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Nanophotonic devices have enabled microscopic control of light with an unprecedented spatial resolution by employing subwavelength optical elements that can strongly interact with incident waves. However, to date, most nanophotonic devices have been designed based on fixed-shape optical elements, and a large portion of their design potential has remained unexplored. It is only recently that free-form design schemes have been spotlighted in nanophotonics, offering routes to make a break from conventional design constraints and utilize the full design potential. In this review, we systematically overview the nascent yet rapidly growing field of free-form nanophotonic device design. We attempt to define the term “free-form” in the context of photonic device design, and survey different strategies for free-form optimization of nanophotonic devices spanning from classical methods, adjoint-based methods, to contemporary machine-learning-based approaches.

Free-form concrete panels (FCPs) require precise lower-shape implementation because lower-shape errors directly affect thickness quality, geometric accuracy, and constructability. Although previous studies have developed several lower-mold systems, the sectional behavior of lower-shape errors and their deformation tendencies under concrete load have not been sufficiently clarified. Therefore, this study investigates the sectional shape error characteristics of the lower silicone mold (LSM) before casting and of the lower shape of the FCP after casting under combined curvature and thickness conditions. Single-curved FCPs were designed with curvatures of 20, 25, and 30 mm and thicknesses of 20, 30, and 40 mm. The lower geometry was divided into middle and edge sections, and statistical analyses were conducted to examine curvature-dependent deformation and load-induced error behavior. Before casting, the mean error of the LSM increased from 0.289 mm to 0.345 mm and 0.425 mm as curvature increased. After casting, the lower-shape error of the manufactured FCPs ranged from 0.313 mm to 0.444 mm. Under the 30 mm curvature and 20 mm thickness condition, the error decreased after casting, indicating partial load compensation, whereas manufacture was not possible under the 30 mm curvature and 40 mm thickness condition because of excessive side-mold displacement. These results provide quantitative evidence for deformation behavior under load and support the need for FCP-specific quality criteria.

Free-form concrete panel production requires an increasing amount of manpower because the molds cannot be reused. There are many limitations when it comes to reproducing accurate forms due to the many manual processes. Therefore, the current study developed side mold control equipment that can automatically fabricate molds for free-form concrete panels. The equipment is capable of molding various shapes and sustainable operation. However, there may be errors as it automatically produces various shapes. Therefore, it is necessary to check the errors between manufactured shapes and designed shapes. The shape created using the side mold control equipment showed less than 0.1° error in side angle and ±3 mm error in side length. Therefore, the equipment manufactured a precise shape. Based on the findings of the study, the side mold control equipment will be used to produce accurate shape of free-form concrete panels automatically.

The blood-brain barrier (BBB) controls the entry of chemicals from the blood to the brain. Since brain drugs need to penetrate the BBB, rapid and reliable prediction of BBB penetration (BBBP) is helpful for drug development. In this study, free-form and in-blood-form datasets were prepared by modifying the original BBBP dataset, and the effects of the data modification were investigated. For each dataset, molecular descriptors were generated and used for BBBP prediction by machine learning (ML). For ML, the dataset was split into training, validation, and test data by the scaffold split algorithm MoleculeNet used. This creates an unbalanced split and makes the prediction difficult; however, we decided to use that algorithm to evaluate the predictive performance for unknown compounds dissimilar to existing ones. The highest prediction score was obtained by the random forest model using 212 descriptors from the free-form dataset, and this score was higher than the existing best score using the same split algorithm without using any external database. Furthermore, using a deep neural network, a comparable result was obtained with only 11 descriptors from the free-form dataset, and the resulting descriptors suggested the importance of recognizing the glucose-like characteristics in BBBP prediction.

In this paper, a simultaneous shape and topology optimization method is presented for designing multi-material structures. The whole shape and the layer’s material distributions of a laminated shell structure composed of multi-materials are optimized. The free-form optimization method for shells and the generalized solid isotropic material with penalization (GSIMP) method are respectively employed and combined effectively for shape and topology optimization. Shape along with fictitious homogenized-density variations are used as design variables and simultaneously determined. In other words, the optimal topology is determined in the variable design surface optimized by shape optimization. Compliance is used as the objective functional and minimized under the volume and the area constraints for each material. The optimal design problem is formulated as a distributed-parameter optimization problem, and the sensitivity functions with respect to shape and density variations are theoretically derived. Both the optimal shape and density variations are determined with the unified H 1 gradient method, where the sensitivity functions are respectively applied as the Robin condition, to the design surface and the domain in order to determine the optimal shape and topology simultaneously. Several numerical results including a comparison with the non-simultaneous methods are presented to show the effectiveness of the proposed method. With the proposed method, the optimal lighter and stiffer multi-material laminated shell structure can be obtained without any design parameterization, free of numerical instabilities such as checkerboard pattern and zigzag shape problems.

