scholarly journals Applied Systems Theory: Mathematical and Numerical Simulation of Strength of Thick-wall Pipe by Using Static Elastic Problems

2021 ◽  
Vol 15 ◽  
pp. 1346-1364
Author(s):  
Natela Zirakashvili
Keyword(s):  
Numerical Simulation ◽  
Systems Theory ◽  
Normal Stress ◽  
Separation Of Variables ◽  
Theory Of Elasticity ◽  
Internal Boundary ◽  
External Boundary ◽  
Thick Wall ◽  
Polar Coordinate System ◽  
Mathematical And Numerical Simulation

In Systems Theory, the Mathematical and numerical simulation of strength of thick-wall pipe by using static elastic problems is an important problem and has attracted the attention of many researches, academicians and practitioners. the The present work studies the change in the strength of a quite long isotropic thick-wall pipe (circular cylinder) for the varying pipe diameter, wall thickness and material. The pipe is in the plane deformed state, i.e. plane deformation is considered. Based on the problems of statics of the theory of elasticity, a mathematical model to calculate the strength of the thick-wall pipe was developed and the problems of statics of the theory of elasticity were set and solved analytically in the polar coordinate system. The analytical solution was obtained by the method of separation of variables, which is presented by two harmonious functions. The dependence of the pipe strength on the thickness and material of the pipe wall, when (a) normal stress is applied to the internal boundary (internal pressure) and external boundary is free from stresses and (b) normal stress is applied to the external boundary (external pressure) and the internal boundary is free from stresses, is studied. In particular, the minimum thicknesses of the walls of homogeneous isotropic circular cylinders of different materials and diameters with a plane deformed mode when the pressures in the cylinders do not exceed the admissible values were identified. Some numerical results are presented as tables, graphs and relevant consideration.

Optimal Solutions for Nonhomogeneous Multiply-Connected Torsional Sections

1989 ◽  
Vol 111 (1) ◽  
pp. 87-93 ◽  
Author(s):  
A. Mioduchowski ◽  
M. G. Faulkner ◽  
B. Kim
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Boundary Value ◽  
Optimization Procedure ◽  
Second Order ◽  
External Boundary ◽  
Optimal Solutions ◽  
Torsion Problem ◽  
Multiply Connected

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

An Analysis on Influencing Factors of Interlayer Separation of Complex Roof in Deep Coal Mining

2010 ◽  
Vol 146-147 ◽  
pp. 976-979
Author(s):  
De Yi Wu ◽  
Ai Lang Wang ◽  
Hua Qiang Liang
Keyword(s):  
Numerical Simulation ◽  
Normal Stress ◽  
Coal Mining ◽  
Influencing Factors ◽  
Friction Angle ◽  
Rock Stress ◽  
Roof Collapse ◽  
Tunnel Width ◽  
Original Rock

In order to control construction face instability of complex roof and predict roof collapse in deep coal mining, by numerical simulation, distribution of normal stress and interlayer separation of construction surface were calculated and influencing factors on separation of construction surface were analyzed in different conditions. The conclusions were drawn that original rock stress, rock characters, rock thickness and tunnel width had obvious influence and cohesion and friction angle of construction surface had little influence on separation of construction surface.

Numerical Simulation of a First Normal Stress Difference-Based Model for Shear-Induced Crystallization of Polyethylene

2011 ◽  
Vol 266 ◽  
pp. 130-134
Author(s):  
Jin Yan Wang ◽  
Jing Bo Chen ◽  
Chang Yu Shen
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Normal Stress ◽  
Viscoelastic Model ◽  
Normal Stress Difference ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Avrami Model ◽  
First Normal Stress Difference ◽  
Induced Crystallization

The paper presents a numerical simulation for the isothermal flow-induced crystallization of polyethylene under a simple shear flow. The effect of flow on crystllization is considered through the simple mathematical relationship between the additional number of nuclei induced by shear treatment and the first normal stress difference. Leonov viscoelastic model and Avrami model are used to describe the normal stress difference and the crystallization kinetics, respectively. It is found that the short-term shear treatment has a large effect on the crystallization dynamics of polyethylene , but the effect of the intensity of the shear flow is not infinite ,which shows a saturation phenomenon, namely, the accelerated degree of crystallization tending to level off when the shear rate or shear time is large enough.

