Efficiency of bars with fractal porosities subject to multiple functions
Amanda Isabela de Campos1; Marcelo Miranda Barros1
1 Universidade Federal de Juiz de Fora
doi:10.20906/CPS/CILAMCE2017-0741
Resumo
Natural systems have to deal with multiple functions, e.g. bones must withstand different loading conditions, absorb impact and exchange molecules such as blood cells. The geometry of bones presents a fractal character, that is self-similar porosity along scale. The high porosity render light structures with high mechanical efficiency and internal surface area. A profound question is why nature develops fractal structures? In the present paper we compare geometric, structural and energetic properties of bars with different cross sections including simple hollow (unique hole), uniform porous (distributed holes with same size) and fractal porous (distributed holes with different sizes and quantities of each characteristic size) cross sections. The Sierpinski Carpet fractal pattern was used as reference geometry for the cross sections. The proposed beams are set to have the same material quantity. The properties investigated were: the internal surface area; stress and strain energy due to external pressure, bending and torsion within the linear elastic regime. Both analytical expressions and numerical simulations (FEM) were used to compare the proposed bars subject to each solicitation. The three proposed cross sections present high mechanical efficiency (stiffness/weight) in comparing with a filled bar. When subjected to pure bending or pure torsion the results show that the simple hollow beam is the best solution for minimizing stress, the worse for energy absorption and presents a very small relative surface area. Bars with uniform porosity are the best for energy absorption, possess high internal surface area but maximize stresses. Bars with fractal porosity present intermediate values for stress and energy absorption and posses the highest internal surface area. However, under external pressure the simple hollow bar maximizes energy absorption, but also presents the highest concentration of stress. Once again the fractal section shows an intermediate behavior between the simple hollow beam and the one with un
Palavras-chave: Multi-scale porosity; Mechanical efficiency; Multiobjective optimization