A Dynamic Topology Optimization Method for Tactical Edge Networks Based on Virtual Backbone Networks.

To address the issues of low survivability and communication efficiency in wireless sensor networks caused by frequent node movement or damage in highly dynamic and high-mobility battlefield environments, we propose a dynamic topology optimization method based on a virtual backbone network. This method involves two phases: topology reconstruction and topology maintenance, determined by a network coverage threshold. When the coverage falls below the threshold, a virtual backbone network is established using a connected dominating set (CDS) and non-backbone node optimization strategies to reconstruct the network topology, quickly restore network connectivity, effectively improve network coverage, and optimize the network structure. When the coverage is above the threshold, a multi-CDS scheduling algorithm and slight position adjustments of non-backbone nodes are employed to maintain the network topology, further enhancing network coverage with minimal node movement. Simulations demonstrate that this method can improve coverage and optimize network structure under different scales of network failures. Under three large-scale failure operational scenarios where the network coverage threshold was set to 80%, the coverage was enhanced by 26.12%, 15.88%, and 13.36%, and in small-scale failures, the coverage was enhanced by 7.55%, 4.90% and 7.84%.

Functionally Graded Materials and Structures: Unified Approach by Optimal Design, Metal Additive Manufacturing, and Image-Based Characterization.

Functionally Graded Materials (FGMs) can outperform their homogeneous counterparts. Advances in digitalization technologies, mainly additive manufacturing, have enabled the synthesis of materials with tailored properties and functionalities. Joining dissimilar metals to attain compositional grading is a relatively unexplored research area and holds great promise for engineering applications. Metallurgical challenges may arise; thus, a theoretical critical analysis is presented in this paper. A multidisciplinary methodology is proposed here to unify optimal design, multi-feed Wire-Arc Additive Manufacturing (WAAM), and image-based characterization methods to create structure-specific oriented FGM parts. Topology optimization is used to design FGMs. A beam under pure bending is used to explore the layer-wise FGM concept, which is also analytically validated. The challenges, limitations, and role of WAAM in creating FGM parts are discussed, along with the importance of numerical validation using full-field deformation data. As a result, a conceptual FGM engineering workflow is proposed at this stage, enabling digital data conversion regarding geometry and compositional grading. This is a step forward in processing in silico data, with a view to experimentally producing parts in future. An optimized FGM beam, revealing an optimal layout and a property gradient from iron to copper along the build direction (bottom-up) that significantly reduces the normal pure bending stresses (by 26%), is used as a case study to validate the proposed digital workflow.

Numerical study on the forward and inverse problems of the mobile pump truck frame.

Aiming at the requirements of strong mobility and high flexibility of rescue and relief mobile pump trucks, this paper designs a new type of mobile pump truck frame based on existing mobile vehicle frame models. The materials used for the frame are 40Cr and Q235, and the finite element method is utilized to carry out static mechanical analysis and dynamic characteristic analysis. Simultaneously utilizing topology optimization and multi-objective genetic algorithm to optimize the design of the frame structure. The results show that the optimized pump truck frame can meet the strength design requirements of four typical working conditions: full load bending, full load torsion, emergency turning and emergency braking, while avoiding resonance phenomena caused by road surface and diesel engine vibration. Compared with the original frame model, the weight of the optimized frame is reduced by 87.88 kg, with a weight reduction rate of 10.89%, realizing the lightweight design requirements.

Topology Optimization Driven Bone-Remodeling Simulation for Lumbar Interbody Fusion.

This study proposes a numerical approach for simulating bone remodeling in lumbar interbody fusion (LIF). It employs a topology optimization method to drive the remodeling process and uses a pixel function to describe the structural topology and bone density distribution. Unlike traditional approaches based on strain energy density or compliance, this study adopts von Mises stress to guide the remodeling of LIF. A novel pixel interpolation scheme associated with stress criteria is applied to the physical properties of the bone, directly addressing the stress shielding effect caused by the implanted cage, which significantly influences the bone remodeling outcome in LIF. Additionally, a boundary inverse approach is utilized to reconstruct a simplified analysis model. To reduce computational cost while maintaining high structural resolution and accuracy, the scaled boundary finite element method (SBFEM) is introduced. The proposed numerical approach successfully generates results that closely resemble human lumbar interbody fusion.

Multiwavelength Achromatic Deflector in the Visible Using a Single-Layer Freeform Metasurface.

