Optimal Density Distribution Research Articles

Deep learning assisted anode porous transport layer inverse design for proton exchange membrane water electrolysis

Proton exchange membrane water electrolysis cell (PEMEC) offers a clean and promising way for hydrogen production. The spatial internal current density and temperature distribution uniformity significantly determines its reliability and durability, as well as the hydrogen production performance. Here, a non-isothermal 3D computational fluid dynamics (CFD) model for PEMEC with parallel flow fields is employed to investigate the impacts of the heterogeneous porosity distribution within the anode porous transport layer (APTL) on the internal current density and temperature distribution uniformity and energy conversion performance. 800 heterogeneous APTL porosity distributions are applied for CFD calculation, providing dataset for deep learning. The deep operator network (DeepONet) is employed to mapping the heterogeneous APTL porosity distribution to the real physical fields such as temperature, oxygen molar fraction and current density distribution fields. Full-connected neural network is employed to construct the relationship between the heterogeneous APTL porosity distribution to the performance metrics. The gradient descent algorithm is applied to obtain APTL porosity distributions corresponding to the optimal internal current density and temperature distribution uniformity, respectively. Compared with the uniform porosity distribution, the current density and temperature uniformity are improved by 45.544 % and 26.680 %, respectively, at an average APTL porosity of 0.5.

Breaking Local Charge Symmetry of Iron Single Atoms for Efficient Electrocatalytic Nitrate Reduction to Ammonia.

The electrochemical conversion of nitrate pollutants into value-added ammonia is a feasible way to achieve artificial nitrogen cycle. However, the development of electrocatalytic nitrate-to-ammonia reduction reaction (NO3-RR) has been hampered by high overpotential and low Faradaic efficiency. Here we develop an iron single-atom catalyst coordinated with nitrogen and phosphorus on hollow carbon polyhedron (denoted as Fe-N/P-C) as a NO3-RR catalyst electrode. Owing to the tuning effect of phosphorus atoms on breaking local charge symmetry of the single-Fe-atom catalyst, it facilitates the adsorption of nitrate ions and enrichment of some key reaction intermediates during the NO3-RR process. The Fe-N/P-C catalyst exhibits 90.3% ammonia Faradaic efficiency with a yield rate of 17980 μg h-1 mgcat-1, greatly outperforming the reported Fe-based catalysts. Furthermore, operando SR-FTIR spectroscopy measurements reveal the reaction pathway based on key intermediates observed under different applied potentials and reaction durations. Density functional theory calculations demonstrate that the optimized free energy of NO3-RR intermediates is ascribed to the asymmetric atomic interface configuration, which achieves the optimal electron density distribution. This work demonstrates the enhanced function of heteroatom doping on single atoms for NO3-RR, and provides an effective strategy for improving the catalytic performance of single atom catalysts in different electrochemical reactions.

Breaking Local Charge Symmetry of Iron Single Atoms for Efficient Electrocatalytic Nitrate Reduction to Ammonia

AbstractThe electrochemical conversion of nitrate pollutants into value‐added ammonia is a feasible way to achieve artificial nitrogen cycle. However, the development of electrocatalytic nitrate‐to‐ammonia reduction reaction (NO3−RR) has been hampered by high overpotential and low Faradaic efficiency. Here we develop an iron single‐atom catalyst coordinated with nitrogen and phosphorus on hollow carbon polyhedron (denoted as Fe−N/P−C) as a NO3−RR electrocatalyst. Owing to the tuning effect of phosphorus atoms on breaking local charge symmetry of the single‐Fe‐atom catalyst, it facilitates the adsorption of nitrate ions and enrichment of some key reaction intermediates during the NO3−RR process. The Fe−N/P−C catalyst exhibits 90.3 % ammonia Faradaic efficiency with a yield rate of 17980 μg h−1 mgcat−1, greatly outperforming the reported Fe‐based catalysts. Furthermore, operando SR‐FTIR spectroscopy measurements reveal the reaction pathway based on key intermediates observed under different applied potentials and reaction durations. Density functional theory calculations demonstrate that the optimized free energy of NO3−RR intermediates is ascribed to the asymmetric atomic interface configuration, which achieves the optimal electron density distribution. This work demonstrates the critical role of atomic‐level precision modulation by heteroatom doping for the NO3−RR, providing an effective strategy for improving the catalytic performance of single atom catalysts in different electrochemical reactions.

