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 Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

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%.

Analysis of shear lag in cylindrical tubes of arbitrary cross section

1983 ◽  
Vol 389 (1797) ◽  
pp. 259-277
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Bending Moment ◽  
General Purpose ◽  
Simple Eigenvalue ◽  
Arbitrary Cross Section ◽  
Longitudinal Distribution ◽  
Shear Lag ◽  
Cylindrical Tubes ◽  
Polynomial Distribution

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.

scholarly journals Analytical description of nanowires. I. Regular cross sections for zincblende and diamond structures

2019 ◽  
Vol 75 (5) ◽  
pp. 788-802 ◽  
Author(s):  
Dirk König ◽  
Sean C. Smith
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Analytical Description ◽  
Data Interpretation ◽  
High Symmetry ◽  
Cross Sectional ◽  
Impurity Atoms ◽  
Si Nanocrystals ◽  
Impurity Doping ◽  
The Cross

Semiconductor nanowires (NWires) experience stress and charge transfer from their environment and impurity atoms. In response, the environment of a NWire experiences a NWire stress response which may lead to propagated strain and a change in the shape and size of the NWire cross section. Here, geometric number series are deduced for zincblende- (zb-) and diamond-structured NWires of diameter d Wire to obtain the numbers of NWire atoms N Wire(d Wire[i]), bonds between NWire atoms N bnd(d Wire[i]) and interface bonds N IF(d Wire[i]) for six high-symmetry zb NWires with the low-index faceting that occurs frequently in both bottom-up and top-down approaches of NWire processing. Along with these primary parameters, the specific lengths of interface facets, the cross-sectional widths and heights and the cross-sectional areas are presented. The fundamental insights into NWire structures revealed here offer a universal gauge and thus could enable major advancements in data interpretation and understanding of all zb- and diamond-structure-based NWires. This statement is underpinned with results from the literature on cross-section images from III–V core–shell NWire growth and on Si NWires undergoing self-limiting oxidation and etching. The massive breakdown of impurity doping due to self-purification is shown to occur for both Si NWires and Si nanocrystals (NCs) for a ratio of N bnd/N Wire = N bnd/N NC = 1.94 ± 0.01 using published experimental data.

Optimization Design of the Cross-Section of the Umbilical Based on the Pseudo Mechanical Mechanism

2020 ◽  
Author(s):  
Zhixun Yang ◽  
Xu Yin ◽  
Dongyan Shi ◽  
Jun Yan ◽  
Lifu Wang ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Optimization Design ◽  
Signal Transmission ◽  
Interaction Force ◽  
Steel Tube ◽  
Iteration Algorithm ◽  
Cross Sectional ◽  
The Cross ◽  
Electrical Cables

Abstract Umbilical is a critical equipment in subsea production system for extracting offshore hydrocarbon resources, providing electrical and hydraulic power, control signal transmission and chemical injection. A diversity of components such as electrical cables, optical cables, steel tubes and filler bodies compose the cross-section of an umbilical. Different components perform different physical properties, so different cross-sections will present different geometrical characteristic, carrying capacities, thermal distribution, the cost and the ease of manufacture. Therefore, the cross-sectional design of the umbilical is a typical multi-objective optimization problem. The methodology of pseudo mechanical mechanism is introduced in this paper. Pseudo forces are assumed based on geometrical characteristics, carrying capacities and thermal productivities of different electrical cables, optical cables, steel tube and filler bodies. Each component is analogized to a sphere with different diameters on a funnel surface. Moreover, potential energy and interaction force between different components are defined to avoid the overlap and congestion. Then, the pseudo mechanical model is established and mathematics description is presented corresponding to the cross-section of an umbilical. Iteration algorithm procedure is given to solve this problem. Finally, a case of an umbilical is studied and the optimal cross-section is obtained, which is compared with the result used in practical engineering. It is shown that the methodology of the pseudo mechanical mechanism is effective to obtain the optimal design of cross-section of an umbilical.

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.

On a model for a time series of cross-sections

1986 ◽  
Vol 23 (A) ◽  
pp. 113-125 ◽  
Author(s):  
P. M. Robinson
Keyword(s):  
Time Series ◽  
Cross Section ◽  
Cross Sections ◽  
Standard Form ◽  
Cross Sectional ◽  
Aggregated Data ◽  
Section Data ◽  
Infinite Population ◽  
The Cross ◽  
Observation Times

Dynamic stationary models for mixed time series and cross-section data are studied. The models are of simple, standard form except that the unknown coefficients are not assumed constant over the cross-section; instead, each cross-sectional unit draws a parameter set from an infinite population. The models are framed in continuous time, which facilitates the handling of irregularly-spaced series, and observation times that vary over the cross-section, and covers also standard cases in which observations at the same regularly-spaced times are available for each unit. A variety of issues are considered, in particular stationarity and distributional questions, inference about the parameter distributions, and the behaviour of cross-sectionally aggregated data.

Comparison of different algorithms used for creating river terrain model based on the cross-sections.