Deflectors are essential for modulating beam direction in optical systems but often face form factor issues or chromatic aberration with conventional optical elements, such as prisms, mirrors, and diffractive/holographic optical elements. Despite recent efforts to address such issues using metasurfaces, their practicality remains limited due to operation wavelengths in the near-infrared or the fabrication difficulties inherent in the multilayer scheme. Here, we propose a novel single-layer metasurface achieving multiwavelength chromatic aberration-free deflection across the visible spectrum by employing the robust freeform design strategy to simplify the fabrication process. By properly selecting diffraction orders for red, green, and blue wavelengths to achieve identical wavelength-diffraction-order products, the metasurface deflects light at a consistent angle of 41.3° with a high efficiency. The coupled Bloch mode analysis explains the physical properties, and experimental fabrication and characterization confirm its effectiveness. This approach holds potential for various applications such as AR/VR, digital cameras, and high-quality optical systems.

Anatomically and mechanically conforming patient-specific spinal fusion cages designed by full-scale topology optimization.

Cage subsidence after instrumented lumbar spinal fusion surgery remains a significant cause of treatment failure, specifically for posterior or transforaminal lumbar interbody fusion. Recent advancements in computational techniques and additive manufacturing, have enabled the development of patient-specific implants and implant optimization to specific functional targets. This study aimed to introduce a novel full-scale topology optimization formulation that takes the structural response of the adjacent bone structures into account in the optimization process. The formulation includes maximum and minimum principal strain constraints that lower strain concentrations in the adjacent vertebrae. This optimization approach resulted in anatomically and mechanically conforming spinal fusion cages. Subsidence risk was quantified in a commercial finite element solver for off-the-shelf, anatomically conforming and the optimized cages, in two representative patients. We demonstrated that the anatomically and mechanically conforming cages reduced subsidence risk by 91% compared to an off-the-shelf implant with the same footprint for a patient with normal bone quality and 54% for a patient with osteopenia. Prototypes of the optimized cage were additively manufactured and mechanically tested to evaluate the manufacturability and integrity of the design and to validate the finite element model.

Multi-Load Topology Optimization Design for the Structural Safety Maintenance of Low- and Intermediate-Level Radioactive Waste Packaging Containers in the Case of a Collision.

This paper presents an optimized design approach using nonlinear dynamic analysis and finite element methods to ensure the structural integrity of square-shaped containers made from ductile cast iron for intermediate- and low-level radioactive waste packaging. Ductile cast iron, with its spherical graphite structure, effectively distributes stress throughout the material, leading to a storage capacity increase of approximately 18%. Considering the critical need for containers that maintain integrity under extreme conditions like earthquakes, the design focuses on mitigating stress concentrations at the corners of square structures. Nonlinear dynamic analyses were conducted in five drop directions: three specified by ASTM-D5276 standards and two additional directions to account for different load patterns. Fractures were observed in four out of the five scenarios. For each direction where fractures occurred, equivalent loads causing similar displacement fields were applied to linear static models, which were then used for multi-load topology optimization. Three optimized models were derived, each increasing the volume by 1.4% to 1.6% compared to the original model, and the design that best met the structural integrity requirements during drop scenarios was selected. To further enhance the optimization process, weights were assigned to different load conditions based on numerical analysis results, balancing the impact of maximum stress, average stress, and plastic deformation energy. The final model, with its increased storage capacity and enhanced structural integrity, offers a practical solution for radioactive waste management, overcoming limitations in previous designs by effectively addressing complex load conditions.

Topology Optimization Enables High-Q Metasurface for Color Selectivity.

Nonlocal metasurfaces, exemplified by resonant waveguide gratings (RWGs), spatially and angularly configure optical wavefronts through narrow-band resonant modes, unlike the broad-band and broad-angle responses of local metasurfaces. However, forward design techniques for RWGs remain constrained at lower efficiency. Here, we present a topology-optimized metasurface resonant waveguide grating (MRWG) composed of titanium dioxide on a glass substrate capable of operating simultaneously at red, yellow, green, and blue wavelengths. Through adjoint-based topology optimization, while considering nonlocal effects, we significantly enhance its diffraction efficiency, achieving numerical efficiencies up to 78% and Q-factors as high as 1362. Experimentally, we demonstrated efficiencies of up to 59% with a Q-factor of 93. Additionally, we applied our topology-optimized metasurface to color selectivity, producing vivid colors at 4 narrow-band wavelengths. Our investigation represents a significant advancement in metasurface technology, with potential applications in see-through optical combiners and augmented reality platforms.

Computationally efficient dominant load-based local bone microstructure reconstruction method using topology optimization.

