A hierarchical finite element for geometrically non-linear vibration of doubly curved, moderately thick isotropic shallow shells

2003 ◽  
Vol 56 (5) ◽  
pp. 715-738 ◽  
Author(s):  
Pedro Ribeiro
Keyword(s):  
Finite Element ◽  
Linear Vibration ◽  
Shallow Shells ◽  
Non Linear ◽  
Doubly Curved ◽  
Hierarchical Finite Element

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 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.

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