Analysis of three-layer composite plates with a new higher-order layerwise formulation

2014 ◽  
Vol 21 (3) ◽  
pp. 401-404
Author(s):  
Dalal A. Maturi ◽  
Antonio J.M. Ferreira ◽  
Ashraf M. Zenkour ◽  
Daoud S. Mashat
Keyword(s):  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Basis Functions ◽  
Numerical Accuracy ◽  
First Order ◽  
The Core ◽  
First Order Theory ◽  
Layer Composite ◽  
Vibration Problems

AbstractIn this paper, we combine a new higher-order layerwise formulation and collocation with radial basis functions for predicting the static deformations and free vibration behavior of three-layer composite plates. The skins are modeled via a first-order theory, while the core is modeled by a cubic expansion with the thickness coordinate. Through numerical experiments, the numerical accuracy of this strong-form technique for static and vibration problems is discussed.

A Simple Higher-Order Theory for Laminated Composite Plates

1984 ◽  
Vol 51 (4) ◽  
pp. 745-752 ◽  
Author(s):  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Order Theory ◽  
Higher Order ◽  
Laminated Composite Plates ◽  
First Order ◽  
First Order Theory

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano [6], but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

scholarly journals HOL-λσ: an intentional first-order expression of higher-order logic

2001 ◽  
Vol 11 (1) ◽  
pp. 21-45 ◽  
Author(s):  
GILLES DOWEK ◽  
THERESE HARDIN ◽  
CLAUDE KIRCHNER
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Search Method ◽  
Order Logic ◽  
Automated Deduction ◽  
Higher Order Logic ◽  
First Order ◽  
Proof Search ◽  
First Order Theory ◽  
Explicit Substitutions

We give a first-order presentation of higher-order logic based on explicit substitutions. This presentation is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, that is, a proposition can be proved without the extensionality axioms in one theory if and only if it can be in the other. We show that the Extended Narrowing and Resolution first-order proof-search method can be applied to this theory. In this way we get a step-by-step simulation of higher-order resolution. Hence, expressing higher-order logic as a first-order theory and applying a first-order proof search method is a relevant alternative to a direct implementation. In particular, the well-studied improvements of proof search for first-order logic could be reused at no cost for higher-order automated deduction. Moreover, as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle.

Effects of higher-order nonlinearity and finite geometry on the propagation of KdV solitons

1988 ◽  
Vol 40 (3) ◽  
pp. 545-552 ◽  
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Planar Waveguide ◽  
Electron Plasma ◽  
Finite Geometry ◽  
Order Theory ◽  
Higher Order ◽  
Ion Acoustic Wave ◽  
Electron Plasma Wave ◽  
First Order ◽  
First Order Theory ◽  
Ion Acoustic

Using reductive perturbation theory and a planar waveguide geometry, the effects of higher-order nonlinearity and finite boundaries on the propagation of electron plasma and ion-acoustic KdV solitons are investigated by taking into account finite electron and ion temperatures. For an electron plasma wave, the higher-order nonlinearity is found to increase the amplitude of the soliton and slightly decrease the width of the soliton compared with that predicted by the first-order theory. For an ion-acoustic wave the higher-order-nonlinearity and finite-boundary effects give rise to a W-shaped soliton.

Decidability and undecidability of extensions of second (first) order theory of (generalized) successor

1966 ◽  
Vol 31 (2) ◽  
pp. 169-181 ◽  
Author(s):  
Calvin C. Elgot ◽  
Michael O. Rabin
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Second Order ◽  
First Order ◽  
First Order Theory ◽  
Function Constant

We study certain first and second order theories which are semantically defined as the sets of all sentences true in certain given structures. Let be a structure where A is a non-empty set, λ is an ordinal, and Pα is an n(α)-ary relation or function4 on A. With we associate a language L appropriate for which may be a first or higher order calculus. L has an n(α)-place predicate or function constant P for each α < λ. We shall study three types of languages: (1) first-order calculi with equality; (2) second-order monadic calculi which contain monadic predicate (set) variables ranging over subsets of A; (3) restricted (weak) second-order calculi which contain monadic predicate variables ranging over finite subsets of A.

Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity

2000 ◽  
Vol 417 ◽  
pp. 1-45 ◽  
Author(s):  
YASUHIDE FUKUMOTO ◽  
H. K. MOFFATT
Keyword(s):  
Vortex Ring ◽  
Higher Order ◽  
The Self ◽  
Large Reynolds Number ◽  
Arbitrary Distribution ◽  
Inviscid Fluid ◽  
Third Order ◽  
First Order ◽  
The Core ◽  
First Order Theory

