Static Analysis of Shells With Middle Surfaces Containing the Main Frame From Three Given Superellipses

An opportunity of conversion of algebraic surfaces with a main frame from three superellipses of general type into ruled surfaces of several views is shown. It is necessary to take one, two, or all of three superellipses in the form of a rhombus, i.e. it is necessary to assume exponents in explicit algebraic equations of suitable superellipses equal to one. It was illustrated that having taken one and the same main frame from three plane curves lying in the main coordinate planes, one can construct three algebraic surfaces of different orders. So, it is possible to introduce into practice great number of ruled surfaces with the preliminary given main frame from three superellipses. Some of them must be in the form of straight lines. As a result, fifteen shapes, i.e. five threes of ruled algebraic surfaces with a main frame from three superellipses were obtained with the help of three explicit equations or with the help of three systems of parametric equations. These surfaces contain a polyhedron on given rhombus plane, some types of cylindroids and conoids, and ruled surfaces not described in scientific literature before. All surfaces were visualized for concrete examples. Earlier, Professor A.V. Korotich introduced into practice a new group of surfaces which he called “Ruled quasipolyhedrons from conoids.” Some of the ruled algebraic surfaces presented in this paper can be put in this group of ruled quasipolyhedrons.

Ruled algebraic surfaces with a main frame from three superellipses

Mamieva

2022

Geometry and static analysis of thin shells in the form of a diagonal translation surface of the velaroidal type

Aleshina

2023

The author presents the results of a study of the geometry and stress-strain state of a surface with a frame of three flat curves in coordinate planes, which have found application today mainly in the shipbuilding industry. The purpose of the work is to identify from the point of view of the stress-strain state from the action of a constant uniformly distributed load the most optimal shell of a diagonal transfer of a velaroidal type with the same main frame of three superellipses. The static calculation was performed using the SCAD program based on the finite element method, designed to perform strength calculations of various types and purposes of structures. The influence of parametric equations for defining a surface depending on the generative family of the same type of cross sections on the distribution pattern of normal stresses and bending moments is shown. The results obtained can help architects and designers with choosing the shape of shells for new projects.

Surfaces with a main framework of three given curves which include one circle

Krivoshapko

2023

Superellipses are becoming more and more in demand in various branches of science and national economy due to their versatility. They found the most application in shipbuilding. Suggestions for the use of superellips in architecture and construction have appeared recently. The author proposes explicit and parametric equations of surfaces with a main framework of three predetermined superellips lying in three coordinate planes. These equations describe a large set of analytical shapes suitable for the formation middle surfaces of thin building shells. One of the superellipses is taken in a form of a circle. The shells can be designed on circular and rhombic plans, and also on plans in the shape of superellips of general type with convex and concave sides. All recommended surfaces are illustrated in 24 examples using computer graphics. A network of curvilinear non-orthogonal coordinates is generated on the surfaces using dimensionless independent parameters. The considered surfaces can become a part of the reserve of surfaces for further application in real structures and facilities.