Mathematical and Computational Applications

566 KiB

Open AccessArticle

by Hikmet Hassanov

Math. Comput. Appl. 2001, 6(1), 75-83; https://doi.org/10.3390/mca6010075 - 1 Apr 2001

Viewed by 1064

The hydrodynamic problem of defining the velocity profile of liquid is resolved, assuming for the liquid density to be compressed in accordance with exponential law along coordinate z. The continuity equation for this liquid is concluded. Influence of barometric index λ on [...] Read more.

The hydrodynamic problem of defining the velocity profile of liquid is resolved, assuming for the liquid density to be compressed in accordance with exponential law along coordinate z. The continuity equation for this liquid is concluded. Influence of barometric index λ on motion character is estimated. Flowrate decrease and coefficient of hydraulic losses for the compressed liquid are found. Principle of quasi - isothermal approximation is established, and the effect of temperature gradient on final result is qualitatively considered. Full article

363 KiB

Open AccessArticle

Determination of the Deflection Function of a Composite Cantilever Beam Using Theory of Anisotropic Elasticity

by Alaattin Aktaş

Math. Comput. Appl. 2001, 6(1), 67-74; https://doi.org/10.3390/mca6010067 - 1 Apr 2001

Cited by 5 | Viewed by 1014

Abstract

In this paper, deflection function of an orthotropic cantilever beam subjected to point and distributed load are obtained using anisotropic elasticity. The deflections at the free end of the beam are calculated numerically using obtained formulas for different fiber directions. Full article

792 KiB

Open AccessArticle

An Elasto-Plastic Stress Analysis in a Polymer Matrix Composite Beam of Arbitrary Orientation Subjected to Transverse Uniformly Distributed Load

by Ümran Esendemir

Math. Comput. Appl. 2001, 6(1), 53-65; https://doi.org/10.3390/mca6010053 - 1 Apr 2001

Cited by 3 | Viewed by 1033

Abstract

Polymer matrix composite beam of arbitrary orientation subjected to transverse uniformly distributed load is studied by an analytical elasto-plastic stress analysis. In the elasto-plastic solution, the material is assumed to be perfectly plastic. A composite consisting of fiber reinforced polymer matrix was produced [...] Read more.

Polymer matrix composite beam of arbitrary orientation subjected to transverse uniformly distributed load is studied by an analytical elasto-plastic stress analysis. In the elasto-plastic solution, the material is assumed to be perfectly plastic. A composite consisting of fiber reinforced polymer matrix was produced for this work. The expansion of the plastic region and the residual stress component of are determined for 0°, 30°, 45°, 60° and 90° orientation angles. The yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. But, it starts first at the upper surface for 30°, 45° and 60° orientation angles. Sample problems are given for various orientation angles, x axis of the beam is used to obtain the location of the elasto-plastic boundary and to calculate elastic, elasto-plastic and residual normal and shear stresses. The intensity of the residual stress component of τ_xy is maximum on or around the x axis of the beam but the residual stress component of σ_x is maximum at the upper and lower surfaces. Full article

354 KiB

Open AccessArticle

Mann and Ishikawa Type Perturbed Iterative Algorithms for Generalized Nonlinear Variational Inclusions

by Hanif Salahuddin, R. Ahmad and M. F. Khan

Math. Comput. Appl. 2001, 6(1), 47-52; https://doi.org/10.3390/mca6010047 - 1 Apr 2001

Cited by 2 | Viewed by 1252

Abstract

In this paper, we consider the generalized nonlinear variational inclusions and develop Mann and Ishikawa type perturbed iterative algorithms for finding the approximate solution of this problem. By using the definition of multivalued relaxed Lipschitz operators, we discuss the convergence criteria for the [...] Read more.

In this paper, we consider the generalized nonlinear variational inclusions and develop Mann and Ishikawa type perturbed iterative algorithms for finding the approximate solution of this problem. By using the definition of multivalued relaxed Lipschitz operators, we discuss the convergence criteria for the perturbed algorithms. Full article

519 KiB

Open AccessArticle

Scattering of SH Waves by Fixed-Rigid Nearly Circular Cylinder

by Adul Hayir and Ibrahim Bakirtas

Math. Comput. Appl. 2001, 6(1), 37-45; https://doi.org/10.3390/mca6010037 - 1 Apr 2001

Cited by 1 | Viewed by 1093

Abstract

A solution for the two-dimensional scattering and diffraction of plane SH waves by fixed-rigid cylinder of arbitrary shape in an elastic infinite medium is presented. The wave field for arbitary geometry in this paper is computed numericaly by the method weighted residues (moment [...] Read more.

