基于弹塑性固有应变法的拓扑优化以减少金属增材制造中的残余应力
Elastoplastic inherent strain-based topology optimization for residual stress reduction in metal additive manufacturing
- Osaka Research Institute of Industrial Science and Technology（大阪产业技术研究所）
- The Hakubi Center for Advanced Research, Kyoto University（京都大学博雅研究高级中心）
- Department of Micro Engineering, Kyoto University（京都大学微工程学科）
- Department of Mechanical Engineering and Science, Kyoto University（京都大学机械工学科学科）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出基于弹塑性固有应变法的拓扑优化方法，通过伴随灵敏度分析线性化计算成本，在柔度约束下最小化残余应力P-范数，减少屈服区域而非峰值应力。
AI中文摘要：
本文提出了一种拓扑优化方法，旨在减少金属增材制造构建过程中产生的残余应力。首先，引入了一种基于弹塑性固有应变法的逐层过程分析模型。在该模型中，每一层步骤重新求解增量位移，并且应力历史被显式地纳入本构方程中，作为累积到前一步的应力，从而在不引入激活应变的情况下保证了层间界面的应力连续性。其次，基于伴随方法推导了该分析模型的设计灵敏度。将应力与等效塑性应变作为状态变量，将层间依赖关系简化为单步递推，伴随场以逐层反向扫描的方式构建，并重用前向分析中获得的系数张量。因此，灵敏度分析的成本随层数线性增长，并与前向分析的成本保持同一量级。随后，基于密度方法构建了优化问题，在体积和最终使用柔度约束下最小化构建过程完成时的残余应力P-范数，并通过与中心有限差分比较验证了所推导的灵敏度。最后，通过二维和三维算例展示了在柔度约束下残余应力最小化的所提方法。结果表明，在弹塑性分析下，最大残余应力受屈服面限制，因此优化减少了屈服和塑性应变累积区域的范围，而非峰值应力值。
英文摘要：
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.
