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Electrical machines traditionally rely on Finite Element Analysis (FEA) to evaluate or simulate their properties by solving the associated partial differential equations (PDEs). However, FEA is computationally costly, which limits its capability for rapid design iteration and real-time simulations. While recent surrogate models such as Physics-Informed Neural Networks (PINNs) have shown promise, they often suffer from slow convergence and scalability issues in complex geometries. In this paper, we propose the use of the Fourier Neural Operator (FNO) as a resolution-invariant surrogate model to significantly reduce the computation time required for FEA-based PDE solutions in electric machines. Previous research has demonstrated the FNO’s ability to learn mappings for time-sequence problems by approximating operators between function spaces. Building on this, we present a methodology to directly predict the later-state electromagnetic fields of a rotating interior permanent magnet (IPM) motor based on its earlier-stage data by approximating the underlying operator that governs these transitions. Our framework enables full-geometry modeling without relying on segmentation, preserving accuracy while dramatically improving computational efficiency. The model was trained and validated on an FEA dataset with multiple boundary conditions and motor configurations, demonstrating strong generalization across different designs and resolutions. Experimental results show that the proposed FNO method achieves a significant reduction in computational time compared to traditional FEA simulations while maintaining an acceptable level of accuracy. This study highlights the potential of neural operators for accelerating electromagnetic simulations, enabling faster design iterations and offering new possibilities for real-time and optimization-based applications in electric machine design. 

The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties. 

Abstract This paper introduces a new computational framework for modeling and designing morphable surface structures based on an integrated approach that leverages circle packing for surface representation, conformal mapping to link local and global kinematics, and topology optimization for actuator design. The framework utilizes a unique strategy for employing optimized compliant actuators as the basic building blocks of the morphable surface. These actuators, designed as circular elements capable of modifying their radius and curvature, are optimized using level set topology optimization, considering both kinematic performance and structural stiffness. Circle packing is employed to represent the surface geometry, while conformal mapping guides the kinematic analysis, ensuring alignment between local actuator motions and desired global surface transformations. The design process involves mapping optimized component designs back onto the circle packing representation, facilitating coordinated control, and achieving harmony between local and global geometries. This leads to efficient actuation and enables precise control over the surface morphology. The effectiveness of the proposed framework is demonstrated through two numerical examples, showcasing its capability to design complex, morphable surfaces with potential applications in fields requiring dynamic shape adaptation. 

Abstract Intracranial aneurysm rupture causes life-threatening sub-arachnoid hemorrhage. Current endovascular devices like coils, flow diverters, and intravascular implants aim to thrombose the aneurysm but have limitations and varying success rates depending on aneurysm characteristics. We propose a new computational framework integrating CFD and topology optimization to design personalized aneurysm implants. The optimization problem aims to reduce blood flow velocity within the aneurysm while ensuring adequate structural integrity of the implant. The fluid dynamics are governed by the Navier-Stokes equations, while the solid mechanics are described by the linear elasticity equations. A Darcy-Brinkman model is employed to simulate flow through the porous implant in the fluid domain, while the Solid Isotropic Material with Penalization (SIMP) method is used to interpolate between solid and void regions in the structural domain during topology optimization. The objective combines fluid energy dissipation ratio and solid strain energy with spatially varying weights. Global and local volume constraints generate personalized implants with porosity and flow-diverting architectures. The approach is demonstrated on patient-specific aneurysm geometries from rotational angiography. This CFD-driven topology optimization method enables personalized aneurysm implant design to potentially improve occlusion rates and reduce complications compared to current devices. Further studies will validate the optimized designs and investigate their efficacy in vitro and in vivo. 

