Fractal-Based Computational Modeling and Shape Transition of a Hyperbolic Paraboloid Shell Structure

Abstract

The concept of Takagi–Landsberg’s fractal surface is applied in this paper for constructing a parametric model of a hyperbolic paraboloid (hypar) shell structure using the Midpoint Displacement Method (MDM) based on the Iterated Function System (IFS) and controlled by the relative size value (w), a factor of fractal dimension. This method of generating a parametric model of a hypar is applied to create a domain of non-integer dimensions through which the hypar surface passes through textural changes, thus transforming the smooth hypar surface from its two-dimensional shape to a higher but non-integer-dimensional irregular surface that results in the changes of structural behavior. This paper briefly compares the structural behavior between the regular hypar and the fractal-based irregular hypar, and also searches the optimal shape of the hypar in terms of minimum deformation from the collection of its regular version and its different levels of irregular versions.