Optimization of Periodic Truss Materials by NIAH Homogenization Method and Metamodeling
Sandmara Lanhi1; Marco Antônio Luersen1; Pablo Andrés Munõz-Rojas2
1 Universidade Tecnológica Federal do Paraná - UTFPR, Campus Curitiba; 2 Universidade do Estado de Santa Catarina - UDESC
doi:10.20906/CPS/CILAMCE2017-0376
Resumo
The technological evolution requires, more and more, the development of low-weight materials able of withstand high loads. A class of materials that has stood out due to its properties are the materials consisting of lattice cells. These ones belong to the family of ultralight materials, which are structured so that their unit cell is repeated many times, forming a periodic material. Due to their periodicity, the physical properties of these materials present low dispersion when compared to those of materials with random structure. Moreover, when designed to combine different properties, they improve the material and allow them to be used in multifunctional applications in areas such as aeronautics, automotive, biomedical and military. However, obtaining the effective properties of these materials can be costly and difficult due to their large scale and the complexity of their microstructure, as well as being closely dependent on the distribution of the latter. Therefore, this work aims to use the novel implementation of asymptotic homogenization (NIAH) to obtain the effective elastic and thermal conductivity properties of these materials. The NIAH has mathematical formulation based on the traditional method, but uses commercial finite element code to calculate displacements, forces, temperatures and heat flows that are used to obtain the effective properties of the cell. As another objective of this work, the NIAH is combined with an optimization technique based on metamodeling to obtain the optimal configuration of the cell for a specific elastic or thermal property. Kriging metamodel is used in association with the efficient global optimization algorithm (EGO) to reduce the computational time during the optimization process, since the evaluation of the objective function can be costly. In this way, the cells are optimized in order to obtain better thermomechanical properties while keeping the relative density constant and using the cross-sectional areas as design variables. Examples of case studies are: the ma
Palavras-chave: Periodic Truss Materials; Homogenization ; Metamodel