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  1. Free, publicly-accessible full text available August 1, 2023
  2. 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.
    Free, publicly-accessible full text available August 1, 2023
  3. Thermal metamaterials are gaining increasing popularity, especially for heat flux manipulation purposes. However, due to the high anisotropy of the structures resulting from the transformation thermotics or scattering cancellation methods, researchers are resorting to topology optimization as an alternative to find the optimal distribution of constituent bulk materials to realize a specific thermal function. This paper proposes to design a thermal cloak using the level-set-based shape and topology optimization. The thermal cloak design is considered in the context of pure heat conduction. The cloaking effect is achieved by reproducing the reference temperature field through the optimal distribution of two thermally conductive materials. The structural boundary is evolved by solving the Hamilton-Jacobi equation. The feasibility and validity of the proposed method to design thermal meta-devices with cloaking functionality are demonstrated through two numerical examples. The optimized structures have clear boundaries between constituent materials and do not exhibit thermal anisotropy, making it easier for physical realization. The first example deals with a circular cloaking region as a benchmark design. The robustness of the proposed method against various cloaking regions is illustrated by the second example concerning a human-shaped cloaking area. This work can inspire a broader exploration of the thermal meta-device inmore »the heat flux manipulation regime.« less
  4. This paper proposes a density-based topology optimization scheme to design a heat sink for the application of a 3D integrated SIC-based 75 kVA Intelligent Power Stage (IPS). The heat sink design considers the heat conduction and convection effects with forced air cooling. The objective function is to minimize the thermal compliance of the whole structure. A volume constraint is imposed to reduce the overall volume of the designed heat sink to make it conformal to the underlying power devices. Some numerical techniques like filtering and projection schemes are employed to render a crisp design. Some 2D benchmarks examples are first provided to demonstrate the effectiveness of the proposed method. Then a 3D heat sink, especially designed for the 3D IPS, is topologically optimized. The classic tree-like structure is reproduced to reinforce the convection effect. Some comparisons with the intuitive baseline designs are made through numerical simulation. The optimized heat sinks are shown to provide a more efficient cooling performance for the 3D integrated power converter assembly.
  5. Generators are considered as the core application of electromagnetic machines, which require high-cost rare-earth-based permanent magnets. The development of generators is moving toward high efficiency and increased environmental friendliness. Minimizing the use of rare earth materials such as magnetic materials under the premise of machine performance emerges as a challenging task. Topology optimization has been promisingly applied to many application areas as a powerful generative design tool. It can identify the optimal distribution of magnetic material in the defined design space. This paper employs the level-set-based topology optimization method to design the permanent magnet for generators. The machine under study is a simplified 2D outer rotor direct-drive wind power generator. The dynamic and static models of this generator are studied, and the magnetostatic system is adopted to conduct the topology optimization. The optimization goals in this study mainly focused on two aspects, namely the maximization of the system magnetic energy and the generation of a target magnetic field in the region of the air gap. The continuum shape sensitivity analysis is derived by using the material time derivative, the Lagrange multiplier method, and the adjoint variable method. Two numerical examples are investigated, and the effectiveness of the proposed design frameworkmore »is validated by comparing the performance of the original design against the optimized design.« less
  6. Ferromagnetic soft materials can generate flexible mobility and changeable configurations under an external magnetic field. They are used in a wide variety of applications, such as soft robots, compliant actuators, flexible electronics, and bionic medical devices. The magnetic field enables fast and biologically safe remote control of the ferromagnetic soft material. The shape changes of ferromagnetic soft elastomers are driven by the ferromagnetic particles embedded in the matrix of a soft elastomer. The external magnetic field induces a magnetic torque on the magnetized soft material, causing it to deform. To achieve the desired motion, the soft active structure can be designed by tailoring the layouts of the ferromagnetic soft elastomers. This paper aims to optimize multi-material ferromagnetic actuators. Multi-material ferromagnetic flexible actuators are optimized for the desired kinematic performance using the reconciled level set method. This type of magnetically driven actuator can carry out more complex shape transformations by introducing ferromagnetic soft materials with more than one magnetization direction. Whereas many soft active actuators exist in the form of thin shells, the newly proposed extended level set method (X-LSM) is employed to perform conformal topology optimization of ferromagnetic soft actuators on the manifolds. The objective function comprises two sub-objective functions,more »one for the kinematic requirement and the other for minimal compliance. Shape sensitivity analysis is derived using the material time derivative and the adjoint variable method. Three examples are provided to demonstrate the effectiveness of the proposed framework.« less
  7. This paper proposes a new way of designing and fabricating conformal flexible electronics on free-form surfaces, which can generate woven flexible electronics designs conforming to free-form 3D shapes with 2D printed electronic circuits. Utilizing our recently proposed foliation-based 3D weaving techniques, we can reap unprecedented advantages in conventional 2D electronic printing. The method is based on the foliation theory in differential geometry, which divides a surface into parallel leaves. Given a surface with circuit design, we first calculate a graph-value harmonic map and then create two sets of harmonic foliations perpendicular to each other. As the circuits are processed as the texture on the surface, they are separated and attached to each leaf. The warp and weft threads are then created and manually woven to reconstruct the surface and reconnect the circuits. Notably, The circuits are printed in 2D, which uniquely differentiates the proposed method from others. Compared with costly conformal 3D electronic printing methods requiring 5-axis CNC machines, our method is more reliable, more efficient, and economical. Moreover, the Harmonic foliation theory assures smoothness and orthogonality between every pair of woven yarns, which guarantees the precision of the flexible electronics woven on the surface. The proposed method provides anmore »alternative solution to the design and physical realization of surface electronic textiles for various applications, including wearable electronics, sheet metal craft, architectural designs, and smart woven-composite parts with conformal sensors in the automotive and aerospace industry. The performance of the proposed method is depicted using two examples.« less
  8. In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The proposed concept is proved through two examples of heat conduction on manifolds.
  9. Abstract Topology optimization has been proved to be an efficient tool for structural design. In recent years, the focus of structural topology optimization has been shifting from single material continuum structures to multimaterial and multiscale structures. This paper aims at devising a numerical scheme for designing bionic structures by combining a two-stage parametric level set topology optimization with the conformal mapping method. At the first stage, the macro-structural topology and the effective material properties are optimized simultaneously. At the second stage, another structural topology optimization is carried out to identify the exact layout of the metamaterial at the mesoscale. The achieved structure and metamaterial designs are further synthesized to form a multiscale structure using conformal mapping, which mimics the bionic structures with “orderly chaos” features. In this research, a multi-control-point conformal mapping (MCM) based on Ricci flow is proposed. Compared with conventional conformal mapping with only four control points, the proposed MCM scheme can provide more flexibility and adaptivity in handling complex geometries. To make the effective mechanical properties of the metamaterials invariant after conformal mapping, a variable-thickness structure method is proposed. Three 2D numerical examples using MCM schemes are presented, and their results and performances are compared. The achievedmore »multimaterial multiscale structure models are characterized by the “orderly chaos” features of bionic structures while possessing the desired performance.« less