Small Slenderness Ratio Research Articles

A mathematical model of the edge-defined film-fed growth process

A model is presented to simulate the steady-state growth of a fiber produced by the edge-defined film-fed growth (EFG) process. Equations describing the axisymmetric transport of heat in the melt and fiber are discussed. Heat transfer between the system and the surrounding environment is assumed to take place via convection and radiation. Given the fiber translation velocity, the external temperature profile, the die temperature, and the input flow rate or the pressure, asymptotic solutions for the temperature profiles in the melt and fiber, and the melt/gas and solidifying interfacial shapes are developed in the limit of a small melt slenderness ratio (fiber radius/approximate melt height). The effect of process parameters on the shape of the fiber system is investigated.

An asymptotic approach to the mathematical modeling of Ohno continuous casting of cored rods

A model is presented to simulate Ohno Continuous Casting (OCC) of cored rods. Equations describing the axisymmetric transport of heat in the mold and cored rod are discussed. Heat transfer between the system and the surrounding environment is assumed to take place via convection. If the velocity of casting, the external temperature profile, the mold temperature, and the mold-cooler distance are given, asymptotic solutions for the temperature profile in the rod are found and expressions for the solidifying interfacial shapes are developed in the limit of a small melt slenderness ratio (mold radius/mold length). The effect of process parameters on the shape of the cored rod system is investigated.

鋼構造新素材(SA440B)を用いた柱模型の高温時の座屈強度

An experimental study was performed to obtain the data about the buckling strength of the column models using new metallic structural material (SA440B) at high temperature. Two kinds of experiments under the centrally compressive load with rectangular cross-sections of thickness lOmm X width 26mm, (1)tests at constant high temperature, and (2), tests at increasingly higher temperature under a constant axial load. By the tests (1), the buckling loads of column models which were enforced axial edge compression at a constant high temperature were examined. And, by the tests (2), the collapse temperatures of the column models at increasingly higher temperature under a constant load were examined. The results of these tests were compared on a chart of buckling curves, and it is observed that the buckling load of the tests(2) was larger than the tests(1) in the region of small slenderness ratio, and the result was reverse in the region of large slenderness ratio. Furthermore, in order to explain this result, numerical analyses were carried out, and the influence of the strain rate and P-Delta effect on the buckling strength of the column models under the elastic-plastic-creep behavior were confirmed.

Non-isothermal flows of Newtonian slender glass fibers

We perform a non-isothermal analysis of axisymmetric Newtonian slender fibers. Lubrication scaling with a small slenderness ratio ε along with restrictions on other dimensionless parameters systematically derives one-dimensional approximations from the full Navier-Stokes equations. At leading-order, we formally obtain the equations of previous analyses when the parameter range is appropriate. Higher-order analyses show the effects of weak two-dimensionality when all appropriate parameters are not sufficiently small. We have also established limitations on the one-dimensional approach of previous analyses. We consider a variable heat-transfer coefficient and show its importance in accurate predictions of fiber diameter. Our analysis is a comprehensive formulation and first step towards a rigorous non-isothermal viscoelastic analysis of the fiber drawing process.

塔状鋼管トラス骨組の座屈耐力に関する研究 : 細長比の小さい柱材で座屈する場合

We have performed the loading tests on buckling strength of tubular trussed towers whose members are bolted each other. These towers are designed to bukle at column members having small slenderness ratios. We have quantitatively clarified effects of bending moment, deformation capacity and stress redistribution of buckling member against strength of towers. And also, we have established the method of estimating the buckling strength of towers. Futhermore, effects of eccenricity ratios and slenderness ratios against buckling strength of pipe members composing the towers have been clarified through the eccentric buckling tests. This paper represents these experimental resuluts.

Micro- and macrobifurcation of fibrous metal-matrix composites under uniaxial compression

The AIM of this paper is to investigate the relation between macrobifurcation of dilute fibrous metal-matrix composites under uniaxial compression. The microbifurcation analysis involves examining the possibility for the existence of shear bands, or formation of either diffuse axisymmetric or asymmetric geometric modes in the representative volume element, which in the present analysis is considered to be the composite cylinder model. The results indicate that for small slenderness ratios (long wavelengths) [slenderness ratio = kR m/L , with R m = outer radius of the composite cylinder, L = fiberlength , and k = wave number (for a fixed R m , this quantity is inversely proportional to the wavelength, 2L/k)], the diffuse asymmetric mode is always the critical mode for microbifurcation. For small to moderate fiber volume fractions, we found a specific slenderness ratio (wavelength) above (below) which the diffuse axisymmetric mode becomes the critical microbifurcation mode. Due to the criticality of the asymmetric mode in the microbifurcation, only this mode has been considered in the macro analysis. The overall incremental moduli in the macrobifurcation study are obtained by using the Voigt approximation. For realistic dimensions of the composite cylinder, the critical strain for asymmetric microbifurcation will be always lower than the critical strain for the macrobifurcation of the same type in a solid cylinder with effective properties and a radius which is larger than that of the composite cylinder. An important aspect of the analysis is that it provides exact solutions to the three-dimensional diffuse bifurcation of the representative volume element under consideration.

