Anisotropic Plates With Various Openings Under Uniform Loading or Pure Bending

1990 ◽  
Vol 57 (3) ◽  
pp. 700-706 ◽  
Author(s):  
Chyanbin Hwu
Keyword(s):  
Approximate Solution ◽  
Stress Concentration ◽  
Hoop Stress ◽  
Anisotropic Plate ◽  
The Other ◽  
Real Form ◽  
Orthotropic Plates ◽  
Pure Bending ◽  
Uniform Loading ◽  
Anisotropic Plates

In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by Lekhnitskii using the complex variable formulation. Solutions for any kind of anisotropic plates with various openings are presented in this paper by applying the Stroh formalism and using the technique of conformal mapping. Unlike the former results, which have different orders of approximation for different openings, the solutions presented here have only one simple unified expression for various openings such as the ellipse, circle, crack, triangle, oval, and square. Two special loading conditions are considered: one is uniform loading, the other is pure bending. Through the use of identities developed in the literature, the hoop stress along the opening boundary is obtained in real form. The results show that the effect of anisotropy on the stress concentration is totally determined through the fundamental elasticity matrices N1 and N3 introduced by Stroh.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

Pure Moment Testing for Spinal Biomechanics Applications: Fixed Versus 3D Floating Ring Cable-Driven Test Designs

2012 ◽  
Author(s):  
Jessica A. Tang ◽  
Justin K. Scheer ◽  
Christopher P. Ames ◽  
Jenni M. Buckley
Keyword(s):  
Spinal Column ◽  
Bending Moments ◽  
Pure Bending ◽  
Uniform Loading ◽  
Flexion Extension ◽  
Driven System ◽  
Accepted Standard ◽  
Pure Moment ◽  
Bending Modes ◽  
Biomechanical Tests

For spine biomechanical tests, the cable-driven system in particular has been widely used to apply pure bending moments. The advantages to pure moment testing lie in its consistency as an accepted standard protocol across previous literature and its ability to ensure uniform loading across all levels of the spinal column. Of the methods used for pure moment testing, cable-driven set-ups are popular due to their low requirements and simple design. Crawford et al [1] were the first to employ this method, but prior work by our group indicated a discrepancy between applied and intended moment for this system in flexion-extension only [2]. We hypothesize that this discrepancy can be observed in other bending modes and minimized with a second-generation floating ring design to eliminate off-axis loads.

Stress Concentration at the Root of Bolt Thread

2010 ◽  
Author(s):  
Yasumasa Shoji ◽  
Toshiyuki Sawa
Keyword(s):  
Finite Element Analysis ◽  
Stress Concentration ◽  
Concentration Factor ◽  
The Other ◽  
Special Technique ◽  
Allowable Stress ◽  
Element Analysis ◽  
Bolt Stress ◽  
Thread Root ◽  
External Loads

The bolt strength is determined based on the concentrated bolt stress at the thread roots. The allowable stress is determined so that the thread root will not yield by the pretension and the external loads, using the stress concentration factor obtained as 3 to 5 from experiments. However, the concentration factor is not clear so far, as it is quite difficult to measure the stress at such a localized region. On the other hand, structural analysis, namely finite element analysis, has the possibility to provide the most-likely stress at the thread root. In this paper, a special technique, a.k.a. submodelling, is used to calculate the stress distribution at thread surfaces very precisely. The result will be useful to solve any stress related problems.

scholarly journals MEMBANGUN SEMANGAT KERASULAN REMAJA KATOLIK DALAM KONTEKS MASYARAKAT PLURALIS DI INDONESIA

2017 ◽  
Vol 17 (9) ◽  
pp. 3-14
Author(s):  
Agustinus Supriyadi
Keyword(s):  
Logical Consequence ◽  
Cross Cultural ◽  
The Other ◽  
Real Form ◽  
Pluralistic Society ◽  
The Real ◽  
Self Discovery ◽  
The One ◽  
The Church

Catholic teens Indonesia is part of the Church in Indonesia and the Indonesian people. Indonesia consists of thousands of islands that stretched from Sabang to Merauke. This fact opens the possibility of a fairly wide occurrence of the encounter between cultures and simultaneous cross-cultural. This diversity is certainly a logical consequence to an enrichment of civilizations and diversity (plurality), although also contains elements of the loss. Plurality of Indonesian society on the one hand can make the Catholic teens swept away in the swift currents of the community to lose our identity or conflict. However Plurality can also awaken in the Catholic teen award nature between one race to the other races, between ethnic or tribal one with the other tribes, between groups with one another. In a pluralistic society such as this, the Catholic teens called to the apostolate. Through the act of self-discovery, live in love and have a sense of tolerance of differences is the real form of the apostolate.

