Accuracy of cross-section stress numerical integration by boundary integration formulae

2014 ◽  
pp. 111-120 ◽  
Author(s):  
A Matuszak ◽  
P Pluciński
Keyword(s):  
Numerical Integration ◽  
Cross Section ◽  
Boundary Integration

scholarly journals PENGARUH BENDUNG TERHADAP PROFIL MUKA AIR SUNGAI BATANG GADIS

2014 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Sudarmanto ,
Keyword(s):  
Numerical Integration ◽  
Cross Section ◽  
Water Surface ◽  
Surface Profile ◽  
Uniform Flow ◽  
Flood Discharge ◽  
Before And After ◽  
Numerical Integration Methods ◽  
The Village ◽  
River Cross Section

Placement of the weir in the river Batang Gadis will cause population anxiety in the village Pulungan which located upstream weir as far as 3 km, due to a weir can cause water surface profile of the river getting higher and ultimately to increase the pool of flooding in residential areas.Assuming modeling of river a uniform flow, river cross-section has a rectangular shape with width 50 m and 40 m, the roughness Manning 0.0025, the profile of water flow floods that occurred in 2 yaears, 25 years, and 100 years before and after the existing weir can be calculated by numerical integration methods.  From the calculation, the length of the water behind the weir is 1.4 km upstream towards the weir, which means that the depth of the water level rises to as far as 1.4 km and after that the depth of water before and after there the weir is same. Because the village Pulungan located 3 km to the upstream, the weir did not affect the increase in the flood waters in the village Pulungan. At 2 years flood discharge does not cause inundation in the village Pulungan, but the flood discharge 25 years and 100 years has led to inundation in the village Pulungan with the depth of each pool 0.971 m and 1.675 m. Keywords: uniform flow, numerical integration, inundation, flood discharge.

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

scholarly journals Developed Mathematical Model for Indeterminate Elements with Variable Inertia and Curved Elements with Constant Cross-Section

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mohamed A. El Zareef ◽  
Mohamed E. El Madawy ◽  
Mohamed Ghannam
Keyword(s):  
Mathematical Models ◽  
Numerical Integration ◽  
Cross Section ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimum Number ◽  
Fe Model ◽  
Constant Cross Section ◽  
Structural Elements ◽  
Good Agreement

Issues such as analysis of indeterminate structural elements that have variable inertia as well as a curved shape still have no closed form solution and are considered one of the major problems faced by design engineers. One method to cope with these issues is by using suitable the finite element (FE) software for analyzing these types of elements. Although it saves time, utilization of FE programs still needs professional users and not all engineers are familiar with it. This paper has two main objectives; first, to develop simple mathematical models for analyzing indeterminate structural elements with variable inertia and that have a curved shape with constant cross section, this model is much easier to be used by engineers compared to the FE model. For simplicity and saving time, a MATLAB program is developed based on investigated mathematical models. The force method combined with numerical integration technique is used to develop these models. The developed mathematical models are verified using the suitable FE software; good agreement was observed between the mathematical and the FE model. The second objective is to introduce a mathematical formula to determine the accurate number of divisions that would be used in the mathematical models. The study proves that the accuracy of analysis depends on the number of divisions used in the numerical integration. The optimum number of divisions is obtained by comparing the output results for both FE and developed mathematical models. The developed mathematical models show a good agreement with FE results with faster processing time and easier usage.

Considering the Friction Equilibrium of an Elastic Rod Constrained to a Cylinder

2015 ◽  
Vol 751 ◽  
pp. 200-204
Author(s):  
Zhao Liu ◽  
Xi Ying Qian ◽  
Jia Le Qu
Keyword(s):  
Numerical Integration ◽  
Cross Section ◽  
Mathematics Model ◽  
Euler Angles ◽  
Balance Equations ◽  
Elastic Rod ◽  
Analytical Integration ◽  
The Cross ◽  
Kirchhoff Theory

Considering the friction and discussing equilibrium of an Elastic Rod constrained to a Cylinder based on the Kirchhoff theory [1].Firstly take Euler angles as variables which describe the attitude of the cross section, establish a simple and clearly physical meanings mathematics model and balance equations, then considering smooth and nonsmooth contact, discuss the balance of an elastic rod constrained to a cylinder under special condition, give its analytical integration [2] and numerical integration, drawing and analysis the influence of force to the shape of an elastic rod constrained to a cylinder.

Calculation of Stress in Crane Hooks

1946 ◽  
Vol 13 (3) ◽  
pp. A239-A242
Author(s):  
A. M. Wahl
Keyword(s):  
Numerical Integration ◽  
Cross Section ◽  
Analytical Method ◽  
Slide Rule ◽  
Irregular Shapes ◽  
Comparison Of The Results

Abstract Two methods for calculating stress in crane hooks which have given good results in practice are described. One method, based on a numerical integration of the curved-bar equations, involves only slide-rule accuracy and may be used for irregular shapes of cross section. The second or analytical method is based on an analysis of an equivalent trapezoidal section, and is applicable to hooks having sections which do not deviate too much from the trapezoidal form. Comparison of the results of the two methods when applied to actual crane hooks indicates that the more rapid analytical method is sufficiently accurate for most practical purposes.

scholarly journals Next-to-leading non-global logarithms in QCD

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Andrea Banfi ◽  
Frédéric A. Dreyer ◽  
Pier Francesco Monni
Keyword(s):  
Phase Space ◽  
Energy Distribution ◽  
Numerical Integration ◽  
Cross Section ◽  
Transverse Energy ◽  
Evolution Equations ◽  
Wide Angle ◽  
Fixed Order ◽  
Standing Problem ◽  
Soft Radiation

Abstract Non-global logarithms arise from the sensitivity of collider observables to soft radiation in limited angular regions of phase space. Their resummation to next-to-leading logarithmic (NLL) order has been a long standing problem and its solution is relevant in the context of precision all-order calculations in a wide variety of collider processes and observables. In this article, we consider observables sensitive only to soft radiation, characterised by the absence of Sudakov double logarithms, and we derive a set of integro-differential equations that describes the resummation of NLL soft corrections in the planar, large-Nc limit. The resulting set of evolution equations is derived in dimensional regularisation and we additionally provide a formulation that is manifestly finite in four space-time dimensions. The latter is suitable for a numerical integration and can be generalised to treat other infrared-safe observables sensitive solely to soft wide-angle radiation. We use the developed formalism to carry out a fixed-order calculation to $$ \mathcal{O}\left({\alpha}_s^2\right) $$ O α s 2 in full colour for both the transverse energy and energy distribution in the interjet region between two cone jets in e+e− collisions. We find that the expansion of the resummed cross section correctly reproduces the logarithmic structure of the full QCD result.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

XUV Absorption Spectra of Carbon Ions

1988 ◽  
Vol 102 ◽  
pp. 71-73
Author(s):  
E. Jannitti ◽  
P. Nicolosi ◽  
G. Tondello
Keyword(s):  
Absorption Spectra ◽  
Cross Section ◽  
Theoretical Calculations ◽  
Photoionization Cross Section ◽  
Carbon Ions

AbstractThe photoabsorption spectra of the carbon ions have been obtained by using two laser-produced plasmas. The photoionization cross-section of the CV has been absolutely measured and the value at threshold, σ=(4.7±0.5) × 10−19cm2, as well as its behaviour at higher energies agrees quite well with the theoretical calculations.

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