VIBRATION REDUCTION BY TUNED MASS DAMPERS INSIDE CAVITIES OF TOPOLOGY OPTIMIZED LATTICE STRUCTURES

AbstractTuned mass dampers may be used to improve vibrational behavior of structures. However, they require space to move. This paper presents an approach to incorporate tuned mass dampers into a lightweight-optimized structure without extra space requirement. It is based on (1) topology optimization (TopOpt) with unit cells and (2) vibration reduction with multiple tuned mass dampers (m-TMD) within the unit cells. The topology optimization is performed with a physics-informed penalty factor, unique to the chosen unit cell. Subsequently, the weight optimal density distribution is realized by populating the design domain with unit cells of ten different densities. To reduce the induced vibration, m-TMDs are placed inside the cavities of the unit cells in the grey scale regions. The effectiveness of the approach is demonstrated for the design of a 2-segment robot arm. The resulting unit cell robotic arm (UC-Arm) is 3.6% lighter than the reference model, maintains the same static performance, and shows a 60% smaller dynamic displacement in the observed frequency range. No extra space is required for the motion of the m-TMD.

Design and optimization of graded lattice structures with load path-oriented reinforcement

Lattice structures have been increasingly used in load-carrying applications due to their exceptional mechanical performance. This study presents a novel load path methodology for designing and optimizing functionally graded lattice structures composed of anisotropic unit cells with directional reinforcement struts. Firstly, the optimal density distribution of the lattice structure is obtained by solid isotropic material with penalization (SIMP) topology optimization. Secondly, pointing stress vectors of the structure are calculated to determine the orientations of the unit cells. Lastly, the lattice model is constructed using tapered beams for a smooth transition between struts with different radii. Two examples of a simply supported beam and a 3-dimensional base support structure are provided. The experimental validation showcases that the proposed design improves the specific stiffness by 75 % compared to the uniform body-centered cubic design. Furthermore, the strength-to-weight ratio is increased by 232 % due to a more desirable stress distribution.

Breaking the Computational Bottleneck: Probabilistic Optimization of High-Memory Spatially-Coupled Codes

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a convolutional manner. The number of partitioned components determines the memory of SC codes. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. While adopting higher memories results in improved SC code performance, obtaining finite-length, high-performance SC codes with high memory is known to be computationally challenging. We break this computational bottleneck by developing a novel probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low-complexity optimization algorithms that minimize the number of detrimental objects to construct high-memory, high-performance quasi-cyclic SC codes. We apply our framework to various objects of interest, from the simplest short cycles, to more sophisticated objects such as concatenated cycles aiming at finer-grained optimization. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and optimized SC codes with uniform partitioning. The performance gain is shown to be universal over a variety of channels, from canonical channels such as additive white Gaussian noise and binary symmetric channels, to practical channels underlying flash memory and magnetic recording systems.

Hybrid manufacturing of topology optimized machine tool parts through a layer laminated manufacturing method

Load-oriented lightweight structures are commonly designed based on topology optimization. For machine tool parts, they enable the reduction of moving masses and therefore increase the resource and energy efficiency of production systems. However, this usually results in complex part structures that are difficult or impossible to produce using conventional manufacturing methods. In this paper, a hybrid layer laminated manufacturing (LLM) method is proposed enabling manufacturing of topology-optimized machine tool parts. The method is referred to as hybrid, as the subtractive structuring of metal sheets is combined with the additive joining of the sheets by adhesive bonding. This enables enclosed inner cavities without support structures, which are used to approximate the optimal density distribution from a topology optimization via manufacturing. The proposed LLM method is validated on the basis of a bearing block of a ball screw feed drive. A experimental study in the time and frequency domain on a test rig confirms the principle suitability of the LLM method for the production of industrial applicable lightweight components.

