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

Abstract

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.