The bone microstructure of the human proximal femur is clinically crucial for diagnosing skeletal pathologies, such as osteoporosis and bone metastases. The topology optimization-based bone microstructure method obtains these bone microstructures by converting low-resolution (LR) images into high-resolution images. However, this method is inherently computationally inefficient as it requires numerous finite elements, iterative analyses, and parallel computations. Therefore, this study proposes a novel topology optimization-based localised bone microstructure reconstruction method using the dominant load, which highly affects the selected region of interest (ROI), for efficient resolution enhancement. The load dependency of selected ROIs is quantified with a load dependency score. Then, the localised finite element model is constructed based on the local load estimation. Finally, the selected dominant load is applied as an input for the topology optimization-based bone microstructure reconstruction method. The reconstructed bone microstructure was similar to that of the conventional method. The localised finite element model applied by the dominant load effectively and accurately reconstructed the bone morphology and exhibited high computational efficiency. In conclusion, the dominant load-based approach can be used to construct a reasonable trabecular bone structure for ROI with high computational efficiency. The predictive performance of the proposed method was validated and showed promise for accurate trabecular bone structure prediction without additional radiation exposure.

Design and optimization of a novel patient-specific subperiosteal implant additively manufactured in yttria-stabilized zirconia.

OBJECTIVE: To design a patient-specific subperiosteal implant for a severely atrophic maxillary ridge using yttria-stabilized additively manufactured zirconia (3YSZ) and evaluate its material properties by applying topology optimization (TO) to replace bulk material with a lattice structure. MATERIALS: A contrast-based segmented skull model from anonymized computed tomography data of a patient was used for the initial anatomical design of the implant for the atrophic maxillary ridge. The implant underwent finite element analysis (FEA) and TO under different occlusal load-bearing conditions. The resulting implant designs, in bulk material and lattice, were evaluated via in-silico tensile tests and 3D printed. RESULTS: The workflow produced two patient-specific subperiosteal designs: a) an anatomically precise bulk implant, b) a TO lattice implant. In-silico tensile tests revealed that the Young's modulus of yttria-stabilized zirconia is 205 GPa for the bulk material and 83.3 GPa for the lattice. Maximum principal stresses in the implant were 61.14 MPa in bulk material and 278.63 MPa in lattice, both tolerable, indicating the redesigned implant can withstand occlusal forces of 125-250 N per abutment. Furthermore, TO achieved a 13.10 % mass reduction and 208.71 % increased surface area, suggesting improved osteointegration potential. SIGNIFICANCE: The study demonstrates the planning and optimization of ceramic implant topology. A further iteration of the implant was successfully implanted in a patient-named use case, employing the same fabrication process and parameters.

[Design and performance study of bone trabecular scaffolds based on triply periodic minimal surface method].

Triply periodic minimal surface (TPMS) is widely used because it can be used to control the shape of porous scaffolds precisely by formula. In this paper, an I-wrapped package (I-WP) type porous scaffolds were constructed. The finite element method was used to study the relationship between the wall thickness and period, the morphology and mechanical properties of the scaffolds, as well as to study the compression and fluid properties. It was found that the porosity of I-WP type scaffolds with different wall thicknesses (0.1 ~ 0.2 mm) and periods (I-WP 1 ~ I-WP 5) ranged from 68.01% ~ 96.48%, and the equivalent elastic modulus ranged from 0.655 ~ 18.602 GPa; the stress distribution of the scaffolds tended to be uniform with the increase of periods and wall thicknesses; the equivalent elastic modulus of the I-WP type scaffolds was basically unchanged after the topology optimization, and the permeability was improved by 52.3%. In conclusion, for the I-WP type scaffolds, the period parameter can be adjusted first, then the wall thickness parameter can be controlled. Topology optimization can be combined to meet the design requirements. The I-WP scaffolds constructed in this paper have good mechanical properties and meet the requirements of repairing human bone tissue, which may provide a new choice for the design of artificial bone trabecular scaffolds.

[Structural design and evaluation of bone remodeling effect of fracture internal fixation implants with time-varying stiffness].

The stiffness of an ideal fracture internal fixation implant should have a time-varying performance, so that the fracture can generate reasonable mechanical stimulation at different healing stages, and biodegradable materials meet this performance. A topology optimization design method for composite structures of fracture internal fixation implants with time-varying stiffness is proposed, considering the time-dependent degradation process of materials. Using relative density and degradation residual rate to describe the distribution and degradation state of two materials with different degradation rates and elastic modulus, a coupled mathematical model of degradation simulation mechanical analysis was established. Biomaterial composite structures were designed based on variable density method to exhibit time-varying stiffness characteristics. Taking the bone plate used for the treatment of tibial fractures as an example, a composite structure bone plate with time-varying stiffness characteristics was designed using the proposed method. The optimization results showed that material 1 with high stiffness formed a columnar support structure, while material 2 with low stiffness was distributed at the degradation boundary and inside. Using a bone remodeling simulation model, the optimized bone plates were evaluated. After 11 months of remodeling, the average elastic modulus of callus using degradable time-varying stiffness plates, titanium alloy plates, and stainless steel plates were 8 634 MPa, 8 521 MPa, and 8 412 MPa, respectively, indicating that the use of degradable time-varying stiffness plates would result in better remodeling effects on the callus.

