Mathematical and Computational Applications

236 KiB

Open AccessArticle

Vibrations of a Stretched Beam with Non-Ideal Boundary Conditions

by M. Pakdemirli and H. Boyacı

Math. Comput. Appl. 2001, 6(3), 217-220; https://doi.org/10.3390/mca6030217 - 01 Dec 2001

Cited by 26 | Viewed by 1108

A simply supported Euler-Bernoulli beam with immovable end conditions is considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections. Approximate analytical solution of the problem is found using the [...] Read more.

A simply supported Euler-Bernoulli beam with immovable end conditions is considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. Full article

618 KiB

Open AccessArticle

On Generalized Mixed Quasivariational Inclusions

by Shamshad Husain

Math. Comput. Appl. 2001, 6(3), 203-215; https://doi.org/10.3390/mca6030203 - 01 Dec 2001

Viewed by 992

Abstract

In this paper, we study a class of generalized mixed quasivariational in-clusions. By using the properties of the resolvent operator associated with maximal monotone mapping in real Hilbert space, we have established an existence theorem of solutions for generalized mixed quasivariational inclusions, suggesting [...] Read more.

In this paper, we study a class of generalized mixed quasivariational in-clusions. By using the properties of the resolvent operator associated with maximal monotone mapping in real Hilbert space, we have established an existence theorem of solutions for generalized mixed quasivariational inclusions, suggesting a new iter-ative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solutions of the generalized mixed quasivariational inclusions. The results proved in this paper are more general than the previously known results in this area. Full article

524 KiB

Open AccessArticle

A Topological Application of the Monodromy Groupoid on Principal Bundles

by Osman Mucuk

Math. Comput. Appl. 2001, 6(3), 195-202; https://doi.org/10.3390/mca6030195 - 01 Dec 2001

Viewed by 981

Abstract

The idea of monodromy groupoid we deal here is due to Pradines [1]. An application of the monodromy groupoid on principal bundles was earlier given in [2]. In this paper, a topological version of this application is given. Full article

303 KiB

Open AccessArticle

Some Generating Function Relations of Multiindex Hermite Polynomials

by HSP Shrivastava

Math. Comput. Appl. 2001, 6(3), 189-194; https://doi.org/10.3390/mca6030189 - 01 Dec 2001

Cited by 2 | Viewed by 960

Abstract

In the present some generating functions relations of Hermite polynomial also of two, three and in turn several index are derived. Some known and unknown particular cases have also been discussed. Full article

638 KiB

Open AccessArticle

Propagation of Cylindrical Magneto-Gasdynamic Shock Wave with Varying Energy in a Rotating, Gravitating, Non-Uniform Atmosphere

by Ashok Ganguly and Shilpa Shinde

Math. Comput. Appl. 2001, 6(3), 177-188; https://doi.org/10.3390/mca6030177 - 01 Dec 2001

Cited by 1 | Viewed by 1057

Abstract

A self similar, theoretical model of propagation of cylindrical magneto-gasdynamic shock wave with varying energy in a non-uniform atmosphere, in the interplanetary region, in the presence of rotation and gravitation, has been developed. Subsequently, its comparison with the gas dynamic case has been [...] Read more.

A self similar, theoretical model of propagation of cylindrical magneto-gasdynamic shock wave with varying energy in a non-uniform atmosphere, in the interplanetary region, in the presence of rotation and gravitation, has been developed. Subsequently, its comparison with the gas dynamic case has been shown with the help of variations of flow variables with distance graphically. It is seen that the presence of magnetic field generates very high energy at the instant of explosion and its absence in gasdynamic model makes the variation of energy docile. Full article

317 KiB

Open AccessArticle

Application of Holditch Theorem to Bezier and Quadratic Uniform B-Spline Curves

by A. Caliskan and B. Tantay

Math. Comput. Appl. 2001, 6(3), 169-176; https://doi.org/10.3390/mca6030169 - 01 Dec 2001

Cited by 1 | Viewed by 1168

Abstract

Parametric polynomial functions are one of the most common types of functions that are used in curve and surface design. Bezier and quadratic uniform B-Spline curves are some common examples of those functions. Crossectional areas between these curves have great importance in computer [...] Read more.

Parametric polynomial functions are one of the most common types of functions that are used in curve and surface design. Bezier and quadratic uniform B-Spline curves are some common examples of those functions. Crossectional areas between these curves have great importance in computer aided geometric design (CAGD) and computer aided geometric manufacturing (CAM). While calculating these areas, the kind of the curves and surfaces of which the objects are composed, is very important. After determining the types of the curves, we choose one of the most suitable methods to calculate the area. In this paper, we used Holditch Theorem to calculate the areas between two Bezier curves and two quadratic uniform B-Spline curves. Full article

756 KiB

Open AccessArticle

An Elasto-Plastic Stress Analysis on a Metal Matrix Composite Beam of Arbitrary Orientation Supported from Two Ends under a Transverse Uniformly Distributed Load

by Mümin Küçük and Ümran Esendemir

Math. Comput. Appl. 2001, 6(3), 155-168; https://doi.org/10.3390/mca6030155 - 01 Dec 2001

Viewed by 1057

Abstract

An analytical elastic-plastic stress analysis is carried out on a metal-matrix composite beam of arbitrary orientation supported from two ends under a transverse uniformly distributed load. The composite layer consists of stainless steel fiber and aluminum matrix. The material is assumed to be [...] Read more.

An analytical elastic-plastic stress analysis is carried out on a metal-matrix composite beam of arbitrary orientation supported from two ends under a transverse uniformly distributed load. The composite layer consists of stainless steel fiber and aluminum matrix. The material is assumed to be perfectly plastic in the elasto-plastic solution. The intensity of the uniform force is chosen at a small value; therefore the normal stress component of σ_y is neglected during the elasto-plastic solution. The expansion of the plastic region and the residual stress component of σ_x are determined for 0°, 30°, 45°, 60° and 90° orientation angles. Plastic yielding occurs for 0° and 90° orientation angles on the lower and upper surfaces of the beam at the same distances from the mid point. However; it starts first at the lower surface for 30°, 45° and 60° orientation angles. The intensity of the residual stress component of σ_x is found maximum at the lower and upper surfaces. However; the intensity of residual stress component τ_xy is maximum on or around the x axis of the beam. Full article

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Math. Comput. Appl., Volume 6, Issue 3 (December 2001) – 7 articles , Pages 155-220

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