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.

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.

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.

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.

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.

[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.

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.

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.

Porous structures inspired by porcupine quill: multiscale design optimization approach.

This paper presents a novel approach for designing a freeform bending-resistant structure from the combination of explicit discrete component-based topology optimization (TO) and the porcupine quill-inspired features. To embed the porcupine quill's features into the TO formulations, the method involves constructing discrete components at various scales to imitate features including solid shell, stochastically distributed pores, and graded stiffeners. The components are iteratively updated, and the optimization process allows for the grading of quill-inspired features while achieving optimal structural compliance under bending loads. The proposed approach is demonstrated to be effective through the resolution of Messershmitt-Bolkow-Blohm (MBB) beam designs, parameterized studies of geometric parameters, and numerical validation of long-span and short-span quill-inspired beam designs. By examining the von Mises stress distribution, the study highlights the mitigation of material yielding at the shell region brought by the geometric features of porcupine quills, leading to the potential theory support for the bending resistance. The optimized MBB beams are manufactured using the material extrusion technique, and three-point bending tests are conducted to explore the failure mitigation capability of the quill-inspired beam under large deformation. Consequently, the study concludes that the proposed quill-inspired component-based TO approach can design a structure with excellent bending resistance according to the improved energy absorption as well as increased deformation after reaching 75% peak load.

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.

Meta-structure enhanced second harmonic S0 waves for material microstructural changes monitoring.

Cumulative second harmonic Lamb waves in nonlinear media feature increasing amplitudes with propagation distance, conducive to the monitoring of material microstructural changes in structures. The phenomenon can be readily generated by zero-order symmetric (S0) mode waves in the low-frequency range. However, in a practical piezoelectric-transducer-activated system, both S0 and A0 (zero-order antisymmetric) mode Lamb waves are inevitably excited, while only the former is responsible for cumulative effects. The generation efficiency of the cumulative second harmonics is then affected by the presence of the A0 waves. To tackle the problem, this study develops a metamaterial structure, referred to as a meta-structure, to tactically enhance the cumulative second harmonic S0 Lamb waves by converting the A0 mode components into S0 mode waves. Topology optimization is conducted to design the meta-structure, which is surface-mounted onto the structure under inspection, to achieve high-efficiency A0-to-S0 wave mode conversion. Through tuning the parameters and constraints of the optimization, the designed single-sided meta-structure breaks the structural symmetry in the thickness direction, while facilitating its practical implementation. Typical scenarios with different meta-structure materials are discussed. Numerical simulations demonstrate that the strain amplitudes of the fundamental S0 mode waves can be increased by 60% with the deployment of the meta-structure, alongside an enhancement of the second harmonic S0 mode waves at different sensing distances. Finally, the designed meta-structure is fabricated via 3D printing technique and tested experimentally on an aluminum plate subjected to thermal aging treatment for monitoring the heating-induced microstructural changes inside the structure. Experimental results confirm an increase in the wave amplitudes of the linear S0 mode waves with the assistance of the meta-structure. The developed system improves the sensitivity of nonlinear Lamb wave-based monitoring methods in characterizing material microstructural changes, which shows great promise for detecting incipient damage in practical structural health monitoring applications.

Topology optimization of embracing fixator considering bone remodeling to mitigate stress shielding effect.

The embracing fixator is one of the widely used internal fixation implants for bone fracture treatment. However, the stress shielding effect, a stress imbalance between the implant and bone caused by the mismatch in mechanical properties between them, is a significant and critical issue that may lead to treatment failure. Thus, it is of great importance to design the implant with an appropriate stiffness which can mitigate the stress shielding effect and provide the most favorable mechanical environment for bone healing and remodeling. To this end, a time-dependent topology optimization algorithm considering bone remodeling is proposed to optimize an embracing fixator used in the tibia fracture treatment. The change of callus density over time is simulated based on a bone remodeling model, and the callus density after a period of bone remodeling is selected to be the design objective to maximize. The design constraints include volume and the compliance of the whole fixation system. Meanwhile, the influence of the constraints on the regularity of material distribution of the optimized result is also studied. Besides, to test the effectiveness of the consideration of the bone remodeling in the embracing fixator design, a topology optimization concerning the minimization of the compliance of the entire system is also performed to make a comparison. Finally, the safety performance of optimized results considering bone remodeling is also verified by static analysis.

Dynamic topology optimization of 3D-Printed transtibial orthopedic implant using tunable isotropic porous metamaterials.

