The methods used to achieve optimal solutions to an engineering problem are diverse. Uniquely analytical approaches are directly dependent on mathematical analysis methods, which implies a high level of complexity or even numerous intractable engineering problems. Conventional topological optimisation approaches focus on empirical knowledge or parameterised studies (e.g., numerical simulation). On the other hand, in heterogeneous materials with a complex internal microstructure, mechanical properties can be difficult to calculate using analytical prediction methods.
In this study, an optimisation framework is proposed for the design and mechanical properties evaluation of cellular materials. Several computational tools for integrated topology optimisation and numerical homogenisation were developed. Furthermore, as both computational tools used the finite element method (MEF), a commercial program (AbaqusCAE6.14-1) and the object-oriented programming language Python for the MEF and calculation modules were used, respectively.
The results show that optimized repetitive volume elements (RVE) solutions were achieved by setting up different initial designs based on density restrictions or forces. Moreover, the proposed framework enabled the design and analysis of complex geometries RVE with a wide range of mechanical properties.
Author Contributions
Conceptualization, M.R.S. and A.M.P.; methodology, M.R.S., A.M.P. and N.M.A.; software, M.R.S.; validation, M.R.S. and A.M.P.; formal analysis, M.R.S. and A.M.P.; investigation, M.R.S.; resources, N.M.A.; writing—original draft preparation, M.R.S.; writing—review and editing, M.R.S., A.J.P., Á.M.S., N.M.A. and A.M.P.; funding acquisition, N.M.A. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the Portuguese Science Funding Foundation FCT—Fundação para a Ciência e a Tecnologia (Grant No. SFRH/BD/130908/2017); PAMI—Portuguese Additive Manufacturing Initiative (Project nº22158—SAICT—AAC—01/SAICT/2016), CDRSP (UIDB/04044/2020), (UIDP/04044/2020); Add.Additive—add additive manufacturing to Portuguese industry (POCI-01-0247-FEDER-024533).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The data presented in this study are available on request from the corresponding author.
Conflicts of Interest
The authors declare no conflict of interest.
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