mechanical design teams

Abstract: Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-revealing analysis selects locally independent scalar constraints. A defect homotopy recovers closure-consistent passive coordinates from approximate estimates along a feasible and regular continuation path. At regular configurations, implicit differentiation yields the local active-to-passive differential mapping, which is subsequently used in a predictor-corrector continuation procedure for prescribed motion. The framework is evaluated on a seven-degree-of-freedom heavy-duty manipulator containing two-path and three-path closed-chain modules. Comparison with Simscape Multibody yields trajectory root-mean-square errors below 8.5 x 10^-10 rad, while predictor-corrector continuation is approximately 45.8 times faster than applying defect homotopy at every trajectory sample.

Abstract: Turbomachinery design optimization involves expensive black-box problems. Sample-efficient multi-fidelity optimization (MFO) offers an efficient solution. By utilizing multi-fidelity surrogates (MFS), the MFO algorithm can use fewer high-fidelity samples aided by low-fidelity samples to establish an accurate surrogate model. However, when MFS is used in sequential sampling optimization, it has been observed that the final optimal solution obtained by single-fidelity optimization (SFO) is better than that of MFO, even though MFO performs better at the early stages. This can be attributed to the assumption of an even and nested distribution of samples, which is incorrect when using a sequential adding strategy. To address these issues, we propose a novel algorithm called multi-single-fidelity optimization (MSFO) to overcome the limitations of the conventional MFO procedures. In the surrogate establishment of MSFO, we use the density-based spatial clustering of applications with noise (DBSCAN) method to detect local areas where low-fidelity samples are no longer effective. A combination of both global MFS and local single-fidelity surrogate model, built using high-fidelity samples alone, is used to establish an ensemble, which improves the anti-interference ability of the algorithm against misleading low-fidelity data. The effectiveness of the MSFO algorithm is verified first on numerical benchmark functions. Then, the algorithm is used to optimize the aerodynamic profile of a turbine and the film cooling layout design of a turbine endwall. Here, high-fidelity sample sources are obtained from fine-mesh CFD simulations, whereas low-fidelity sample sources are obtained from the same simulations run on a coarser mesh. The results demonstrate that our MSFO algorithm performs significantly better than the conventional SFO and MFO processes, with a higher level of robustness.

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.