Parabolic Revolution Surfaces of Finite Type in Simply Isotropic 3-spaces

In this paper, we classify parabolic revolution surfaces in the three-dimensional simply isotropic space [Formula: see text] under the condition [Formula: see text] where [Formula: see text] is the Laplace operator with respect to first and second fundamental form and [Formula: see text], [Formula: see text] are some real numbers. Also, as an application, we give some explicit examples for these surfaces.

REVOLUTION SURFACES FORMED IN THE GALILEAN MOTION

This article highlights the existence of surfaces, relative to the system of curvilinear coordinate, which was introduced by A. Artykbaev. Moreover, the study of revolution surfaces formed in the Galilean motion is provided. In Galileo's space, the differential characteristics of these revolution surfaces are studied, and surfaces with constant curvature and minimal ones are indicated

Geometric modelling and materially nonlinear numerical analysis of shells in the shape of one-sheet hyperboloid of revolution

Aims of research. A surface of revolution is generated by rotation of a plane curve z = f(x) about an axis Oz called the axis of rotation. This paper provides information on hyperboloids of revolution surfaces and their classification. Their geometric modeling, linear and materially nonlinear analysis are worked out. Methods. Hyperboloids of revolution middle surface is plotted using the software MathCAD. The linear and materially nonlinear numerical analyses of thin shells of the shape of an hyperboloid of revolution surfaces on stress-strain state is given in this paper, using the finite elements method in a computer software R-FEM, the material which we use in our model is concrete with isotopic nonlinear 2D/3D stress-strain curve for materially nonlinear analysis and linear stress-strain curve for linear analyses. Comparison is done with the result of the finite elements linear analysis of their strain-stress results. Results. That displacements in the investigated shells subject to self-weight, wind load with materially nonlinear analysis are bigger than which done by linear analysis, in the other side the displacements is similarity subjected to free vibration load case. Based on these results, conclusions are made for the whole paper.

MODELISASI BENDA ONYX DAN MARMER MULTI-SUMBU DENGAN BANTUAN PERMUKAAN PUTAR/GESER BEZIER

We simulate application of Bezier revolution surfaces for modeling onyx and marmer objects in three steps as the following. Firstly, formulating the parametric representation of Bezier revolution surfaces in different axis direction of revolution is done. Secondly, we calculate various cylinder sections bounded by plans. Finally, the application of those formulas for modeling onyx and marmer objects of revolution multi axes by using computer are simulated.

CRITERIO DE OPTIMIZACION POR COMPENSACION EN EL DISEÑO DE BOTELLAS CON SUPÈRFICIES LATERALES DE REVOLUCION USADOS POR EMPRESAS EN LA COMERCIALIZACION DE ALIMENTOS Y BEBIDAS

CRITERIO DE OPTIMIZACION POR COMPENSACION EN EL DISEÑO DE BOTELLAS CON SUPÈRFICIES LATERALES DE REVOLUCION USADOS POR EMPRESAS EN LA COMERCIALIZACION DE ALIMENTOS Y BEBIDAS OPTIMIZATION CRITERION BY COMPENSATION FOR DESIGNING BOTTLES WITH SURFACE OF REVOLUTION USED BY FACTORIES FOR COMMERCIALIZING FOODS AND DRINKS Lizandro B. Reyna-Zegarra , Teodoro Moore-Flores DOI: https://doi.org/10.33017/RevECIPeru2009.0013/ RESUMEN En el presente artículo, se expone el resultado de un trabajo de investigación realizado con el propósito de validar un criterio a seguir con la finalidad de optimizar el ahorro de material en el diseño de botellas comerciales con superficies laterales de revolución y bases planas fundamentalmente. A tal criterio de optimización se le denomino Criterio de Optimización por Compensación el cual usa como herramienta principal los métodos numéricos y un programa computacional. La característica fundamental de diseño optimo es que el contenedor debe ser talque su área superficial interna debe ser mínima para un cierto volumen dado. El criterio quedo validado al mostrarse que en casi la totalidad de botellas comerciales se usa mas material que el establecido por el Criterio de Optimización por Compensación. Palabras clave: Optimización, Diseño de botellas comerciales. ABSTRACT In the present article is expounded the result of a research work performed in order to validate a criterion to fallow to optimize material for designing commercial bottles with lateral revolution surfaces and flat bases mainly. Such optimization criterion was called Optimization Criterion by Compensation which uses as main tools, numerical methods and a computer program. The fundamental characteristic of optimum design is that the container must be in such a way the area of its total internal surface must be a minimum for a given volume. Such criterion was validated when it was shown that in most commercial bottles it is used much more material than the Optimization Criterion by Compensation tell us. Keywords: Optimization, Design of commercial bottles.

Graphical Method in CAD Environment for Profiling End Mill Tool

The actives surfaces of screw compressors are helical surfaces, cylindrical and uniform pitch. The generation of helical surfaces can be done using tools bordered by revolution surfaces (as end mill cutter, or disk cutter). The shaping of generating tools is based on fundamentals theorem of the enveloping surfaces. This paper consists to propose a graphic solution, using specific tools of the design environment AUTOCAD, to problem concerning the shaping end mill tool which generates the helical flute of male rotor component of screw compressor. The algorithm has been developed based on a complementary theorem - "The theorem of substituting circles family".

Comparative Analytical Solutions to the Problem of Profiling the End Mill Cutter to Generate Helical Surfaces

In this paper, we present, comparatively, two analytical methods for profiling the tools delimited by revolution surfaces, used to generate helical surfaces with constant pitch. The first method lays on a complementary theorem used for tools profiling, namely the Minimum distance theorem. A specific algorithm for applying it has been developed, in order to profile the tools delimited by revolution surfaces, which generates helical surfaces with constant pitch by enwrapping. The methodic is referring, here, to a tool whose symmetry axis is incident and, at the same time, normal to the helical surface axis – the end mill cutter. The other analytical method here applied grounds on Nikolaev classical theorem. We also present an example of application for both methods, in the case of profiling the end mill cutter used to generate a helicoid with circular frontal generatrix. The tool axial sections are determined and compared in a numerical representation.