Inelastic Buckling of Reinforcing Bars

A special beam‐column element is developed for the finite element inelastic buckling analysis of reinforcing bars in concrete columns. The material considered is elastic‐plastic‐strain hardening. A strain reversal rule is also included to model the unloading from compression once buckling occurs. The element is used to trace the post‐buckling load‐deflection path of a reinforcing bar supported laterally by sufficiently stiff ties of the column and initially loaded axially to the yielding load. The post‐buckling load‐deflection path depends on the slenderness ratio of the bar. For a very small slenderness ratio, an interesting [straightening] phenomenon is present after the buckling at the yielding load, followed by a second buckling at a higher load. For a larger slenderness ratio, the post‐buckling load carrying capacity may or may not exceed the yielding load. A critical slenderness ratio is found by equating the maximum load to the yielding load.

Three-dimensional acoustic waves in the ear canal and their interaction with the tympanic membrane

The long and slender geometry of the ear canal supports an infinite number of cross-sectional acoustic modes. The lower mode(s) travel along the length of the ear canal, while the higher modes are trapped near the ends of the canal. Many of these waves are introduced as a result of the complex vibrational shape of the eardrum. A three-dimensional mathematical model of the ear canal is formulated that includes this acoustic interaction. The coupled system is solved using matched asymptotic expansions that take advantage of the small slenderness ratio. This solution in the ear canal is in the form of a series of modes, the first being the plane-wave solution. As an illustrative example, the analysis is applied to a geometry that partially represents the ear canal and eardrum of a cat. The results indicate that the plane-wave solution is supplemented by multidimensional trapped modes at low frequencies and by a limited number of traveling waves at high frequencies. The magnitude of these higher modes generally increases with frequency and can significantly influence the acoustic coupling of the ear.

In-plane vibration of circular arc beam, cross sections of which suddenly vary stepwise. Case of small slenderness ratio.

When the circular arc beam, of which the centerline is a circular arc, and the cross sections suddenly very stepwise, vibrates in the plane of the beam, the frequency equation is determined by using Hamilton's principle. This analysis was carried out by taking into account the effects of shearing deformation, rotary inertia, and moreover, deviation of the centroid from the neutral plane. Since the frequency equation became a transcendental equation, its solution was determined by the method of iterative calculation using a computer. However, it was assumed that the material quality of the beam used for the numerical calculation was the same in all steps, and that the cross sections were circular. Besides, the supporting condition at both ends was assumed to be fixed. Then, the relation of the dimensionless natural frequency with the diameter ratio and opening angle, and the natural mode of vibration were shown in figures.

On the Application of Slender Body Theory to Antisymmetric Motions

In the previous report, a new composite solution in slender body theory was presented. The solution is more suitable than an ordinary solution of slender body theory for antisymmetric motions such as sway and yaw in ship manoeuvring motion.In this report, the method is extended to shallow water problems. The composite solution in shallow water is also composed of two dimensional potential at cross section and three dimensional correction terms like in deep water.As water depth increases, shallowness assumption that far field solution is approximated by horizontal plan flow does not hold good, and antisymmetric component of the solution converges to usual strip method.Consept of equivalent body is used in three dimensional correction terms. As water depth decrease, slenderness ratio of equivalent body increases. Then the restriction to small slenderness ratio becomes more strict than in deep water, but slenderness ratio of usual ship is within this limit.The practical effectiveness of this method is shown for acceleration coefficients of ships by comparing results of model tests, three dimensional calculations and this method.

初期たわみを有する弾塑性棒の縦衝撃による残留変形

Behavior of a slightly curved bar under longitudinal impact with a heavy rigid hammer at a low velocity was analyzed numerically, and the residual deformation of the bar was investigated. Dynamic elasto-plastic deformation was discussed for the bar subjected to the plastic strain of the same order as the elastic one. Because of difficulty in obtaining a closed form of solution for this problem due to geometric and material nonlinearity, the solid bar was replaced by a lumped-parameter model, and the equations of motion were integrated numerically.The stress at each point on the cross section was evaluated by taking account of a detailed deformation history of that point. The bending moment was calculated by integrating these stresses. This method has been confirmed to give more accurate results than using the conventional method for analyzing the behavior of bars of small slenderness ratios, in which the stress distribution over the cross section is highly nonlinear.The residual deformation of the bar was evaluated by the residual axial displacement of the struck end. The effects of the following two factors on the residual axial displacement were investigated; the ratio of the mass of the rigid hammer to that of the bar, and the impact velocity of the rigid hammer. As the result, it was shown that the residual axial displacement was expressed by the product of the power function of the mass ratio and that of the impact velocity.

