In-Plane Bending of Curved Circular Tubes

1968 ◽  
Vol 90 (4) ◽  
pp. 666-670 ◽  
Author(s):  
D. H. Cheng ◽  
H. J. Thailer
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Compatibility Condition ◽  
Circular Tube ◽  
Series Expansions ◽  
Center Line ◽  
Complementary Energy ◽  
Circular Tubes ◽  
Binomial Expansion ◽  
Plane Bending

A general solution is presented for a thin, curved circular tube under in-plane bending. It includes the solution given by Clark and Reissner as a particular case in which the ratio of the radius of the tube to the radius of its center line is very small. The series expansions satisfy the equilibrium equation for any radius ratio while the compatibility condition is guaranteed by minimizing the complementary energy. The minimization is achieved in the manner of Raileigh-Ritz whereas the evaluation of integrals are facilitated by the use of binomial expansion. Numerical results correlate well with the experimental data. The solution is more rapidly convergent as compared to the existing analytical methods.

scholarly journals Some categorical aspects of the inverse limits in ditopological context

2018 ◽  
Vol 19 (1) ◽  
pp. 101
Author(s):  
Filiz Yildiz
Keyword(s):  
Compatibility Condition ◽  
Natural Transformation ◽  
Inverse Limits ◽  
Infinite Products ◽  
Inverse Systems ◽  
Finite Products

<p>This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if<strong>PDitop</strong>, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category <strong>Inv<sub>ifPDitop</sub></strong> consisting of the inverse systems constructed by the objects and morphisms of if<strong>PDitop</strong>, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in if<strong>PDitop</strong> and the ditopological infinite products are characterized by the finite products via inverse limits.</p>

Entropy principle as a restrictive condition on kinetic equations

1981 ◽  
Vol 59 (5) ◽  
pp. 698-707 ◽  
Author(s):  
Miroslav Grmela
Keyword(s):  
Compatibility Condition ◽  
Kinetic Equations ◽  
Restrictive Condition ◽  
Freedom Of Choice ◽  
Equilibrium Thermodynamics ◽  
Entropy Principle

A family of kinetic equations involving undetermined quantities is introduced. The requirement that the kinetic equations are compatible with equilibrium thermodynamics implies a compatibility condition restricting the freedom of choice of the undetermined quantities.

An extension of the coupled derivative nonlinear Schrödinger hierarchy

2018 ◽  
Vol 32 (02) ◽  
pp. 1850016
Author(s):  
Siqi Xu ◽  
Xianguo Geng ◽  
Bo Xue
Keyword(s):  
Conservation Laws ◽  
Spectral Problem ◽  
Compatibility Condition ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Nonlinear Schrödinger ◽  
Matrix Spectral Problem

In this paper, a 3 × 3 matrix spectral problem with six potentials is considered. With the help of the compatibility condition, a hierarchy of new nonlinear evolution equations which can be reduced to the coupled derivative nonlinear Schrödinger (CDNLS) equations is obtained. By use of the trace identity, it is proved that all the members in this new hierarchy have generalized bi-Hamiltonian structures. Moreover, infinitely many conservation laws of this hierarchy are constructed.

Positively bitter and negatively sweet?

Pragmatics ◽  
2020 ◽  
Author(s):  
Suwon Yoon
Keyword(s):  
Compatibility Condition ◽  
Literal Meaning ◽  
Conventional Implicature ◽  
Figurative Meaning ◽  
Condition Model ◽  
Pragmatic Analysis ◽  
Expressive Meaning ◽  
Occurrence Pattern ◽  
Expressive Dimension

Abstract The goal of this study is to propose a pragmatic analysis of what we call Emotive Taste Terms (ETTs) in Korean, compared to English. What makes Korean taste adjectives special is its multidimensional meaning: In descriptive dimension, (i) the literal meaning concerns the taste; or (ii) it can be extended toward the situation, yielding a figurative meaning. In expressive dimension, (iii) the choice of particular derivation form reflects the speaker’s positive or negative emotional attitude; and (iv) another potential expressive meaning concerns honorification, thought it is not part of the meaning of ETTs. We thus propose that ETTs are a novel subcase of expressive elements, triggering Conventional Implicature. We show how the analysis of ETTs as a CI allows us to successfully derive subtle connotational differences amongst numerous variants. Finally, we show how the co-occurrence pattern of multiple expressives, ETTs and other expressives, within the sentence can be captured by Compatibility Condition Model.

Numerical simulations of the humid atmosphere above a mountain

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Arthur Bousquet ◽  
Mickaël D. Chekroun ◽  
Youngjoon Hong ◽  
Roger M. Temam ◽  
Joseph Tribbia
Keyword(s):  
Boundary Conditions ◽  
Finite Volume ◽  
Compatibility Condition ◽  
Stokes Equations ◽  
Numerical Study ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Small Scale ◽  
Spatial Discretization ◽  
Humid Atmosphere

AbstractNew avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.

A New and Consistent Approach for Deriving Brinson’s 1-D Constitutive Equation for Shape Memory Alloys

2008 ◽  
Author(s):  
Rasoul Khandan ◽  
Mojtaba Mahzoon ◽  
Seyed Ahmad Fazelzadeh ◽  
Ali Hemmasizadeh
Keyword(s):  
Constitutive Equation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Compatibility Condition ◽  
Constitutive Equations ◽  
Modified Model ◽  
Clear Cut ◽  
Straightforward Approach ◽  
Consistent Approach

One of the first 1-D constitutive equations for shape memory alloys was presented by Brinson L.C in 1993 that became the base of later works typically. In Brinson’s equation, several proposed functions are considered in order to simplify the model and obtain the constitutive equation for SMA. In a recent paper V. R. Buravalla and A. Khandelwal (2007) have shown certain anomalies in Brinson’s model and have tried to present a modified model which unlike Brinson’s model satisfies the compatibility condition. However, their formulation, besides being lengthy, lacks clarity and in particular does not address proper expressions for transformation tensors Ωs and ΩT. In the present work, Brinson’s constitutive equation is derived from fundamental relations using a simple, clear-cut and straightforward approach. Without any extra and unnecessary assumption the consistency of the model is confirmed.

Sign in / Sign up

Export Citation Format

Share Document