A new nonlinear higher-order shear deformation theory with thickness variation for large-amplitude vibrations of laminated doubly curved shells

2013 ◽  
Vol 332 (19) ◽  
pp. 4620-4640 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Shear Deformation ◽  
Large Amplitude ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Thickness Variation ◽  
Doubly Curved Shells ◽  
Large Amplitude Vibrations ◽  
Doubly Curved

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.

scholarly journals Thermal postbuckling analysis of FG-CNTRC doubly curved panels with elastically restrained edges using Reddy's higher order shear deformation theory

2020 ◽  
Vol 42 (3) ◽  
pp. 307-320
Author(s):  
Hoang Van Tung ◽  
Nguyen Dinh Kien ◽  
Le Thi Nhu Trang
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
External Pressure ◽  
Higher Order ◽  
Postbuckling Behavior ◽  
Geometrical Imperfection ◽  
Thermal Postbuckling ◽  
Doubly Curved ◽  
Curved Panels

For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.

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