Foot and ankle joint models are widely used in the biomechanics community for musculoskeletal and finite element analysis. However, personalizing a foot and ankle joint model is highly time-consuming in terms of medical image collection and data processing. This study aims to develop and evaluate a framework for constructing a comprehensive 3D foot model that integrates statistical shape modeling (SSM) with free-form deformation (FFD) of internal bones. The SSM component is derived from external foot surface scans (skin measurements) of 50 participants, utilizing principal component analysis (PCA) to capture the variance in foot shapes. The derived surface shapes from SSM then guide the FFD process to accurately reconstruct the internal bone structures. The workflow accuracy was established by comparing three model-generated foot models against corresponding skin and bone geometries manually segmented and not part of the original training set. We used the top ten principal components representing 85 % of the population variation to create the model. For prediction validation, the average Dice similarity coefficient, Hausdorff distance error, and root mean square error were 0.92 ± 0.01, 2.2 ± 0.19 mm, and 2.95 ± 0.23 mm for soft tissues, and 0.84 ± 0.03, 1.83 ± 0.1 mm, and 2.36 ± 0.12 mm for bones, respectively. This study presents an efficient approach for 3D personalized foot model reconstruction via SSM generation of the foot surface that informs bone reconstruction based on FFD. The proposed workflow is part of the open-source Musculoskeletal Atlas Project linked to OpenSim and makes it feasible to accurately generate foot models informed by population anatomy, and suitable for rigid body analysis and finite element simulation.

Planning tool paths on free-form surfaces is a widely discussed issue. However, satisfying all the requirements of blade machining using traditional path-planning methods remains a challenge. Herein, a new iso-parametric path-planning strategy, based on a novel parameterization method and combined with conformal transformation theory, is proposed. The presented strategy adapts to the curvature of blade surfaces, improving the kinematic performance of the machining process, reducing the complexity of multi-axis coordinated motion control, and improving the machining quality. A comparison between the proposed and three traditional methods is also discussed. The influence of the tool path on the kinematic performance of the machine tool is quantitatively examined based on the kinematic models of two different machines. Finally, the results of a deep-cutting milling experiment conducted to verify the improvement of the machining quality due to kinematic optimization are described. The proposed method provides a more reasonable path-planning approach for blade machining on a five-axis machine tool, which can significantly reduce the cost of blade machining, minimize the risks of blade failure, and enhance the large-scale automated production of blades.

In order to solve the problem of deviation between actual and theoretical machining paths due to the presence of rotation axis in five-axis machining, an interpolation algorithm based on the optimization of swing cutter trajectory and the method of corresponding nonlinear error compensation are proposed. Taking A-C dual rotary table five-axis machine tool as an example, the forward and reverse kinematic model of the machine tool is established according to the kinematic chain of the machine tool. Based on the linear interpolation of rotary axis, the generation mechanism of nonlinear error is analyzed, the modeling methods of cutter center point, and cutter axis vector trajectory are proposed respectively, and the parameterized model of swing cutter trajectory is formed. The formula for the nonlinear error is obtained from the two-dimensional cutter center point trajectory. According to the established model of swing cutter trajectory, the synchronous optimization method of cutter center point trajectory and cutter axis vector trajectory is proposed, and the nonlinear error compensation mechanism is established. First, pre-interpolation is performed on the given cutter location data to obtain a model of the swing cutter trajectory for each interpolated segment. Then, the magnitude of the nonlinear error is calculated based on the parameters of the actual interpolation points during formal interpolation, and the nonlinear error is compensated for the interpolation points where the error exceeds [ε]. In the VERICUT simulation, the maximum machining error was reduced from 50 to 5 μm by this paper method. In actual machining, the surface roughness of the free-form surface was reduced from 10.5 μm before compensation to 1.8 μm. The experimental results show that the proposed method can effectively reduce the impact of nonlinear errors on processing, and is of high practical value for improving the accuracy of cutter position and the quality of complex free-form machining in five-axis machining.

Free-form surface is widely applied in the manufacturing industries due to its excellent geometric characteristics. Surface finishing of free-form surface is a critical manufacturing process to meet the target quality requirement. In this work, a magnetorheological shear thickening finishing (MSTF) method was employed with the designed finishing tool and the developed MSTF media for the finishing of a typical free-form surface, i.e., Sine surface. The finishing tool was designed as a slotted cylindrical permanent magnetic pole with radial magnetization. The magnetic pole was fabricated to dominate MSTF performance of the finishing media. To obtain sufficiently large magnetic flux density and magnetic field gradients in the finishing zone, finite element analysis (FEA) was used to optimize the dimension of the finishing tool. The MSTF principle was illustrated in detail. The mathematical model of the material removal was established. Finishing experiments were conducted on the SUS304 Sine surface using the developed MSTF media. The effects of finishing parameters on surface roughness were evaluated quantitatively. The results showed that the material was uniformly removed across the entire Sine surface with over 87% improvement in surface roughness (Sa). It is quite potential for the surface finishing free-form surface in a wide manufacturing industrial applications.

Many studies have been conducted for the accuracy of free-form concrete panel fabrication, but there still are errors in the process of fabrication. This study developed a connection technology of detachable shape part that can be applied to the existing multi-point Computer Numerical Control (CNC) to enhance the accuracy of fabrication. The detachable type can place a silicone plate on top of the rod without additional fixtures. The accuracy of the technology was verified by curvature test and free-form concrete panel fabrication test. Three curves were created to compare the discrepancies between the designed shapes and the fabricated shapes through quality test. As a result, the detachable type decreased the error by up to 2 mm. In addition, a panel was fabricated to analyze the error to verify the rigidity of the developed molds. The error caused by concrete deflection under load or the error caused by repeated fabrication was about 0.5 mm. The shape error was within 3.5 mm. This small error proved greater accuracy compared to the existing technology.