells.

scholarly journals Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Shi ◽  
Teijun Yang ◽  
Shiliang Jiang ◽  
W. L. Li ◽  
Zhigang Liu
Keyword(s):  
Boundary Conditions ◽  
Current Method ◽  
Vibration Characteristics ◽  
Shallow Shells ◽  
Various Boundary Conditions ◽  
Curvature Effects ◽  
Fourier Series Method ◽  
Vibration Problems ◽  
Elastic Restraints ◽  
Doubly Curved

Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

scholarly journals Non-linear analysis on stability of corrugated cross-ply laminated composite plates

2006 ◽  
Vol 28 (4) ◽  
pp. 197-206
Author(s):  
Dao Huy Bich ◽  
Khuc Van Phu
Keyword(s):  
Laminated Composite ◽  
Composite Plates ◽  
Sine Wave ◽  
Laminated Composite Plates ◽  
Non Linear ◽  
Post Buckling ◽  
Corrugated Plates ◽  
The Stability ◽  
Analytical Expressions ◽  
Linear Stability Problem

In the present paper the governing equations for corrugated cross-ply laminated composite plates in the form of a sine wave are developed based on the Kirchoff-Love's theory and the extension of Seydel's technique. By using Bubnov-Galerkin method approximated analytical solutions to the non-linear stability problem of corrugated laminated composite plates subjected to biaxial loads are investigated. The post buckling load-deflection curve of corrugated plates and analytical expressions of the upper and lower buckling loads are presented. The effectiveness of corrugated plates in enhancing the stability compared with corresponding fiat plates is given.

scholarly journals Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 1: Governing equations

2017 ◽  
Vol 39 (3) ◽  
pp. 245-257
Author(s):  
Dang Thuy Dong ◽  
Dao Van Dung
Keyword(s):  
Nonlinear Vibration ◽  
Thermal Loading ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Governing Equations ◽  
Shallow Shells ◽  
Geometrical Imperfection ◽  
Graded Material ◽  
Doubly Curved

Nonlinear vibration of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners subjected to mechanical and thermal loading are investigated based on the first-order shear deformation theory (FSDT) with von Karman type nonlinearity, taking into account initial geometrical imperfection and smeared stiffener technique. Four material models of the FGM sandwich shells are presented. Explicit expressions for natural frequencies, nonlinear frequency-amplitude relation, and time-deflection curves of the FGM sandwich shallow shells are derived using Galerkin method.

Non-linear vibrations of orthotropic doubly-curved shallow shells

1973 ◽  
Vol 31 (1) ◽  
pp. 89-103 ◽  
Author(s):  
B.R. El-Zaouk ◽  
C.L. Dym
Keyword(s):  
Shallow Shells ◽  
Non Linear ◽  
Linear Vibrations ◽  
Doubly Curved
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