Numerical Simulation on Interface Crack Propagation for Non-Uniform Welded Joint

2012 ◽  
Vol 602-604 ◽  
pp. 2065-2068
Author(s):  
Xiang Hong Zhang ◽  
Can Duo Shen ◽  
Chang Qing Sun
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Composite Material ◽  
Normal Stress ◽  
Fracture Resistance ◽  
Welded Joint ◽  
The Finite Element Method ◽  
Stress Criterion ◽  
Maximum Normal Stress

Maximum normal stress criterion can be used to determine the cracking angle in the uniform and non-uniform zone. According to this theory, the propagating process of the crack in non-uniform composite material is simulated based on the finite element method. The results show that the crack advances wave-like and basically along the direction perpendicular to the maximum normal stress, which is of great guiding significance for the fracture resistance of such kind of structure.

scholarly journals APLIKASI OPERASI HIMPUNAN DAN MATEMATIKA MORFOLOGI PADA PENGOLAHAN CITRA DIGITAL

2016 ◽  
Vol 10 (2) ◽  
pp. 83-96
Author(s):  
V. Y. I. Ilwaru ◽  
Y. A. Lesnussa ◽  
E. M. Sahetapy ◽  
Z. A. Leleury
Keyword(s):  
Edge Detection ◽  
Internal Boundary ◽  
External Boundary

Perkembangan teknologi pengolahan citra dewasa ini berkembang dengan sangat pesat, baik itu jumlah pemakai maupun jenis teknologi yang menggunakan pengolahan citra. Salah satu teknik pengolahan citra yang digunakan adalah deteksi tepi (edge detection). Pendeteksian tepi digunakan untuk meningkatkan penampakan garis batas suatu daerah atau obyek di dalam citra. Selain itu deteksi tepi digunakan untuk memperbaiki detail dari citra yang kabur, yang terjadi karena error atau adanya efek dari akuisisi citra. Pada penelitian ini dibahas pengolahan citra digital melibatkan operasi himpunan dan matematika morfologi dengan operasi yang digunakan yaitu Erosi, Dilasi, Opening, Closing, Internal Boundary, External Boundary, Morfologi Gradien, dan Filtering. Kemudian menerapkan setiap operasi dimaksud dalam mengolah image sehingga diperoleh hasil citra image dari setiap operasi himpunan dan matematika morfologi.

Steady vibration problems in the coupled linear theory of porous elastic solids

2019 ◽  
Vol 25 (3) ◽  
pp. 768-790 ◽  
Author(s):  
Merab Svanadze
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Existence Theorems ◽  
Theory Of Elasticity ◽  
Boundary Integral ◽  
External Boundary ◽  
Classical Solutions ◽  
Elementary Functions ◽  
Basic Properties ◽  
Steady Vibrations

This paper concerns the coupled linear theory of elasticity for isotropic porous materials. In this theory the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established and Green’s identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single layer and double layer) and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

scholarly journals Noise Reduction Evaluation of Multi-Layered Viscoelastic Infinite Cylinder under Acoustical Wave Excitation

2008 ◽  
Vol 15 (5) ◽  
pp. 551-572 ◽  
Author(s):  
M.R. Mofakhami ◽  
H. Hosseini Toudeshky ◽  
Sh. Hosseini Hashemi
Keyword(s):  
Noise Reduction ◽  
Viscoelastic Material ◽  
Viscoelastic Properties ◽  
Separation Of Variables ◽  
Theory Of Elasticity ◽  
Acoustic Medium ◽  
Viscoelastic Layer ◽  
Infinite Cylinder ◽  
Frequency Dependent ◽  
Uniform Noise

In this paper sound transmission through the multilayered viscoelastic air filled cylinders subjected to the incident acoustic wave is studied using the technique of separation of variables on the basis of linear three dimensional theory of elasticity. The effect of interior acoustic medium on the mode maps (frequency vs geometry) and noise reduction is investigated. The effects of internal absorption and external moving medium on noise reduction are also evaluated. The dynamic viscoelastic properties of the structure are rigorously taken into account with a power law technique that models the viscoelastic damping of the cylinder. A parametric study is also performed for the two layered infinite cylinders to obtain the effect of viscoelastic layer characteristics such as thickness, material type and frequency dependency of viscoelastic properties on the noise reduction. It is shown that using constant and frequency dependent viscoelastic material with high loss factor leads to the uniform noise reduction in the frequency domain. It is also shown that the noise reduction obtained for constant viscoelastic material property is subjected to some errors in the low frequency range with respect to those obtained for the frequency dependent viscoelastic material.Noise reduction analyses are also performed for the infinite cylinder subjected to the periodic incident wave with uniform and piecewise form.

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