TY  - CHAP
A1  - Asayama, Shuichi
A1  - Mae, Toshifumi
T1  - Fractal Truss Structure and Automatic Form Generation Using Iterated Function System
N2  - This paper describes a couple of new truss structures based on fractal geometry. One is the famous Sierpinski Gasket and another is a fractal triangle derived by means of applying a process forming leaves of a cedar tree using M. F. Barnsley’s contraction mapping theory. Therefore a pair of x-y coordinates of an arbitrary nodal point on the structures are generated easily if IFS(Iterated Function System) codes and a scale of them are specified. Structural members are defined similarly. Thus data for frame analysis can be generated automatically, which is significant if the objective structure has complex configuration. Next analytical results under vertical and wind loadings in Japanese Building Code are shown. Here members are assumed to be timber and to have cross section of 15cm×15cm. Finally authors conclude that geometrically new truss structures were developed and automatic data generation for frame analysis was attained using IFS. Analytical results show they contribute to saving material when compared it with King-post truss.
KW  - Konzipieren <Technik>
KW  - Bauwerk
KW  - Fraktal
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-1046
ER  - 
TY  - JOUR
A1  - Perepelitsa, V. A.
A1  - Pinchuk, V. P.
A1  - Sergeeva, L. N.
A1  - Pozdnjakova, A. J.
T1  - Fractal Graphs and their Properties
N2  - The idea of representing urban structure and various communication systems (water and energy supply, telephone and cable TV networks) as fractal objects is not absolutely new. However, known works, devoted to this problem use models and approaches from fractal physics. For example, to simulate urban growth Diffusion Limited Aggregation (DLA) model and Dielectric Breakdown (DB) model are used. This study introduces a different approach. Net structure of communication system is described by a graph of special type called regular G(l,r,n)-graph. Authors provide description of such graph, develop iterative process for its generation and prove its self-similarity, i.e. that every regular graph is a pre-fractal. After the infinite number of steps this process generates a fractal. The devised algorithm for generation and grathical representation of regular G(l,r,n)-graphs with different values of l,r and n has been programmed to receive computer simulations. For optimal graphic presentation of pre-fractals the Optimal Space Ordering method was suggested. It is based on the minimization of the >graph energy< value about vertices' coordinates. The effective procedure for optimization was developed that takes into account specific properties of graph energy as objective function For the fractal graph introduced the Hausdorff-Besikovich and similarity dimensions were calculated. It has been shown that >graph energy< is directly related to the graph's fractal properties. For G(3,3,n) and G(4,4,n) graphs fractal dimensions calculated by different methods are the same (D=1,5 and D=2 respectively), while topological dimension of both graphs is 1.
KW  - Versorgungsnetz
KW  - Fraktal
KW  - Graphentheorie
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-5166
ER  -