Design of functionally graded gyroid foams using optimization algorithms and the finite element method

• Published in: International journal of advanced manufacturing technology Vol. 114; no. 3-4; pp. 725 - 739
• Main Authors: Pais, Ana, Alves, Jorge Lino, Belinha Jorge
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.05.2021
• Subjects: Algorithms; Cellular structure; Density; Finite element method; Functionally gradient materials; Greenhouse gases; Legislation; Mathematical analysis; Meshless methods; Model testing; Optimization; Redevelopment; Software; Stiffness; Weight reduction
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-020-06542-w

Weight reduction is one of the main concerns when designing any component as it reduces material cost and green house gas emissions, among other aspects. Several numerical approaches exist in the literature with the objective of having any component with known mechanical loading become optimized in terms of mass minimization and stiffness maximization. Thus, the objective of this work is the development of optimized structures maintaining the same geometry by means of cellular materials, namely the gyroid infill, and generating functionally graded cellular structures with higher stiffness-to-weight ratio. Remodelling algorithms based on biological phenomena, namely bone growth, as well as Bi-evolutionary structural optimization (BESO) were employed to obtain the density map allowing the material functional gradient distribution. Smoothing functions were tested as a possibility of enhancing stiffness as abrupt density changes are avoided. The gyroid infill was characterized in order to create a phenomenological law based on bone remodelling laws. The gyroid law was implemented on the analysis FEMAS (opens-source, academic and educational FEM and meshless method software) software which presented the density map as an output. Each gradient consisted on areas at a similar density being concatenated into one solid. The different solids, at different density levels, are assembled thus creating the material functional gradient. Lastly, simulations consisted on three distinct and benchmark flexural load cases. Specimens were printed using FFF technology in PLA (E = 3145 MPa, ν = 0.3) having then been tested experimentally according to the appropriate load case. Numerical results correlated with the experimental results in terms of accuracy between theoretical and experimental stiffness where there was a greater accuracy for the specimens subject to a Four-Point bending load case, where only a 16% gap was verified between numerical and experimental flexural stiffness.