In this paper, we introduce the design and manufacturing process of a transtibial orthopedic implant. We used medical-grade polyurethane polymer resin to fabricate a 3D porous architected implant with tunable isotropy, employing a high-speed printing method known as Continuous Liquid Interface Production (CLIP). Our objective is to enhance the weight-bearing capabilities of the bone structures in the residual limb, thereby circumventing the traditional reliance on a natural bridge. To achieve a custom-made design, we acquire the topology and morphology of the residual limb as well as the bone structure of the tibia and fibula, utilizing computed tomography (CT) and high-resolution 3D scanning. We employed a dynamic topological optimization method, informed by gait cycle data, to effectively reduce the mass of the implant. This approach, which differs from conventional static methods, enables the quantification of variations in applied forces over time. Using the Euler-Lagrange energy approach, we propose the equations of motion for a homologous multibody model with three degrees of freedom. The versatility of the Solid Isotropic Material with Penalization (SIMP) method facilitates the integration of homogenization methods for microscale porous architectures into the optimized domain. The design of these porous architectures is based on a bias-driven tuning symmetry isotropy of a Triply Periodic Minimal Surface (Schwarz Primitive surface). The internal porosity of the structure significantly reduces weight without compromising the isotropic behavior of the implant.

Development of a density-based topology optimization of homogenized lattice structures for individualized hip endoprostheses and validation using micro-FE.

Prosthetic implants, particularly hip endoprostheses, often lead to stress shielding because of a mismatch in compliance between the bone and the implant material, adversely affecting the implant's longevity and effectiveness. Therefore, this work aimed to demonstrate a computationally efficient method for density-based topology optimization of homogenized lattice structures in a patient-specific hip endoprosthesis. Thus, the root mean square error (RMSE) of the stress deviations between the physiological femur model and the optimized total hip arthroplasty (THA) model compared to an unoptimized-THA model could be reduced by 81 % and 66 % in Gruen zone (GZ) 6 and 7. However, the method relies on homogenized finite element (FE) models that only use a simplified representation of the microstructural geometry of the bone and implant. The topology-optimized hip endoprosthesis with graded lattice structures was synthesized using algorithmic design and analyzed in a virtual implanted state using micro-finite element (micro-FE) analysis to validate the optimization method. Homogenized FE and micro-FE models were compared based on averaged von Mises stresses in multiple regions of interest. A strong correlation (CCC > 0.97) was observed, indicating that optimizing homogenized lattice structures yields reliable outcomes. The graded implant was additively manufactured to ensure the topology-optimized result's feasibility.

Finite element-based optimization procedure for an irregular domain with unstructured mesh.

At present, structural optimization is a highly demanding area of research in engineering. Engineers aim to minimize material in a body while maintaining its usability and safety at the same time. Developing a user-friendly program to optimize a structure using the finite element method (FEM) is the goal of the current study. With the advent of additive manufacturing, the production of complex-shaped designs is showing promise. A detailed optimization algorithm based on solid isotropic material with penalization (SIMP) is presented in this paper. UnTop2D: An object-oriented Python program with a graphical user interface (GUI) has been developed, which can be applied to structures with both structured and unstructured meshes. The mesh is not required to be topologically ball and can be imported from professional meshing software. Any selected element can be frozen to prevent its removal during optimization, and wall elements can also be frozen for real-world scenarios. The optimized structure can be exported as an Abaqus input file for structural analysis and STL file for 3D printing. This paper presents several examples to demonstrate the effectiveness of the proposed procedure.

Lightweight and High-Stiffness Metal Optical Systems Based on Additive Manufacturing.

To build a long-wave infrared catadioptric optical system for deep space low-temperature target detection with a lightweight and wide field of view, this work conducted a study that encompasses a local cooling optical system, topology optimization-based metal mirror design, and additive manufacturing. First, a compact catadioptric optical system with local cooling was designed. This system features a 55 mm aperture, a 110 mm focal length, and a 4-degree by 4-degree field of view. Secondly, we applied the principles of topology optimization to design the primary mirror assembly, the secondary mirror assembly, and the connecting baffle. The third and fourth modes achieved a resonance frequency of 1213.7 Hz. Then, we manufactured the mirror assemblies using additive manufacturing and single-point diamond turning, followed by the centering assembly method to complete the optical assembly. Lastly, we conducted performance testing on the system, with the test results revealing that the modulation transfer function (MTF) curves of the optical system reached the diffraction limit across the entire field of view. Remarkably, the system's weight was reduced to a mere 96.04 g. The use of additive manufacturing proves to be an effective means of enhancing optical system performance.