On The Role of a Non-Newtonian Fluid in Short Bearing Theory

The importance of rheological properties of lubricants has arisen from the realization that non-Newtonian fluid effects are manifested over a broad range of lubrication applications. In this paper a theoretical investigation of short journal bearings performance characteristics for non-Newtonian power-law lubricants is given. A modified form of the Reynolds’ equation for hydrodynamic lubrication is studied in the asymptotic limit of small slenderness ratio (i.e., bearing length to diameter, L/D = λ→0). Fluid film pressure distributions in short bearings of arbitrary azimuthal length are studied using matched asymptotic expansions in the slenderness ratio. The merit of the short bearing approach used in solving a modified Reynolds’ equation by the method of matched asymptotic expansions is emphasized. Fluid film pressure distributions are determined without recourse to numerical solutions to a modified Reynolds’ equation. Power-law rheological exponents less than and equal to one are considered; power-law fluids exhibit reduced load capacities relative to the Newtonian fluid. The cavitation boundary shape is determined from Reynolds’ free surface condition; and the boundary shape is shown to be independent of the bearing eccentricity ratio.

水平力を受ける H 形鋼柱の弾塑性曲げ捩れ座屈に関する実験的研究

The lateral-torsional buckling tests of H-shaped steel beam-columns subjected to axial force and horizontal load, are performed in the form of L-shaped frame consisting of an H-shaped column and a box beam to investigate the maximum strength and the deformation behavior. The effects of the axial force ratio, the slenderness ratio and the beam-to-column relative stiffness ratio on the lateral-torsional buckling load and the in-plane load-displacement relation are discussed by comparing the test results with the theoretical results. Summarizing the results of parametric tests, the following conclusions are derived; (1) The maximum strength of a beam-column obtained in the test is generally higher than the theoretical lateral-torsional buckling strength. Detailed investigation on this point is yet needed together with the post-buckling analysis. The effect of the lateral-torsional buckling clearly apperars in the grave strength reduction after the maximum strength is attained. (2) As to the beam-columns with the slenderness ratio larger than or equal to 120, the sudden decrease in the strength takes place right after the maximum strength is attained, and the rotation capacity scarcely expected in these beam-columns. (3) The decrease in the value of the beam to-column relative stiffness ratio reduces the rotation capacity in the range of relatively small slenderness ratio, because of the combined effect of the in-plane P・△ moment and lateral-torsional buckling deformation.

Post‐Buckling Instability of Steel Beam‐Columns

This paper describes an investigation of buckling and post‐buckling behavior of steel beam‐columns. Beam‐columns having a H‐shaped cross section were studied for their deformability as well as ultimate strength. A constant axial thrust and monotonically increasing end moments were applied to the beam‐columns. Both experimental and analytical investigations were made in the study. Variables in the experimental study were cross‐sectional shape, length, and intensity of axial force. Numerical analysis demonstrated its capability to properly simulate the behavior of the tested beam‐columns. On the basis of parametric study using the numerical analysis, important findings can be drawn. First, lateral torsional deflection is more distinguished for beam‐columns with less axial force. Second, beam‐columns having a small slenderness ratio do not lead to instability by lateral torsional buckling, indicating a stable plastic range. Third, deformability drastically decreases once the slenderness ratio exceeds a certa...

A Method for the Estimation of Collapse Loads of Corner Girders and Struts

The equivalent thickness of deflected panels under compression and bending moment are estimated by the energy method. The effective flexural rigidity of columns with rather small slenderness ratio are estimated by using Johnson's and Euler's formula. Using these equivalent thickness and effective flexural rigidity, the collapse load of corner girders and struts are calculated by elastic finite element method. The collapse load and collapse mechanism are compared with experimental results. This method will be usefull at the initial design stage for the simplicity.

H 形断面材の塑性曲げ捩れ座屈実験

Tests on laterally unbraced H-shaped beam-columns were conducted to study the lateral torsional buckling strength and deformation behavior in the inelastic range. Beam-columns were subjected to constant axial compression and gradually applied end moments about strong axis of cross section. Main findings obtained from test results are as following : 1. Members with relatively large slenderness ratio collapse immediately after buckling initiates. Tangent modulus loads well correspond to ultimate strength of such members. 2. Members with relatively small slenderness ratio have a considerable post-buckling strength and failure is caused by the combination of lateral torsional buckling and local buckling of the compression flange. Tangent modulus loads are not reliable indices of ultimate strength of such members. 3. Most of specimens collapse suddenly after maximum bending moment in the member reaches a certain value. Thus the maximum bending moment may be taken for an index of failure of the members.