Non-one-dimensional combustion of specimens with rectangular cross section

1983 ◽  
Vol 19 (4) ◽  
pp. 377-380 ◽  
Author(s):  
V. A. Vol'pert ◽  
A. V. Dvoryankin ◽  
A. G. Strunina
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
One Dimensional

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

Simulation on Composite Backscattering from Rough Surface with Target above it

2012 ◽  
Vol 490-495 ◽  
pp. 603-607
Author(s):  
Wei Tian ◽  
Xin Cheng Ren
Keyword(s):  
Rough Surface ◽  
Root Mean Square ◽  
Cross Section ◽  
Correlation Length ◽  
Rectangular Cross Section ◽  
Mean Square ◽  
Method Of Moment ◽  
Backscattering Coefficient ◽  
One Dimensional ◽  
Surface Fluctuation

One-dimensional Gaussion rough surface is simulated and employed by Monte Carlo Method, the composite backscattering from one-dimensional Gaussion rough surface with rectangular cross-section column above it is studied using Method of Moment. The curves of composite backscattering coefficient with scattering angle and frequency of incident wave are simulated by numerical calculation, the influence of the root mean square and the correlation length of rough surface fluctuation, the height between the center of the rectangular cross-section column and the rough surface, the length and the width of the rectangular cross-section column is discussed. The characteristic of the composite back-scatting from one-dimensional Gaussion rough surface with a rectangular cross-section column above it is obtained. The results show that the influences of the root mean square and the correlation length of rough surface fluctuation, the height between the center of the rectangular cross-section column and the rough surface, the width of the rectangular cross-section column on the composite backscattering coefficients are obvious while the influences of the length of the rectangular cross-section column on the complex backscattering coefficient is less.

One-dimensional model of fourth order for rods with loading on lateral boundary: The case of rectangular cross section

2016 ◽  
Vol 22 (12) ◽  
pp. 2269-2287 ◽  
Author(s):  
Erick Pruchnicki
Keyword(s):  
Cross Section ◽  
Fourth Order ◽  
Displacement Field ◽  
Rectangular Cross Section ◽  
Transverse Dimension ◽  
Lateral Boundary ◽  
Dimensional Model ◽  
Equilibrium Equations ◽  
Lagrange Equations ◽  
One Dimensional

We propose deducing from three-dimensional elasticity a one dimensional model of a beam when the lateral boundary is not free of traction. Thus the simplification induced by the order of magnitude of transverse shearing and transverse normal stress must be removed. For the sake of simplicity we consider a beam with rectangular cross section. The displacement field in rods can be approximated by using a Taylor–Young expansion in transverse dimension of the rod and we truncate the potential energy at the fourth order. By considering exact equilibrium equations, the highest-order displacement field can be removed and the Euler–Lagrange equations are simplified.

Calculation of Self Inductance and Mutual Inductance of Coils with Rectangular Cross Section

2014 ◽  
Vol 9 (1) ◽  
pp. 10-14
Author(s):  
Aleksandr Ivanov
Keyword(s):  
Numerical Calculation ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Mutual Inductance ◽  
One Dimensional ◽  
Dimensional Integral

An inductance and mutual inductance of coils with rectangular cross section is given in a form of one-dimensional integral. The formula is appropriate for numerical calculation of the inductances with given accuracy

One-Dimensional Theories of Wave Propagation and Vibrations in Elastic Bars of Rectangular Cross Section

1966 ◽  
Vol 33 (3) ◽  
pp. 489-495 ◽  
Author(s):  
M. A. Medick
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Isotropic Material ◽  
Rectangular Cross Section ◽  
One Dimensional ◽  
Anisotropic Elastic

A method for constructing rational, one-dimensional theories of various orders of approximation, descriptive of wave propagation and vibrations in anisotropic elastic bars of rectangular cross section, is presented. As illustrations, several approximate theories are derived which are applicable to extensional motion in rectangular bars of isotropic material.

NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART I

2012 ◽  
Vol 22 (03) ◽  
pp. 1150016 ◽  
Author(s):  
LORENZO FREDDI ◽  
MARIA GIOVANNA MORA ◽  
ROBERTO PARONI
Keyword(s):  
Cross Section ◽  
Elastic Energy ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Scaling Factor ◽  
One Dimensional ◽  
Thin Walled ◽  
The Cross ◽  
Limit Models ◽  
Cross Section Part

Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. More precisely, denoting by h and δh the length of the sides of the cross-section, with δh ≪ h, and by [Formula: see text] the scaling factor of the bulk elastic energy, we analyze the cases in which δh/εh → 0 (subcritical) and δh/εh → 1 (critical).

scholarly journals Internal inductance of a conductor of rectangular cross-section using the proper generalized decomposition

2016 ◽  
Vol 35 (6) ◽  
pp. 2007-2021 ◽  
Author(s):  
Manuel Pineda-Sanchez ◽  
Angel Sapena-Baño ◽  
Juan Perez-Cruz ◽  
Javier Martinez-Roman ◽  
Ruben Puche-Panadero ◽  
...  
Keyword(s):  
Cross Section ◽  
Distribution Systems ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Numerical Procedure ◽  
Magnetic Vector Potential ◽  
Proper Generalized Decomposition ◽  
Content Type ◽  
One Dimensional ◽  
Internal Inductance

Purpose Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors. Design/methodology/approach The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance. Findings The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation. Research limitations/implications The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires. Originality/value The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II

2013 ◽  
Vol 23 (04) ◽  
pp. 743-775 ◽  
Author(s):  
LORENZO FREDDI ◽  
MARIA GIOVANNA MORA ◽  
ROBERTO PARONI
Keyword(s):  
Cross Section ◽  
Elastic Energy ◽  
Rectangular Cross Section ◽  
Limit Behavior ◽  
Rigorous Derivation ◽  
One Dimensional ◽  
Thin Walled ◽  
Dimensional Models ◽  
Nonlinear Elastic ◽  
Cross Section Part

In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with a rectangular cross-section. Denoting by h and δh ≪ h the length of the sides of the cross-section of the beam, we analyze the limit behavior of a nonlinear elastic energy which scales as [Formula: see text] when ϵh/δh → 0.

Elastic Guided Waves in a Layered Plate With a Rectangular Cross Section

2002 ◽  
Vol 124 (3) ◽  
pp. 319-325 ◽  
Author(s):  
O. M. Mukdadi ◽  
S. K. Datta ◽  
M. L. Dunn
Keyword(s):  
Cross Section ◽  
Guided Waves ◽  
Rectangular Cross Section ◽  
Ultrasonic Guided Waves ◽  
Finite Width ◽  
Phonon Modes ◽  
Anisotropic Plates ◽  
One Dimensional ◽  
Number Of Layers ◽  
Propagating Waves

Ultrasonic guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) are studied in this paper. A semi-analytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the long dimension of the plate is used. The method is applicable to an arbitrary number of layers of anisotropic properties and is similar to that used earlier to study guided waves in layered anisotropic plates of infinite width. Numerical results are presented for acoustic phonon modes of quasi-one-dimensional (QID) wires. For homogeneous wires, these agree well with recently reported results for dispersion of these modes.

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