Calculation of Non-Homogeneous Anisotropic Rectangular Plates with Arbitrary Fixation on the Contur

2019 ◽  
Vol 968 ◽  
pp. 444-449
Author(s):  
Nikolay Zavrak
Keyword(s):  
Main Idea ◽  
Isotropic Case ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Anisotropic Plates ◽  
Practical Applications ◽  
Internal Forces ◽  
The Relationship ◽  
Difficult Cases ◽  
Anisotropic Rectangular Plates

The developing of the effective methodic of elastic orthotropic plates’ calculation and the research on the base of their state under different boundary conditions are of great importance nowadays. The representation of the received results in the form, convenient for practical use, is also important. For practical applications in engineering are important tables for determining deflections and internal forces of structures. Such tables for the isotropic case under various conditions of plate support on the contour are given in many works. As for the anisotropic plates, there are no such tables, with the exception of one Huber table compiled for a freely supported rectangular orthotropic plate, depending on the relationship between the stiffness values. Here is a method of calculating the non-homogeneous anisotropic rectangular plates with arbitrary fixation on the contour is set forth, which is reduced to a boundary value problem. The main idea of a calculated general methodic of linear marginal differential tasks calculation is based on underlying of the main part of a solution. Such approach is proved by means of development and some generalization of common positions of a variational method of marginal tasks of mathematical physics of self-conjugated tasks solution. To solve a system of equations in terms of displacements using finite difference method (FDM) in combination with different variations of analytical solutions. It is advisable to construct a numerical solution of the problem so that in difficult cases the support fixing and uploading solution sought, not directly, but in the form of amendments to the known solution for simple cases of reference to consolidate and uploading at finding the solutions which the analytical methods or the FDM with sparse mesh may be used. Given as examples are the results of calculation for a series of square orthotropic plates with a fixed boundary under the action of uniformly distributed load.

Orthotropy and geometry effects on stress concentration factors for short rectangular plates with a centred circular opening

2007 ◽  
Vol 42 (7) ◽  
pp. 551-555 ◽  
Author(s):  
K Bakhshandeh ◽  
I Rajabi
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Finite Width ◽  
Rectangular Plates ◽  
Circular Opening ◽  
Orthotropic Plates ◽  
Plate Length ◽  
Transition Length ◽  
Stress Concentration Factors

In this study, the effects of orthotropy ratio and plate length on the stress concentration factor for orthotropic plates with a centred circular opening under the action of uniaxial tension loads are investigated by use of the finite element method. This work demonstrates that the stress concentration factor depends on the length of the member in addition to other established geometric parameters. The value of the transition length between long and short plates is computed and reported as well. This study has shown that Tan's equation for a finite width orthotropic plate is accurate for a ratio of the opening radius to plate semiwidth of less than 0.35 for orthotropy ratios less than 50. A new concept is introduced, namely the transition ratio.

Calculation of stress-concentration factors for grooved shafts in bending using the point-matching technique

1973 ◽  
Vol 8 (2) ◽  
pp. 113-118 ◽  
Author(s):  
G J Matthews ◽  
C J Hooke
Keyword(s):  
Stress Concentration ◽  
Numerical Technique ◽  
Pure Bending ◽  
Point Matching ◽  
Matching Technique ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Stress Concentration Effect ◽  
Axisymmetric Bodies ◽  
Good Agreement

A general numerical technique is presented for the solution of the problem of elastic bending of axisymmetric bodies. Results obtained by this method are compared with existing results for grooved and shouldered shafts in pure bending and good agreement is obtained in each case. Additional results are presented for the stress-concentration effect of flat-bottomed circumferential grooves in cylindrical shafts for which no experimental or analytical results are available.

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