A refined theory of laminated shells with higher-order transverse shear deformation

1997 ◽  
Vol 34 (6) ◽  
pp. 673-683 ◽  
Author(s):  
Xiao-Ping Shu
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Higher Order ◽  
Transverse Shear Deformation ◽  
Refined Theory ◽  
Laminated Shells

scholarly journals THE REFINED THEORY OF ELASTIC PLATES AS ASYMPTOTIC APPROACH OF 3D PROBLEM

2018 ◽  
Vol 196 ◽  
pp. 02037
Author(s):  
Nelly Rogacheva
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Three Dimensional ◽  
Transverse Shear Deformation ◽  
Refined Theory ◽  
Elastic Plates ◽  
Asymptotic Approach ◽  
Thick Plates ◽  
Kirchhoff Theory ◽  
3D Problem

The refined theory of elastic thin and thick plates is constructed by the asymptotic method for reducing three-dimensional (3D) equations of linear elasticity to two-dimensional ones without the use of any assumptions. The resulting refined theory is much more complicated than the known classical Kirchhoff theory: the required values of the refined theory vary in thickness of the plate by more complex laws; the system of partial differential equations of the refined theory has a higher order than the system of equations of the classical theory. A comparison of the obtained theory with the popular refined theory of Timoshenko and E. Reissner, taking into account the transverse shear deformation is made. It is shown that the inclusion only of the transverse shear deformation is insufficient. In addition to the transverse shear deformation, many additional terms having the same order as the transverse shear deformation must be taken into account.

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.

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