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Topology optimization for additive manufacturing

Grant number: 20/14288-0
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): February 01, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Maicon Ribeiro Correa
Grantee:Geovane Augusto Haveroth
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
Associated scholarship(s):23/00822-2 - Multimaterial topology optimization for additive manufacturing, BE.EP.PD


The purpose of this research project is to introduce and develop a new theoretical and computational framework for topology optimization (TO) of mechanical components produced by additive manufacturing (AM). The essential substantial extension of the standard TO formulation is that the layer-by-layer manufacturing process is included as a series of state problems in addition to the final product state problem. An ideal mathematical problem formulation - the archetype problem- is stated already in this application. It includes optimization of shape andtopology as well asthe layer-by-layer manufacturing process. Multiphysics modeling involving temperature, displacement and fluid flow in both the final component and in partially manufactured components can be included. The general framework is to be specialized to some different novel cases, particularly to optimal cooling structures and load carrying structures involving residual stresses. The former will involve considerations of integrity of partly built structures which in a less detailed formulation implies overhang constraints. The latter involves modelling residual stresses through the inherent strain method and a worst-case oriented robust formulation. These two specializations are inspired by our recent work on TO for AM in industry related research projects.AM induced material in homogeneities and anisotropy will be considered, introducing the possibility of not only optimizing geometrical shape but also AMbuild strategy and support structure design. The computational complexity involved in multi-physics and multistate-problem TO also implies special considerations related to computational efficiency and high-performance computing. Optimal designs can be 3D printed for visualization and experimental verification of performance.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
HAVEROTH, G. A.; THORE, C-J; CORREA, M. R.; AUSAS, R. F.; JAKOBSSON, S.; CUMINATO, J. A.; KLARBRING, A.. Topology optimization including a model of the layer-by-layer additive manufacturing process. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 398, p. 26-pg., . (20/14288-0, 13/07375-0)
DA COSTA-HAVEROTH, T. C.; HAVEROTH, G. A.; KUHL, A.; BOLDRINI, J. L.; BITTENCOURT, M. L.; SASSE, F. D.; POLAK, M. A.; MUNOZ-ROJAS, P. A.. Aspects on viscoelasticity modeling of HDPE using fractional derivatives: Interpolation procedures and efficient numerical scheme. MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, . (15/20188-0, 20/14288-0)

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