Higher-order asymptotic model for a heterogeneous beam, including corrections due to end effects

2000 ◽  
Author(s):  
Natacha Buannic ◽  
Patrice Cartraud
Keyword(s):  
Higher Order ◽  
Asymptotic Model ◽  
End Effects

scholarly journals Application of the refined asymptotic model for describing of the transient extensional edge wave exited by a tangential load applied to the edge

2020 ◽  
pp. 146-154
Author(s):  
Григорий Николаевич Белосточный ◽  
Мария Владимировна Вильде ◽  
Мария Юрьевна Сурова
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Edge Wave ◽  
Asymptotic Model ◽  
Explicit Model ◽  
Refined Model ◽  
Transient Waves ◽  
Tangential Load ◽  
Dispersion Effects ◽  
Higher Order Theory

Изучается возможность применения уточненной асимптотической модели планарной краевой волны в задаче о действии нестационарной касательной нагрузки, приложенной на торце. При построении уточненной модели используется асимптотическая двумерная теория растяжения пластин высшего порядка точности. Приводятся результаты сравнения с решением по трехмерной теории упругости для различных законов распределения нагрузки. Показано, что уточненная модель позволяет достаточно точно описать влияние дисперсии краевой волны, не учитываемое в первом приближении. The possibility of application of the refined explicit model for extensional edge wave in the problem of transient waves excitation by an edge tangential load is investigated. The refined model is based on the higher order theory of plate extension. The results of comparison with the 3D solution for various distributions of the load are presented. It is shown that the refined model allows correct describing of dispersion effects which are not taken into account in the leading approximation.

Higher Order Effects on Bending of Helical Armor Wire Inside an Unbonded Flexible Pipe

2005 ◽  
Author(s):  
Zhimin Tan ◽  
Michael Case ◽  
Terry Sheldrake
Keyword(s):  
Higher Order ◽  
Thickness Ratio ◽  
Order Effects ◽  
Geometrical Shape ◽  
Flexible Pipe ◽  
End Effects ◽  
Mathematical Expressions ◽  
Bending Stresses ◽  
The Wire ◽  
Geometrical Effects

This paper investigates the higher order geometrical effects on the deflections of a helical armour wire when the pipe is subjected to uniform bending and is away from any end effects from its remaining fittings (end fittings), and the effect on the subsequent bending stresses. Due to its complexity in both geometrical shape and loading conditions, the approaches found in the literature are often to assume either a bent helix or geodesic as its deflected configuration with linearized mathematical expressions for simplification. The bending stresses are then calculated based on the geometrical difference between the assumed deflection and the original helical shape. The effect of the wire cross-section characteristics, for example the width and thickness ratio, over its deflection are often ignored. This paper presents an analytical strain energy model to quantify the influence of the wire width and thickness ratio over its final deflection. The higher order geometrical effects are fully considered in determining the wire deflection by using the exact mathematical expressions, and in the subsequent wire deformation and stress calculations. The paper also discusses briefly the structural coupling behavior between the pipe axial and bending deformations raised by using the exact expressions. The analytical results are validated by finite element simulation of an identical structure. The results are shown in good agreement in both deflection and the bi-normal bending stress. The results also show desirable conservatism in the normal and the total bending stresses. The presented analytical approach is demonstrated as an efficient and conservative way for investigating the behaviour of such a helical wire.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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