Optimal Beam Theory through Dynamic Variational-Asymptotic Procedure

2020 ◽  
Vol 24 (4) ◽  
pp. 36-44
Author(s):  
Ri-Kyoung Yoon ◽  
Chang-Young Lee
Keyword(s):  
Beam Theory ◽  
Variational Asymptotic ◽  
Optimal Beam

Proper Inclusion of Interiorly Applied Loads With Beam Theory

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jimmy C. Ho ◽  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Asymptotic Method ◽  
Beam Theory ◽  
Elliptic Cylinder ◽  
Conventional Approach ◽  
Body Forces ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Elasticity Solutions ◽  
Precise Distribution

An error is introduced by the conventional approach of applying beam theory in the presence of interiorly applied loads. This error arises from neglecting the influence of the precise distribution of surface tractions and body forces on the warping displacements. This paper intends to show that beam theory is capable of accounting for this influence on warping and accomplishes this by the variational asymptotic method. Correlations between elasticity solutions and beam solutions provide not only validations of beam solutions, but also illustrate the resulting errors from the conventional approach. Correlations are provided here for an isotropic parallelepiped undergoing pure extensional deformations and for an isotropic elliptic cylinder undergoing pure torsional deformations.

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Anurag Rajagopal ◽  
Dewey H. Hodges
Keyword(s):  
Cross Section ◽  
Ad Hoc ◽  
Beam Theory ◽  
Reference Line ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Variational Asymptotic ◽  
Validation Set ◽  
3D Elasticity ◽  
Sectional Analysis

Structural and aeroelastic analyses using beam theories by default choose a cross section that is perpendicular to the reference line. In several cases, such as swept wings with high AR, a beam theory that allows for the choice of a cross section that is oblique to the reference line may be more convenient. This work uses the variational asymptotic method (VAM) to develop such a beam theory. The problems addressed are the planar deformation of a strip and the full 3D deformation of a solid, prismatic, right-circular cylinder, both made of homogeneous, isotropic material. The motivation for choosing these problems is primarily the existence of 3D elasticity solutions, which comprise a complete validation set for all possible deformations and which are shown to be accurately captured by the current analysis. A secondary motivation was that the development and final results of the beam theory, i.e., the cross-sectional stiffness matrix and stress-strain-displacement recovery relations, are obtainable as closed-form analytical expressions. These results, coupled with the VAM-based beam analysis being devoid of ad hoc assumptions, culminate in what is expected to be of significance when formulating a general oblique cross-sectional analysis for beams with anisotropic material and initial curvature/twist, the detailed treatment of which will be alluded to in a later paper.

Observation of faint contrast at planar faults in alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 340-341
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi
Keyword(s):  
Reciprocal Lattice ◽  
Beam Theory ◽  
Al Alloys ◽  
Small Displacement ◽  
Electron Microscopic ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Planar Fault ◽  
Lattice Displacement ◽  
The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

2020 ◽  
Author(s):  
Gibin Gil ◽  
Sujin Lee
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Beam Theory ◽  
Slip Angle ◽  
Wear Properties ◽  
Angle Change ◽  
Foundation Model ◽  
Plane Bending ◽  
Stiffness Characteristics ◽  
Brush Model

ABSTRACT In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high. During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration. In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

Atomic disruption beam theory

2016 ◽  
pp. 3524-3528
Author(s):  
Casey Ray McMahon
Keyword(s):  
Neutron Beam ◽  
Beam Theory ◽  
Solid Material ◽  
Material Matter ◽  
Solid Matter ◽  
Plasma Generation ◽  
Resulting Effect ◽  
Drilling Operations ◽  
The Stability

In this paper, I discuss the theory behind the use of a dense, concentrated neutron particle-based beam. I look at the particle based physics behind such a beam, when it is focused against solid material matter. Although this idea is still only theoretical, it appears that such a beam may be capable of disrupting the stability of the atoms within solid matter- in some cases by passing great volumes of neutrons between the electron and nucleus thus effectively “shielding” the electron from the charge of the nucleus. In other cases, by disrupting the nucleus by firing neutrons into it, disrupting the nucleus and weakening its bond on electrons. In either case- the resulting effect would be a disruption of the atom, which in the case of material matter would cause said material matter to fail, which would appear to the observer as liquification with some plasma generation. Thus, a dense neutron particle based beam could be used to effectively liquefy material matter. Such a beam could bore through rock, metal, or even thick, military grade armour, like that used on tanks- causing such materials to rapidly liquefy. The denser and thicker the neutron beam, the more devastating the effect of the beam- thus the faster material matter will liquefy and the greater the area of liquification. Such a beam would have applications in Defence, mining and drilling operations.

Validation of the variational asymptotic beam sectional analysis

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 2105-2112 ◽  
Author(s):  
W. Yu ◽  
V. Volovoi ◽  
D. H. Hodges ◽  
X. Hong
Keyword(s):  
Variational Asymptotic ◽  
Sectional Analysis

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Miguel Abambres
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
Flow Theory ◽  
Promising Alternative ◽  
Inelastic Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Gaussian-beam theory of lenses with annular aperture

1978 ◽  
Vol 2 (4) ◽  
pp. 105 ◽  
Author(s):  
C.J.R. Sheppard ◽  
T. Wilson
Keyword(s):  
Gaussian Beam ◽  
Beam Theory ◽  
Annular Aperture
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