Design, fabrication and clinical characterization of additively manufactured tantalum hip joint prosthesis.

The joint prosthesis plays a vital role in the outcome of total hip arthroplasty. The key factors that determine the performance of joint prostheses are the materials used and the structural design of the prosthesis. This study aimed to fabricate a porous tantalum (Ta) hip prosthesis using selective laser melting (SLM) technology. The feasibility of SLM Ta use in hip prosthesis was verified by studying its chemical composition, metallographic structure and mechanical properties. In vitro experiments proved that SLM Ta exhibited better biological activities in promoting osteogenesis and inhibiting inflammation than SLM Ti6Al4V. Then, the topological optimization design of the femoral stem of the SLM Ta hip prosthesis was carried out by finite element simulation, and the fatigue performance of the optimized prosthesis was tested to verify the biomechanical safety of the prosthesis. A porous Ta acetabulum cup was also designed and fabricated using SLM. Its mechanical properties were then studied. Finally, clinical trials were conducted to verify the clinical efficacy of the SLM Ta hip prosthesis. The porous structure could reduce the weight of the prosthesis and stress shielding and avoid bone resorption around the prosthesis. In addition, anti-infection drugs can also be loaded into the pores for infection treatment. The acetabular cup can be custom-designed based on the severity of bone loss on the acetabular side, and the integrated acetabular cup can repair the acetabular bone defect while achieving the function of the acetabular cup.

Optimization design of battery bracket for new energy vehicles based on 3D printing technology.

Nowadays, what captures consumers' primary attention is how to purchase electric vehicles with long range and desirable price. Lightweight construction stands as one of the most effective approaches for prolonging range and lowering costs. As a consequence, it is particularly imperative to undertake lightweight design optimization for the battery bracket of new energy vehicles by applying 3D printing technology. To actualize this goal, Rhino software was initially employed for 3D modeling to design the battery bracket system for a pure electric vehicle in China. Subsequently, topology optimization design of the battery bracket was carried out by adopting Altair Inspire software. Last but not least, manufacturing and assembly inspection were completed using a 3D printer. The results show that the maximum displacement of the battery lower tray bracket after topology optimization is 3.20 mm, which is slightly higher than before, but still relatively small. The maximum Mises equivalent stress rose to 240.7 MPa post-optimization, but brought about a uniform stress distribution at the bottom of the bracket. In comparison, the minimum factor of safety met design requirements at 1. The mass was lessened to 0.348 kg, representing a 49.2% decrease in comparison with pre-optimization levels. The 3D-printed bracket was fabricated by employing a 3D printer, thereby achieving the aforementioned mass abatement. The battery pack parts exhibited a bright surface with low roughness and no discernible warping or deformation defects. As revealed by the assembly results, the components of the battery pack bracket are tightly coordinated with each other, with no evident assembly conflicts, revealing that the dimensional accuracy and fit of the completed parts meet production requirements. These findings lay solid groundwork for the mass production of high-performance battery pack brackets.

Topological optimization and fatigue life prediction of a single pad externally adjustable fluid film bearing.

This work focuses on the prediction and comparison of the fatigue life of topologically optimized pads in an externally adjustable fluid film (EAFF) bearing. It integrates one-way/two-way fluid-structure interaction analysis, topological optimization (TO), and design modifications of the pad of an externally adjustable fluid film bearing. The major goal is to create an optimum pad design that minimizes weight and maintains structural integrity, and then to predict and compare the fatigue life of these alternative designs. The outcomes of the present study are as follows: (i) Two-way FSI results show a decrease of 65.64% in hydrodynamic fluid film pressure when compared to one-way FSI results because they take into account modifications in the fluid region's geometry caused by pad deformation; (ii) even though the maximum pad deformation in optimized pad geometry (Type-4) resulting from oil film pressure is relatively small (0.0036551 mm), the influence of pad deformation on the fluid domain due to hydrodynamic fluid film pressure cannot be understated; and (iii) when comparing the TO technique's results with fatigue life results, four elongated holes in the radial direction (Type-4) are most appropriate.

Geometric Complexity Control in Topology Optimization of 3D-Printed Fiber Composites for Performance Enhancement.

