RT journal article
T1 Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
A1 Pavón Domínguez, Pablo
A1 Portillo García, Pablo
A1 Rincón Casado, Alejandro
A1 Rodríguez Parada, María Lucía
A2 Ingeniería Mecánica y Diseño Industrial
K1 fractal dimension
K1 topology optimization
K1 static analysis
K1 box-counting
K1 Michell’s beam
AB In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (F-D). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity of the optimized solutions to be efficiently distributed in the design space. Furthermore, the possible relationships between the fractal dimension and beams' mechanical properties are explored. First, a set of theoretical beams are studied based on their well-known fractal dimension. A 3D fractal called Menger sponge is reproduced on a Michell's beam (cantilever with a single force applied at the end). The programming codes that generate those beams are created in Matlab software, as are the algorithms for estimating the fractal dimension (box-counting method). Subsequently, identical beams are modelled in the software Inspire in order to apply the topology optimization and determine the mechanical parameters from the static analysis. Results indicate that the fractal dimension is affected by the design geometry and proposed optimized solutions. In addition, several relationships among fractal dimension and some mechanical resistance parameters could be established. The obtained relations depended on the objectives that were initially defined in the topology optimization.
PB MDPI
SN 2076-3417
YR 2021
FD 2021-11
LK http://hdl.handle.net/10498/26173
UL http://hdl.handle.net/10498/26173
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 07-nov-2026