This paper presents the numerical elastic solution for a real problem, functionally graded chamber of hydraulic gear pumps under internal pressure. Because of the similarity and complexity for the considering geometry, a bipolar cylindrical coordinate system is used to extract the governing equations. The material properties are considered to vary along the two tangled circles with a power-law ...

Partial differential equations (PDEs) play an important role in describing many physical, industrial, and biological processes. Their solutions could be considerably facilitated by using appropriate coordinate transformations. There are many coordinate systems besides the well-known Cartesian, polar, and spherical coordinates. In this article, we illustrate how to make such transformations usin...

A cylindrical coordinate colour space (lightness, saturation/chroma, hue) is derived from an opponent colour space in the RGB space. It is shown how cylindrical coordinate colour models widely used in the literature are related to or can be reduced to the derived model, thereby contributing to creating a unified cylindrical coordinate colour model. In particular, the widely used saturation expr...

In the present research, the elastic buckling of composite cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on shear deformation theory and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately acc...

In 2001, the use of cylindrical coordinates was demonstrated to be more suitable than was the use of polar coordinates for accurate computer calculations during treatment planning for 192Ir intravascular brachytherapy sources. In the present work, we investigated the applicability of cylindrical coordinate-based TG-43U1 parameters for dosimetric evaluation and dose calculations for RadioCoil 10...

The transformation of the RGB colour space to a hue, saturation and brightness colour space is essentially a conversion from a rectangular coordinate system to a cylindrical coordinate system. Nevertheless, a bewildering array of such conversions exist. We show that one of the main reasons for this is the dependence of the saturation values on the choice of the brightness function, and suggest ...

(paraxial wave equation) in bipolar coordinate system. A new type of exact solution of the reduced 3 dimensional spatial PWE (paraxial wave equation) for the case of bipolar coordinates is presented here. First, we consider a self-similar representation of the solution in a bipolar coordinate system, the second we additionally reduce PWE under a proper paraxial assumption. Analyzing the structu...