Abstract
This paper presents a topology optimization algorithm to deal with elastoplastic and layer-by-layer simulation for the additive manufacturing process. The objective of the optimization problem is to minimize the P-norm stress or the displacement in the build direction by modifying the design variable in the support domain in order to prevent build failures or large deformations. The elastoplastic model follows an elastic predictor plastic corrector algorithm under the assumption of small deformation with the von mises criterion and bilinear hardening. The topology optimization is density based and the gradient of the objective function is obtained with the adjoint method. Both forward and adjoint problems are solved with the finite element method with a matrix-free approach on Graphics Processing Unit (GPU). The numerical cases include a verification of the mechanical problem against Ansys, a verification of the sensitivity analysis with a finite difference comparison and the calculation of optimized support designs for two geometries: a rectangular block and a bracket for a more complex part. The influence of several parameters are investigated: the number of layers in the simulation, the effect of plasticity, the use of different objective functions and of different mesh sizes.
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The financial support from the NASA University Leadership Initiative (ULI) program is gratefully acknowledged.
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The STL files for the numerical cases are given as additional data. The voxelisation is done in Matlab based on this code: Adam A (2022). Mesh voxelisation (https://www.mathworks.com/matlabcentral/fileexchange/27390-mesh-voxelisation), MATLAB Central File Exchange. Retrieved September 4, 2022. The implementation of the forward problem follows the modeling approach (linear shape function, voxel mesh, Newton’s method, elastic predictor–plastic corrector) of Čermák et al. (2019) in which a Matlab code is provided. The MMA solver comes from (https://github.com/jdumas/mma), more details are given in introduction. Other algorithmic details are given in the article.
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Dugast, F., To, A.C. Topology optimization of support structures in metal additive manufacturing with elastoplastic inherent strain modeling. Struct Multidisc Optim 66, 105 (2023). https://doi.org/10.1007/s00158-023-03565-1
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DOI: https://doi.org/10.1007/s00158-023-03565-1