Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

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.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

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.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

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 super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

scholarly journals Effects of Bridge-Shaped Microchannel Geometry on the Performance of a Micro Laminar Flow Fuel Cell

Micromachines ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 822
Author(s):  
Muhammad Tanveer ◽  
Kwang-Yong Kim
Keyword(s):  
Fuel Cell ◽  
Numerical Model ◽  
Laminar Flow ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Narrow Channel ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Square Channel

A laminar flow micro fuel cell comprising of bridge-shaped microchannel is investigated to find out the effects of the cross-section shape of the microchannel on the performance. A parametric study is performed by varying the heights and widths of the channel and bridge shape. Nine different microchannel cross-section shapes are evaluated to find effective microchannel cross-sections by combining three bridge shapes with three channel shapes. A three-dimensional fully coupled numerical model is used to calculate the fuel cell’s performance. Navier-Stokes, convection and diffusion, and Butler-Volmer equations are implemented using the numerical model. A narrow channel with a wide bridge shape shows the best performance among the tested nine cross-sectional shapes, which is increased by about 78% compared to the square channel with the square bridge shape.

Three-Dimensional Stratigraphic Characterization for Geotechnical Exploration

1996 ◽  
Vol 1526 (1) ◽  
pp. 183-190
Author(s):  
Patrick Kinnicutt ◽  
Herbert Einstein ◽  
Carlos Noack
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Engineering Practice ◽  
Borehole Data ◽  
Cross Sectional ◽  
Site Model ◽  
Indicator Cokriging ◽  
A Site ◽  
Gis Software

In current geotechnical engineering practice, soil or rock stratigraphy is usually obtained from borehole data. Interpolation between boreholes is performed by projecting borehole data on a cross-sectional plane, either by hand drawings or by using CAD or GIS software, then manually interpolating between the boreholes. This methodology for obtaining the geology of a site does not truly represent the three-dimensional nature of the data, and it does not capture the uncertainties in the interpolation. This study describes NOMAD, a three-dimensional ground profiler developed for education and research that runs on the UNIX platform. The focus is on features available in NOMAD for visualizing uncertainties, creating ground profiles from site data, and updating the model with new subjective and objective data. One such feature, which will be described in detail, is the ability to modify a cross section of the site and have this modification automatically propagated to the site model and other cross sections, allowing users to visualize how changes in one cross section affect other cross sections. Also discussed is a model incorporated in NOMAD for creating ground profiles from borehole data. This model makes use of Indicator CoKriging and Bayesian Updating for modeling both the subjective and objective information about a site, taking into account the true three-dimensional nature of the data.

Study on Effects of Novel Cross Sections of Microchannel Heat Sink on Thermohydraulic Performance

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Abhilash K. Tilak ◽  
Ranjit S. Patil
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Heat Sinks ◽  
Microchannel Heat Sink ◽  
The Novel ◽  
Cross Sectional ◽  
The Heat Transfer Coefficient ◽  
Three Dimensional Simulations

Abstract In this paper, three-dimensional simulations to study the performance of microchannel heat sinks (MCHS) with rectangular, hexagonal, semicircular and various novel cross section (such as barrel, fan shaped, L shaped, inverted T shaped, inverted T shaped with semicircular ends at base (ITSCEB)) were carried out using de-ionized water. Numerical results were validated with the published experimental data and further simulations were performed on various novel cross section at a constant heat flux of 50 W/cm2 with Reynolds number varying in the range of 300–1500. The comparative analysis of various novel MCHS having the same cross-sectional area was carried out to figure out the suitable cross section capable of better cooling performance. This work shows that the novel ITSCEB cross section was giving the highest pressure drop, however considerable improvement was noted in the heat transfer coefficient around 21% more than conventional rectangular and around 11–55% more than other proposed cross section in this study.

Three-Dimensional Vibration Analysis of Toroidal Sectors With Solid Circular Cross-Sections

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
D. Zhou ◽  
Y. K. Cheung ◽  
S. H. Lo
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Small Strain ◽  
Boundary Function ◽  
Mode Shapes ◽  
Curvature Radius ◽  
Linear Elasticity Theory ◽  
Energy Principle ◽  
Cross Sectional ◽  
The Cross

This paper studies the free vibration of circular toroidal sectors with circular cross-sections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted.

scholarly journals Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

2021 ◽  
Author(s):  
Dang-Bao Tran ◽  
Jaroslav Navrátil
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Local Analysis ◽  
3D Analysis ◽  
Shear Lag ◽  
Isoparametric Element ◽  
Cross Sectional ◽  
The Cross

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

scholarly journals Theory of “dissolution” and “condensation” of the physical geometric characteristics of an arbitrary cross-section under the action of torsion with bending

2019 ◽  
Vol 15 (4) ◽  
pp. 261-270
Author(s):  
Vladimir I. Kolchunov ◽  
Aleksej I. Demyanov ◽  
Nikolay V. Naumov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Strain State ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Large Circle ◽  
Stress Strain ◽  
Cross Sectional ◽  
Tangential Stresses ◽  
Stress Strain State

Aim of research - to continue the development of methods for determining the stress-strain state of rods during torsion using materials resistance methods. Methods. A new approach for determining tangential torsional stresses for arbitrary cross sectional rods, based on simplified assumptions of material resistance, is proposed. The main feature of this approach is the approximation of rectangular or any complex cross section of reinforced concrete structures by describing a large circle around the cross section and splitting it into small squares with circles inscribed into them. Results. Three theorems have been formulated, the first of which relates the accumulation of tangential stresses (increments) from the edges of a rectangle to the middle of a rectangular section with the formula for determining tangent stresses for round sections. The second theorem allows to establish a connection between the tangential stresses calculated for each of the small squares-circles and the tangent stresses of the large circle through their increments. The third theorem makes it possible to find tangential stresses for each of the small square circles. The proposed approach allows to remove the need to use special tables for the calculation and not only in the elastic stage. It also makes it possible to separate the stress-strain state in the whole set of round cross-sections from the additional field caused by the deplanation of the rectangular cross-section. In addition, the proposed approach makes it possible to take into account the concentration of angular deformations in the incoming angles and other places with changing geometric parameters.

A Simple Method for the Design of Supersonic Nozzles of Arbitrary Cross Section Shape

2020 ◽  
Author(s):  
N. Boughazi ◽  
A. Haddad
Keyword(s):  
Cross Section ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Simple Method ◽  
Supersonic Nozzles ◽  
De Laval Nozzle

Abstract A simple approach for the design of supersonic nozzles of complex 3D shapes is presented. The Method of characteristics is primarily applied to compute the axisymmetric flow field of the supersonic section of the de-Laval nozzle. Two-dimensional simulations are performed for the axisymmetric flow fields. The 3D configuration is then generated from the desired exit axisymmetric cross-sectional shape chosen through tracing its geometrical parameters back.to the throat. Elliptical, corrugated and two-dimensional wedge nozzles were designed using this approach. Preliminary results show a smooth geometrical transition from the throat to the exit cross section. Further three-dimensional analyses of the obtained geometries along with cold flow testing constitute the next steps to be performed.

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