Abstract This paper presents a new computational framework for the co-optimization and co-control of morphable surface structures using topology optimization and circle-packing algorithms. The proposed approach integrates the design of optimized compliant components and the system-level control of the overall surface morphology. By representing the surface shape using circle packing and leveraging conformal mapping, the framework enables smooth deformation between 2D and 3D shapes while maintaining local geometry and global morphology. The morphing surface design problem is recast as designing circular compliant actuators using level-set topology optimization with displacements and stiffness objectives. The optimized component designs are then mapped back onto the circle packing representation for coordinated control of the surface morphology. This integrated approach ensures compatibility between local and global geometries and enables efficient actuation of the morphable surface. The effectiveness of the proposed framework is demonstrated through numerical examples and physical prototypes, showcasing its ability to design and control complex morphable surfaces with applications in various fields. The co-optimization and co-control capabilities of the framework are verified, highlighting its potential for realizing advanced morphable structures with optimized geometries and coordinated actuation. This integrated approach goes beyond conventional methods by considering both local component geometry and global system morphology and enabling coordinated control of the morphable surface. The general nature of our approach makes it applicable to a wide range of problems involving the design and control of morphable structures with complex, adaptive geometries. 

Abstract Minimally invasive endovascular therapy (MIET) is an innovative technique that utilizes percutaneous access and transcatheter implantation of medical devices to treat vascular diseases. However, conventional devices often face limitations such as incomplete or suboptimal treatment, leading to issues like recanalization in brain aneurysms, endoleaks in aortic aneurysms, and paravalvular leaks in cardiac valves. In this study, we introduce a new metastructure design for MIET employing re-entrant honeycomb structures with negative Poisson’s ratio (NPR), which are initially designed through topology optimization and subsequently mapped onto a cylindrical surface. Using ferromagnetic soft materials, we developed structures with adjustable mechanical properties called magnetically activated structures (MAS). These magnetically activated structures can change shape under noninvasive magnetic fields, letting them fit against blood vessel walls to fix leaks or movement issues. The soft ferromagnetic materials allow the stent design to be remotely controlled, changed, and rearranged using external magnetic fields. This offers accurate control over stent placement and positioning inside blood vessels. We performed magneto-mechanical simulations to evaluate the proposed design’s performance. Experimental tests were conducted on prototype beams to assess their bending and torsional responses to external magnetic fields. The simulation results were compared with experimental data to determine the accuracy of the magneto-mechanical simulation model for ferromagnetic soft materials. After validating the model, it was used to analyze the deformation behavior of the plane matrix and cylindrical structure designs of the Negative Poisson’s Ratio (NPR) metamaterial. The results indicate that the plane matrix NPR metamaterial design exhibits concurrent vertical and horizontal expansion when subjected to an external magnetic field. In contrast, the cylindrical structure demonstrates simultaneous axial and radial expansion under the same conditions. The preliminary findings demonstrate the considerable potential and practicality of the proposed methodology in the development of magnetically activated MIET devices, which offer biocompatibility, a diminished risk of adverse reactions, and enhanced therapeutic outcomes. Integrating ferromagnetic soft materials into mechanical metastructures unlocks promising opportunities for designing stents with adjustable mechanical properties, propelling the field towards more sophisticated minimally invasive vascular interventions. 

Given a loop or more generally 1-cycle r r of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle this problem in the quantum setting. Given an oracle that one can use to query the inclusion of edges on a closed curve, we design a quantum algorithm for such a homology detection with a constant running time, with respect to the size or the number of edges on the loop r r , requiring only a single usage of oracle. In contrast, classical algorithm requires \Omega(L) Ω ( L ) oracle usage, followed by a linear time processing and can be improved to logarithmic by using a parallel algorithm. Our quantum algorithm can be extended to check whether two closed loops belong to the same homology class. Furthermore, it can be applied to a specific problem in the homotopy detection, namely, checking whether two curves are not homotopically equivalent on a closed two-dimensional manifold. 

Abstract With specific fold patterns, a 2D flat origami can be converted into a complex 3D structure under an external driving force. Origami inspires the engineering design of many self-assembled and re-configurable devices. This work aims to apply the level set-based topology optimization to the generative design of origami structures. The origami mechanism is simulated using thin shell models where the deformation on the surface and the deformation in the normal direction can be simplified and well captured. Moreover, the fold pattern is implicitly represented by the boundaries of the level set function. The folding topology is optimized by minimizing a new multiobjective function that balances kinematic performance with structural stiffness and geometric requirements. Besides regular straight folds, our proposed model can mimic crease patterns with curved folds. With the folding curves implicitly represented, the curvature flow is utilized to control the complexity of the folds generated. The performance of the proposed method is demonstrated by the computer generation and physical validation of two thin shell origami designs.