A large-Reynolds-number asymptotic solution of the Navier–Stokes equations is sought for the motion of an axisymmetric vortex ring of small cross-section embedded in a viscous incompressible fluid. In order to take account of the influence of elliptical deformation of the core due to the self-induced strain, the method of matched of matched asymptotic expansions is extended to a higher order in a small parameter ε = (v/Γ)1/2, where v is the kinematic viscosity of fluid and Γ is the circulation. Alternatively, ε is regarded as a measure of the ratio of the core radius to the ring radius, and our scheme is applicable also to the steady inviscid dynamics.We establish a general formula for the translation speed of the ring valid up to third order in ε. This is a natural extension of Fraenkel–Saffman's first-order formula, and reduces, if specialized to a particular distribution of vorticity in an inviscid fluid, to Dyson's third-order formula. Moreover, it is demonstrated, for a ring starting from an infinitely thin circular loop of radius R0, that viscosity acts, at third order, to expand the circles of stagnation points of radii Rs(t) and R˜s(t) relative to the laboratory frame and a comoving frame respectively, and that of peak vorticity of radius R˜p(t) as Rs ≈ R0 + [2 log(4R0/√vt) + 1.4743424] vt/R0, R˜s ≈ R0 + 2.5902739 vt/R0, and Rp ≈ R0 + 4.5902739 vt/R0. The growth of the radial centroid of vorticity, linear in time, is also deduced. The results are compatible with the experimental results of Sallet & Widmayer (1974) and Weigand & Gharib (1997).The procedure of pursuing the higher-order asymptotics provides a clear picture of the dynamics of a curved vortex tube; a vortex ring may be locally regarded as a line of dipoles along the core centreline, with their axes in the propagating direction, subjected to the self-induced flow field. The strength of the dipole depends not only on the curvature but also on the location of the core centre, and therefore should be specified at the initial instant. This specification removes an indeterminacy of the first-order theory. We derive a new asymptotic development of the Biot-Savart law for an arbitrary distribution of vorticity, which makes the non-local induction velocity from the dipoles calculable at third order.

scholarly journals Ultraproducts and Higher Order Models

2021 ◽  
Author(s):  
◽  
Wilfred Gordon Malcolm
Keyword(s):  
Order Theory ◽  
Higher Order ◽  
Embedding Theorems ◽  
First Order ◽  
First Order Theory ◽  
Higher Order Theory ◽  
Higher Order Models

<p>The programme of work for this thesis began with the somewhat genenal intention of parallelling in the context of higher order models the ultraproduct construction and its consequences as developed in the literature for first order models. Something of this was, of course, already available in the ultrapower construction of W.A.J. Luxemburg used in Non Standand Analysis. It may have been considered that such a genenal intention was not likely to yield anything of significance oven and above what was already available from viewing the higher order situation as a 'many sorted' first order one and interpreting the first order theory accordingly. In the event, however, I believe this has proved not to be so. In particular the substructure concepts developed in Chapter II of this thesis together with the various embedding theorems and their applications are not immediately available fnom the first order theory and seem to be of sufficient worth to warrant developing the higher order theory in its own terms. This, anyway, is the basic justification for the approach and content of the thesis.</p>

scholarly journals Evaporation and combustion of a slowly moving liquid fuel droplet: higher-order theory

1996 ◽  
Vol 307 ◽  
pp. 135-165 ◽  
Author(s):  
M. A. Jog ◽  
P. S. Ayyaswamy ◽  
I. M. Cohen
Keyword(s):  
Flow Field ◽  
Order Theory ◽  
Higher Order ◽  
Second Order ◽  
Spherical Particles ◽  
General Nature ◽  
Fuel Droplet ◽  
First Order ◽  
First Order Theory ◽  
Higher Order Theory

The evaporation and combustion of a single-component fuel droplet which is moving slowly in a hot oxidant atmosphere have been analysed using perturbation methods. Results for the flow field, temperature and species distributions in each phase, inter-facial heat and mass transfer, and the enhancement of the mass burning rate due to the presence of convection have all been developed correct to second order in the translational Reynolds number. This represents an advance over a previous study which analysed the problem to first order in the perturbation parameter. The primary motivation for the development of detailed analytical/numerical solutions correct to second order arises from the need for such a higher-order theory in order to investigate fuel droplet ignition and extinction characteristics in the presence of convective flow. Explanations for such a need, based on order of magnitude arguments, are included in this article. With a moving droplet, the shear at the interface causes circulatory motion inside the droplet. Owing to the large evaporation velocities at the droplet surface that usually accompany drop vaporization and burning, the entire flow field is not in the Stokes regime even for low translational Reynolds numbers. In view of this, the formulation for the continuous phase is developed by imposing slow translatory motion of the droplet as a perturbation to uniform radial flow associated with vigorous evaporation at the surface. Combustion is modelled by the inclusion of a fast chemical reaction in a thin reaction zone represented by the Burke–Schumann flame front. The complete solution for the problem correct to second order is obtained by simultaneously solving a coupled formulation for the dispersed and continuous phases. A noteworthy feature of the higher-order formulation is that both the flow field and transport equations require analysis by coupled singular perturbation procedures. The higher-order theory shows that, for identical conditions, compared with the first-order theory both the flame and the front stagnation point are closer to the surface of the drop, the evaporation is more vigorous, the droplet lifetime is shorter, and the internal vortical motion is asymmetric about the drop equatorial plane. These features are significant for ignition/extinction analyses since the prediction of the location of the point of ignition/extinction will depend upon such details. This article is the first of a two-part study; in the second part, analytical expressions and results obtained here will be incorporated into a detailed investigation of fuel droplet ignition and extinction. In view of the general nature of the formulation considered here, results presented have wider applicability in the general areas of interfacial fluid mechanics and heat/material transport. They are particularly useful in microgravity studies, in atmospheric sciences, in aerosol sciences, and in the prediction of material depletion from spherical particles.

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