This paper investigates the impact of varying the part geometric complexity and 3D printing process setup on the resulting structural load bearing capacity of fiber composites. Three levels of geometric complexity are developed through 2.5D topology optimization, 3D topology optimization, and 3D topology optimization with directional material removal. The 3D topology optimization is performed with the SIMP method and accelerated by high-performance computing. The directional material removal is realized by incorporating the advection-diffusion partial differential equation-based filter to prevent interior void or undercut in certain directions. A set of 3D printing and mechanical performance tests are performed. It is interestingly found that, the printing direction affects significantly on the result performance and if subject to the uni direction, the load-bearing capacity increases from the 2.5D samples to the 3D samples with the increased complexity, but the load-bearing capacity further increases for the 3D simplified samples due to directional material removal. Hence, it is concluded that a restricted structural complexity is suitable for topology optimization of 3D-printed fiber composites, since large area cross-sections give more degrees of design freedom to the fiber path layout and also makes the inter-layer bond of the filaments firmer.

Thermo-Mechanical Optimization of Die Casting Molds Using Topology Optimization and Numerical Simulations.

Conventional cooling channels used in die casting molds exhibit significant drawbacks, resulting in extended cooling times for cast parts. Issues such as the formation of dirt, limescale, and corrosion substantially diminish the thermal efficiency of these channels, leading to challenges in achieving uniform cooling and potential quality issues. In response to these challenges, this study proposes Topology Optimization as a novel approach. It involves designing cooling structures through Topology Optimization to replace traditional cooling channels, incorporating both Discrete and Gaussian boundary conditions to optimize thermal efficiency. Additionally, Structural Topology Optimization is employed to ensure structural integrity, preventing deformation or yielding under high loads during the die casting process. Numerical analysis revealed superior thermal performance compared to conventional channels, particularly when subjected to Discrete and Gaussian boundary conditions. Furthermore, the application of the latter establishes conformal cooling and minimizes temperature gradients in the casting, reducing casting defects such as shrinkage porosity. These findings highlight the efficacy of Topology Optimization in addressing the challenges of traditional cooling methods, with wide-ranging implications for manufacturing processes utilizing permanent molds for shaping materials.

Topology optimization of the flat steel shear wall based on the volume constraint and strain energy assumptions under the seismic loading conditions.

In structural engineering systems, shear walls are two-dimensional vertical elements designed to endure lateral forces acting in-plane, most frequently seismic and wind loads. Shear walls come in a variety of materials and are typically found in high-rise structures. Because steel shear walls are lighter, more ductile, and stronger than other concrete shear walls, they are advised for usage in steel constructions. It is important to remember that the steel shear wall has an infill plate, which can be produced in a variety of forms. The critical zones in flat steel shear walls are the joints and corners where the infill plate and frame meet. The flat infill plate can be modified to improve the strength and weight performance of the steel shear walls. One of these procedures is Topology Optimization (TO) and this method can reduce the weight and also, increase the strength against the cyclic loading sequences. In the current research paper, the TO of the infill steel plate was considered based on the two methods of volume constraint and maximization of strain energy. Four different volumes (i.e., 60%, 70%, 80%, and 90%) were assumed for the mentioned element in the steel shear wall. The obtained results revealed that the topology configuration of CCSSW with 90% volume constraint presented the highest seismic loading performance. The cumulated energy for this type of SSW was around 700 kJ while it was around 600 kJ for other topology optimization configurations.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials.

Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This article also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pretrained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pretraining.

Topology Optimization Method of Stamping Structures Based on the Directional Density Field.

The stamping process produces thin-walled structures that, in general, have uniform wall thickness and no enclosed cavity. However, it is difficult to satisfy the above geometric requirements with the current density-based topology optimization method, since configuring the related geometric constraints is challenging. In order to solve this problem, a topology optimization method for stamping structures based on a directional density field is proposed. Specifically, the directional density field is developed to enable the adding and removing of materials only along the stamping direction, so as to avoid internal voids and concave features. The geometric control for uniform wall thickness is realized by tuning the truncation threshold of the Heaviside projection that processes the directional density field into the 0-1 binary field. At the same time, a calibrated filter radius of the truncation thresholds will facilitate the drawing angle control of the stamping ribs. The effectiveness of the established method has been verified by a number of numerical case studies. Results show that the proposed method can perform topology optimization for stamping structures with tunable uniform thickness and drawing angle control of the ribs. No internal voids or undercuts appear in the results. The results also disclose that a constant truncation threshold increment does not guarantee uniform wall thickness, and varying the threshold increments through surface offset and polynomial fitting is necessary.