Rotating Moderately Thick Annular Disks via an Extension to Classical Theory

2012 ◽  
Vol 28 (2) ◽  
pp. 355-360 ◽  
Author(s):  
A. M. Zenkour
Keyword(s):  
Classical Theory ◽  
Order Theory ◽  
Equilibrium Equations ◽  
Annular Disk ◽  
First Order ◽  
First Order Theory ◽  
Distributed Load ◽  
Vertical Displacements ◽  
Bending Stresses ◽  
Annular Disks

AbstractThe problem of rotating annular disk subjected to a uniformly distributed load is treated in two ways. Stress is divided into a rotating part because of the angular velocity and a bending part due to force loading. New set of equilibrium equations with small deflections is developed. Solutions for radial displacement, deflection, forces and moment resultants, and the rotating and bending stresses of the first-order theory are presented in terms of corresponding quantities of annular disks based on the classical theory. The boundary conditions at the edges of the annular disk are roller supported, clamped or free. Several examples are presented to illustrate the use and accuracy of these relationships. The effects of several parameters on the radial and vertical displacements and rotating and bending stresses are studied. It is observed that the classical theory is sufficient to study the problem of rotating annular disks. However, the inclusion of the effect of shear deformation is necessary to study precisely the curvature of moderately thick annular disks.

scholarly journals A Mindlin multilayered hybrid-mixed approach for laminated and sandwich structures without shear correction factors

2010 ◽  
pp. 725-742
Author(s):  
Achraf Tafla ◽  
Rezak Ayad ◽  
Lakhdar Sedira
Keyword(s):  
Transverse Shear ◽  
Order Theory ◽  
Shear Stresses ◽  
Correction Factors ◽  
Equilibrium Equations ◽  
First Order Theory ◽  
Static Condensation ◽  
Bending Stresses ◽  
Mixed Approach ◽  
Laminated Structures

A new hybrid-mixed variational approach for the linear analysis of laminated and sandwich plates, without transverse shear correction factors, is presented. It’s based on the first order theory of Reissner/Mindlin. A quadratic approximation through the thickness is proposed for transverse shear stresses (continuity C-1), and two equilibrium equations are used for their approximation. This reduces in consequence the number of interpolation parameters of bending stresses, which are eliminated using the static condensation technique. The proposed approach has been adapted to a quadrilateral 4-node finite element, free of locking, to which performances have been analyzed using some known problems of sandwich and laminated structures.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

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