A solution for the two-dimensional scattering and diffraction of plane SH waves by fixed-rigid cylinder of arbitrary shape in an elastic infinite medium is presented. The wave field for arbitary geometry in this paper is computed numericaly by the method weighted residues (moment method). Dynamic stress concentration factors around the arbitrary obstacles are obtained with respect to various dimensionless wave numbers. When the cavity is circular, results obtained from the analytical solutions are the same. Full article

921 KiB

Open AccessArticle

Thermal Stress Analysis in the Coated Upper Canine

by Mümin Küçük

Math. Comput. Appl. 2001, 6(1), 23-35; https://doi.org/10.3390/mca6010023 - 1 Apr 2001

Cited by 1 | Viewed by 1013

Abstract

The aim of this study is to investigate the thermal stresses caused by temperature change on the upper canine coated by various dental materials. In this study, first of all the modeling of tooth has been done by using a specific computer program [...] Read more.

The aim of this study is to investigate the thermal stresses caused by temperature change on the upper canine coated by various dental materials. In this study, first of all the modeling of tooth has been done by using a specific computer program Ansys 5.3 that is capable of both finite element modeling and stress-strain analysis. Secondly, themal stresses arising from the temperature difference between the tooth temperature and the temperatures of the food and drinks taken to mouth have been examined. It has been demonstrated that the lowest thermal stresses occur in metal crowns, while the highest thermal stresses occur in metal- ceramic crowns. It has been shown that metal-ceramic crowns are more prone in terms of heat compared to metal crowns and that these crowns may deteriorate in time and may even become unusable. Full article

585 KiB

Open AccessArticle

Frictionless Contact Problem between an Elastic Layer Bonded to a Rigid Support and a Rigid Stamp

by Volkan Kahya, Ahmet Birinci and Ragıp Erdöl

Math. Comput. Appl. 2001, 6(1), 13-22; https://doi.org/10.3390/mca6010013 - 1 Apr 2001

Cited by 5 | Viewed by 1056

Abstract

The plane contact problem for an elastic layer bonded to a rigid support on its top surface is considered according to the theory of elasticity. The layer is subjected to a concentrated load at its bottom surface by means of a rigid stamp. [...] Read more.

The plane contact problem for an elastic layer bonded to a rigid support on its top surface is considered according to the theory of elasticity. The layer is subjected to a concentrated load at its bottom surface by means of a rigid stamp. Profile of the rigid stamp is taken in the form as circular, parabolic and rectangular. It is assumed that the contact between the layer and the stamp is frictionless and that only compressive normal tractions can be transmitted through the interface. The problem is formulated in terms of a singular integral equation. Numerical results for various dimensionless quantities are presented and discussed. Full article

652 KiB

Open AccessArticle

Behavior of Ships in Shallow and Restricted Waters

by Metin Taylan

Math. Comput. Appl. 2001, 6(1), 1-11; https://doi.org/10.3390/mca6010001 - 1 Apr 2001

Cited by 4 | Viewed by 1460

Abstract

Ship motions in open waters and waves are always dynamic and most of the time are nonlinear. Even though behavior of ships in shallow and restricted waters does not sound as violent at first thought, it is equally important in terms of capsizing. [...] Read more.

Ship motions in open waters and waves are always dynamic and most of the time are nonlinear. Even though behavior of ships in shallow and restricted waters does not sound as violent at first thought, it is equally important in terms of capsizing. There has been so many casualties reported that claimed so many lives. In this study, squat phenomenon is dealt with especially addressing its determination in the preliminary design stage. For this purpose, approximate formulae have been proposed to predict bow squat of ships and compared with the other methods and experimental data found in the literature to come up with a pragmatic method to guide naval architects and masters towards avoiding excessive squat in shallow water. It is known that forward speed plays an important role in squat, hence there exist a Froude number, called critical speed, for a particular ship at which squat characteristics start changing drastically. This fact is also taken into account in the regressional analysis. Some of the results are then compared with that of the similar studies and a real life incident. It has been found that the method compared fairly well with other methods and experiments. Full article

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Math. Comput. Appl., Volume 6, Issue 1 (April 2001) – 8 articles , Pages 1-83

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