A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

2010 ◽  
Author(s):  
M. Amabili ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Geometrically Nonlinear ◽  
Geometric Imperfections ◽  
Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

A New Nonlinear Higher-Order Shear Deformation Theory With Thickness Variation for Large-Amplitude Vibrations of Laminated Doubly Curved Shells

2012 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Shear Deformation ◽  
Large Amplitude ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Higher Order ◽  
Forced Response ◽  
Curvilinear Coordinates ◽  
Thickness Variation ◽  
Geometrically Nonlinear ◽  
Thickness Variations

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape allowing for thickness variation by using six variables; geometric imperfections are also taken into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements. They are presented in curvilinear coordinates in a formulation that can be readily implemented in computer codes. This new theory is applied to laminated circular cylindrical shells complete around the circumference and simply supported at the ends. Linear (natural frequencies) and geometrically nonlinear (large-amplitude forced response) vibrations are studies by using the present theory and results are compared to those obtained by using the refined Amabili-Reddy higher-order shear deformation nonlinear shell theory, which neglects thickness variations.

A Higher Order Theory for Bending of Cross Ply Laminated Cylindrical Shell under Hygrothermal Loads

2015 ◽  
Vol 1115 ◽  
pp. 509-512 ◽  
Author(s):  
J.S. Mohamed Ali ◽  
Saleh Alsubari ◽  
Yulfian Aminanda
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Order Theory ◽  
Higher Order ◽  
Graphical Form ◽  
Laminated Shells ◽  
Elasticity Solutions ◽  
3D Elasticity ◽  
Higher Order Theory

The combined effect of moisture and temperature on the bending behaviour of simply supported cross ply composite laminated shells has been investigated. A 13 term accurate higher order shear deformation theory with zigzag function is used in this analysis in which the effects of transverse shear deformation are taken into account. The results are presented for thermal load cases are validated against available 3D elasticity solutions in the literature and useful results for combined hygrothermal loading are presented in tabular and graphical form.

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