2020 ◽  
Author(s):  
Luděk Bureš ◽  
Radek Roub ◽  
Petra Sychová
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Hydrodynamic Model ◽  
Linear Interpolation ◽  
Cross Sectional ◽  
Terrain Model ◽  
Model Based ◽  
Interpolation Techniques ◽  
The Cross

&lt;p&gt;Various techniques can be used to create a river terrain model. The most common technique uses 3D bathymetric points distributed across the main channel. The terrain model is then created using common interpolation techniques. The quality of this terrain depends on the number of the measured points and their location.&lt;/p&gt;&lt;p&gt;An alternative method may be an application of a set of cross-sections. Special interpolation algorithms are used for this purpose. These algorithms create new bathymetric points between two adjacent cross-sections that are located in a composite bathymetric network (CBN). Common interpolation techniques can be used to create a river terrain model. The advantage of this approach is a necessity of smaller dataset.&lt;/p&gt;&lt;p&gt;We present a comparison of four different algorithms for creating a river terrain model based on measured cross-sections. The first algorithm (A1) adopts a method of linear interpolation to create CBN [1]. The second algorithm (A2) reshapes the cross-sections and then applies linear interpolation. This reshaping allows better take into the account the thalweg line [2]. The third algorithm (A3) uses cross-sectional reshaping and uses cubic hermit splines to create CBN [3]. The last algorithm (A4) &amp;#160;implies the channel boundary and the thalweg line as additional inputs. Additional inputs define the shape of the newly created river channel [4].&lt;/p&gt;&lt;p&gt;Three different distances among individual cross-sections were used for the performance tests (50, 100 and 200 meters). The quality of topographic schematization and its impact on hydrodynamic model results were evaluated. Preliminary results show that there is almost no difference in the performance of the algorithms at cross-section distance of 50 m. The A4 algorithm outperforms/surpass its competitors in the case that input data (the cross-section distance is) are in 200 m spacing.&lt;/p&gt;&lt;p&gt;This research was supported by the Operational Programme Prague &amp;#8211; Growth Pole of the Czech Republic, project No. CZ.07.1.02/0.0/0.0/17_049/0000842, Tools for effective and safe management of rainwater in Prague city &amp;#8211; RainPRAGUE.&lt;/p&gt;&lt;p&gt;[1]&amp;#160; &amp;#160;&amp;#160;&amp;#160;&amp;#160; Vetter, M., H&amp;#246;fle, B., Mandelburger, G., Rutzinger, M. Estimating changes of riverine landscapes and riverbeds by using airborne LiDAR data and river cross-sections. Zeitschrift f&amp;#252;r Geomorphologie, Supplementary Issues, 2011, 55.2: 51-65.&lt;/p&gt;&lt;p&gt;[2]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; Chen, W., Liu, W. Modeling the influence of river cross-section data on a river stage using a two-dimensional /three-dimensional hydrodynamic model. Water, 2017, 9.3: 203.&lt;/p&gt;&lt;p&gt;[3]&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; Caviedes-Voulli&amp;#232;me, D.; Morales-Hern&amp;#225;ndez, M.; L&amp;#243;pez-Marijuan, I.; Garc&amp;#237;a-Navarro, P. Reconstruction of 2D river beds by appropriate interpolation of 1D cross-sectional information for flood simulation. Environ. Model. Softw., 2014, 61, 206&amp;#8211;228.&lt;/p&gt;&lt;p&gt;[4] &amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; Merwade, V.; Cook, A.; Coonrod, J. GIS techniques for creating river terrain models for hydrodynamic modeling and flood inundation mapping. Environ. Model. Softw., 2008, 23, 1300&amp;#8211;1311.&lt;/p&gt;

A Procedure to Include Slip Damping in a VIV Analysis of an Umbilical

2016 ◽  
Author(s):  
Elizabeth Passano ◽  
Shahriar Abtahi ◽  
Torfinn Ottesen
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Deep Water ◽  
Operating Conditions ◽  
Response Analysis ◽  
Material Damping ◽  
Structural Damping ◽  
Cross Sectional ◽  
The Cross ◽  
The Individual

Ocean currents may cause vortex induced vibrations (VIV) of deep-water umbilicals. The VIV response may give significant contributions to the total fatigue damage. Good estimations of the VIV response and damage are therefore important for the design of deep-water umbilicals. As VIV response is very sensitive to the structural damping, good response and fatigue estimates will be dependent on good estimates of the damping and that they are included in the VIV response analysis in a consistent way. A complex cross section such as an umbilical or a flexible riser will have two sources of structural damping; damping due to the strain variation in the individual materials that make up the cross sections, and damping due to the different layers slipping against one another. The first may be denoted material damping and is present at all response levels, and will be particularly important at low response levels. The second may be denoted slip damping and will contribute when the curvature exceeds the initial slip curvature. Ideally, accurate data for both the material and the slip damping are available. Unfortunately, this is not always the case and the damping parameters must then be estimated. The material damping may be estimated from the material properties of the various layers in the cross section, taking operating conditions such as temperature into account. The slip damping may be estimated from detailed cross-sectional analyses. As the slip damping is dependent on the curvature, iterations are needed to ensure that the applied damping and the calculated response are consistent with each other. A procedure to include these iterations within a VIV response calculation is proposed. A case study is presented demonstrating the use of the proposed procedure for a deep-water umbilical in a lazy wave configuration. For the case studied, the maximum curvatures caused by VIV are significantly reduced.

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