Topology optimization reduces stress in metal 3d printing parts
Elastoplastic inherent strain-based topology optimization for residual stress reduction in metal additive manufacturing
Computational Engineering, Finance, and Science
Summary
Metal 3D printing can create leftover stresses inside parts that make them weaker or prone to damage. The authors developed a method to redesign the shape of parts to lower these leftover stresses during printing. Their approach uses a detailed analysis that models how each layer of metal deforms and accumulates stress. By cleverly calculating how small changes affect stress, they can efficiently improve designs while keeping parts strong. Their results show that their method limits areas of metal that permanently deform, helping create more reliable 3D-printed parts.
residual stressmetal additive manufacturingtopology optimizationelastoplastic inherent strainadjoint methoddensity methodplastic strainyield surfacecompliance constraintfinite differences
Authors
Takao Miki, Jike Han, Kazuhiro Izui, Shinji Nishiwaki
Abstract
This paper proposes a topology optimization method for reducing the residual stress arising in the building process of metal additive manufacturing. First, a layer-by-layer process analysis model based on an elastoplastic inherent strain method is introduced. In this model, the incremental displacement is solved anew at each layer step, and the stress history is explicitly incorporated into the constitutive equation as the stress accumulated up to the previous step, which guarantees the stress continuity across layer interfaces without introducing activation strains. Next, the design sensitivity of this analysis model is derived based on the adjoint method. Taking the pair of the stress and the equivalent plastic strain as the state variables reduces the dependency between layer steps to a one-step recurrence, and the adjoint fields are constructed as a layer-by-layer reverse sweep that reuses the coefficient tensors obtained in the forward analysis. Consequently, the cost of the sensitivity analysis scales linearly with the number of layers and remains of the same order as that of the forward analysis. An optimization problem is then formulated based on the density method to minimize the P-norm of the residual stress at the completion of the building process under the volume and final-use compliance constraints, and the derived sensitivities are verified by comparison with central finite differences. Finally, the proposed method is demonstrated through two- and three-dimensional examples of residual stress minimization under a compliance constraint. The results clarify that, under the elastoplastic analysis, the maximum residual stress is bounded by the yield surface, and the optimization therefore reduces the extent of the yielded and plastic strain accumulating regions rather than the peak stress value.