mechanical design engineers

Abstract: This paper presents a comparative study of compliant mechanisms generated using a robust topology optimization technique involving design-dependent pressure loads. Design domains are parameterized using standard and higher-order quadrilateral elements. Both eroded and blueprint configurations are considered. A min-max optimization model combined with an output-spring method is employed to extremize the mechanisms' output displacements. A volume and a strain energy constraint are applied to the blueprint and the eroded designs, respectively. The optimization process is executed using the method of moving asymptotes. Numerical experiments are performed to optimize the pressure-actuated inverter and gripper mechanisms using Q4, Q8, and Q9 elements, and the results are compared. The research highlights how quadrilateral element selection influences both the resulting topologies and performance characteristics.

Abstract: Load-adaptive gravity balancing mechanisms (LA-GBMs) can accommodate various loading conditions by passively changing their characteristics in response to payload variations. However, their design is difficult because both the desired mechanism motion and static equilibrium under variable payloads must be satisfied simultaneously. This study proposes a general design methodology for LA-GBMs that does not depend on specific mechanism architectures or mechanical elements. The necessary conditions for the potential fields of LA-GBMs are formulated, and two general forms are derived: an affine form representing the effect of payload mass and a factorized form representing state transitions associated with load adaptation and gravity balancing. These forms are then provided to generative AI as design requirements to generate candidate potential functions. The generated functions are analytically verified in terms of their conformity to the two general forms and the conditions required for valid LA-GBMs. Furthermore, the obtained potential functions are decomposed into individual terms, and an example of a method for constructing an LA-GBM by combining springs, counterweights, and function-generating linkage mechanisms is presented. By using potential functions as an intermediate representation, the proposed framework enables the generation of LA-GBM design candidates without prescribing a mechanism architecture in advance. Mechanical realizability and manufacturability of the generated potential fields remain important issues for future work.

Abstract: Topology optimization (TO) remains computationally intensive due to repeated finite element analysis (FEA) evaluations required at each iteration. While neural network-based surrogates offer potential acceleration, existing approaches often suffer from gradient inconsistency between predicted objectives and sensitivities, leading to optimization instability. This work presents KATOsuper, an objective-agnostic framework that couples neural-reparameterized topology optimization with a Sensitivity-Consistent Fourier Neural Operator (SC-FNO). The framework employs the forward_split architecture, which derives deployed sensitivities via automatic differentiation through the predicted objective field and thereby preserves consistency between the predicted objective and the gradient used for optimization. The case studies include three 2D benchmark problems and three 3D structures considering compliance or stress minimization. A physics-informed multi-channel input encoding with Fourier position embedding enables resolution-invariant learning, supporting zero-shot extrapolation beyond the training resolution, with useful performance at moderate scaling factors and topology-preserving exploration at up to 64x without retraining. The framework extends to 3D through KATO3D, featuring novel KANConv3D blocks with learnable B-spline activations. KATOsuper demonstrates 15--110x deployment-time speedup over MATLAB baselines while maintaining competitive optimality, with the clearest gains observed in complex 3D and stress-optimization cases. The insight that sensitivity direction matters more than magnitude enables robust optimization even with approximate physics evaluation, extensible to other differentiable physics-driven design objectives.

Abstract: This paper presents a comparative study of multimaterial topology optimization (MMTO) using the extended SIMP, Discrete Ma- terial Optimization (DMO), and generalized shape functions (gSF) ap- proaches. The design domain is parametrized using hexagonal elements. Each element has six neighboring elements, thereby improving element connectivity and yielding a relatively uniform local mesh structure. This characteristic reduces mesh-related effects on the optimized designs com- pared with conventional triangular and quadrilateral discretizations. Struc- tural compliance is minimized at the prescribed volume fractions. The optimization is performed using the method of moving asymptotes. The resulting optimized topologies are compared in terms of material distri- bution, structural performance, convergence behavior, and the character- istics of the obtained material interfaces. The comparative investigation provides insights into the working principles and performance of the ex- tended SIMP, DMO, and gSF interpolation schemes for MMTO.

Abstract: Topology optimization (TO) represents a significant step towards automating the design process: given a working simulation, TO can produce a viable prototype at the press of a button by differentiating the simulation and iteratively improving the design. In practice, however, TO is riddled with ``magic numbers''---hyperparameters whose tuning significantly affects the outcome. Finding the right values typically requires not only deep problem-specific knowledge but also extensive trial-and-error. While practitioners can use surrogate-assisted hyperparameter optimization as an alternative, this approach requires strictly limiting the number of hyperparameters through careful problem formulation. Here, we propose differentiating TO itself using automatic differentiation. This yields ``hypergradients'' that allow us to tune these hyperparameters in tandem with the primary optimization. We show that evaluating just one or two steps of TO is sufficiently informative and that the method scales favorably to thousands of hyperparameters at an expense comparable to only a few standard TO runs. We demonstrate this approach on stress-constrained and compliance problems, with the latter utilizing a neural parameterization of the density field.