Theoretical and experimental study of braid pattern in mandrels with arbitrary cross-sections

2018 ◽  
Vol 52 (29) ◽  
pp. 4009-4022 ◽  
Author(s):  
Jalil Hajrasouliha ◽  
Reza Jafari Nedoushan ◽  
Mohammad Sheikhzadeh ◽  
Wonjin Na ◽  
Woong-Ryeol Yu

Braid angle is a key factor associated with the mechanical properties of braided composites, so accurate prediction of this angle is of vital importance for the design and manufacture of braided preforms. This paper presents a theoretical model for the prediction of braid angle at any point of a mandrel with constant arbitrary cross-section by taking into account the kinematic parameters of circular braiding machine. The proposed theoretical model pays particular attention to two parameters that strongly affect the braid angle, namely the position of fell point on the mandrel’s surface and the yarn length between this point and the carrier. Both of these parameters undergo continuous change during braiding and thus should be calculated on a point-to-point basis. The model was validated by a series of braiding experiments conducted, using a circular braiding machine, on mandrels with circular, elliptical, and oval cross-sections and then determining the resulting braid angles over the mandrel’s surface by an image processing method. The experimental results showed the high accuracy of the proposed theoretical model in predicting the braid angle for mandrels with constant arbitrary cross-section. Thus, the proposed model can contribute to faster and more accurate design and manufacture of braided composite preforms.

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.


Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.


Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.


A very general analysis is given of the phenomenon of shear lag in thin-walled cylindrical tubes, with single-cell cross sections of arbitrary shape, containing any number of concentrated longitudinal booms that carry direct stress only, and subjected to any longitudinal distribution of bending moment and torque. Two equations relating the distributions of direct and shearing stresses on the cross section are derived for the most general case where the tube is non-uniform because of an arbitrary longitudinal variation of wall thicknesses and boom areas. These equa­tions, which are remarkably simple in view of their generality, incor­porate all the requirements of equilibrium and compatibility and provide corrections to the stresses, curvature and twist calculated from the engineers’ theory of bending and torsion. They also govern the distri­bution of stresses arising from the application of self-equilibrating systems of tractions to the end cross sections. Exact solutions are ob­tained for the case of a uniform, but otherwise arbitrary, cross section under any polynomial distribution of bending moment and torque, and it is shown how conditions at the end cross sections can be satisfied with the aid of solutions of a simple eigenvalue problem. The equations are in a particularly ideal form for incorporating into a general purpose com­puter program for the automatic numerical solution of any problem of this type.


1948 ◽  
Vol 159 (1) ◽  
pp. 313-334 ◽  
Author(s):  
J. Kestin ◽  
A. K. Oppenheim

Calculations of the flow of gases in pipes or ducts of varying cross-sections are important in the design of turbines and compressors, nozzles for various applications, exhaust or radiator ducts, thrust augmenting devices, etc. Provided certain simplifying assumptions are made, there is no difficulty in writing down the basic equations, but when the velocities are comparable to that of sound and compressibility effects cannot therefore be neglected, the solution of the transcendental equations present difficulties which hinder a clear discussion of the physical phenomena. Here the problem is solved by the use of a generalized entropy chart, off which results may be directly read. For example, if the conditions in the reservoir from which the gas is assumed to be discharged are known, the complete conditions at any given cross-section may be read off when two parameters at the section considered are specified. The parameters may include the velocity, pressure, density, temperature, local Mach number, local velocity of sound, area of cross-section, mass flow per unit area, momentum per second, etc. The method is not confined to isentropic flows and may be applied to such problems as the flow in straight pipes or convergent and divergent nozzles including losses by either friction or condensation shocks. The co-ordinates of the chart are: dimensionless entropy σ = ( s— s0) J/R and dimensionless enthalpy ι = h/h0 = T/T0 where the meaning of the symbols is given later. All other variables are expressed in terms of these two co-ordinates and tables for several values of the ratio of specific heats are included to facilitate the drawing of such charts. The method does not aim at presenting new facts, but its usefulness lies in the provision of a comprehensive graphical means of calculating one-dimensional flow of compressible fluids. The charts lend themselves to the construction of a mechanical device for simplifying their use, such as a portable scale with sliding curves.


1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.


1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.


Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process.


Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process, and the second part of the material presented contains corresponding numerical examples, prepared in accordance with the theoretical foundations given in the first part.


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