Computer Simulation of New Forms of Shell Structures

Abstract

Abstract. A large number of new surfaces are presented, formed by congruent curves with variable curvature, but remaining in the same class, and superellipses. All surfaces are included in the class-es Rotation Surfaces, Velaroidal Translaation Surfaces, and Algebraic Surfaces with a Carcass of Three Main Flat Curves. All surfaces of the same class are defined by the same general explicit and para-metric equations, and thanks to the presence of many constants in the superellipse equation, it is possible to obtain a lot of known and new surfaces. Despite the fact that the method of construction of the considered surfaces is known, in the presented article it is il-lustrated and visualized on many examples. The surfaces were constructed using a numeric computing environment MATLAB. The surfaces of a general-view superellipse were built on the basis of a new computer program that allows them to be visualized in a multimedia mode by a set change in the exponents contained in the meridian-superellipse formula. All built rotation surfaces have a common name — superellipsoids of rotation. For the first time it is shown that algebraic surfaces with a given frame in three mutually perpendicular planes, applied in shipbuilding, can also find application in the architecture of public buildings. Superellipses are used as the rigid frame of surfaces. In the overview section of the article on the basis of the available publications it is shown that the geometry of the form affects the stress-deformable state of shells with the proposed medial surfaces. The materials of the article give an opportunity in the future to find the optimal shells outlined on the considered analytical surfaces of three different classes, which are considered in the article, taking into account the criteria of optimality applied in architecture, construction, engineering and shipbuilding.