Bio-inspired lattice structure optimisation with strain trajectory aligned trusses

Lattice structures have great potential for lightweight additively manufactured parts. This paper presents a bio-inspired functionally graded lattice structure optimisation approach for compliance minimisation of statically loaded structures. Topology optimisation determines the optimal relative density distribution within a design space and the associated strain fields. A lattice structure is then generated within this design space, comprised of trusses aligned with principal strain trajectories. The trusses have a rectangular cross-section, resulting in three size variable per node during the final sizing step. A minimum feature size is implemented so that the designs are suited to the particular additive manufacturing process print resolution. The presented approach is further demonstrated to efficiently solve problems with multiple load cases and produce lattice topologies that mimic those found in bone. The optimised lattice structure examples presented are on average 12% less stiff in comparison to a conventional SIMP topology optimisation approach. However, they are well suited to multifunctional applications such as heat transfer where the surface area is increased by an average of 94%. The optimised lattice structures are also shown to be able to eliminate additive manufacturing support structure requirements.

Design of graded lattice structures in turbine blades using topology optimization

ABSTRACT Designing and manufacturing lattice structures with Topology Optimization (TO) and Additive Manufacturing (AM) techniques is a novel method to create light-weight components with promising potential and high design flexibility. This paper proposes a new design of lightweight-graded lattice structures to replace the internal solid volume of the turbine blade to increase its endurance of high thermal stresses effects. The microstructure design of unit cells in a 3D framework is conducted by using the lattice structure topology optimization (LSTO) technique. The role of the LSTO is to find an optimal density distribution of lattice structures in the design space under specific stress constraints and fill the inner solid part of the blade with graded lattice structures. The derived implicit surfaces modelling is used from a triply periodic minimal surfaces (TPMS) to optimize the mechanical performances of lattice structures. Numerical results show the validity of the proposed method. The effectiveness and robustness of the constructed models are analysed by using finite element analysis. The simulation results show that the graded lattice structures in the improved designs have better efficiency in terms of lightweight (33.41–40.32%), stress (25.52–48.55%) and deformation (7.35–19.58%) compared to the initial design.

Topology optimization of microlattice dome with enhanced stiffness and energy absorption for additive manufacturing

The synergy of additive manufacturing (AM) with topology optimization has become a useful method for developing ultralight, ultrastiff structures with high energy absorption capability. To improve the weight-specific stiffness and energy absorption capability of the conventional dome commonly used as the core of sandwich sheets, a new concept of filling the solid part of the dome with stretch-dominated microlattices is proposed. The optimal density distribution of microlattices is obtained by integrating the homogenization-based topology optimization method with the lattice structure. The compressive and bending stiffnesses of the optimized variable-density microlattice domes are demonstrated to be 41.8% and 33.7% higher than those of the conventional solid domes, while the energy absorption of the microlattice dome during compression and three-point bending is increased by 297.5% and 85%, respectively. Investigation of the cell size effect on the mechanical properties of the microlattice dome reveals that a larger cell size contributes more to the weight-specific stiffness and energy absorption capability at a given overall volume fraction constraint. The topology optimization and construction methods described in this paper are universal and can be used for the further development of ultralight, ultrastiff structures with arbitrary macro shapes with microlattices as constituent units.

Construction and simulation of performance evaluation index system of Internet of Things based on cloud model

Due to the lack of corresponding scientific evaluation standards and effective evaluation methods for the overall performance of the Internet of Things system, the Internet of Things industry and the market are in a chaotic state, and the quality of various products is uneven. It is difficult for users to select a more suitable application system, which seriously restricts the development process of the industrialization of Internet of Things technology. Therefore, it is very necessary for us to conduct research on the performance evaluation methods of IoT systems. In this paper, the performance of IoT system is selected as the performance evaluation index of the system, and the evaluation system is constructed. The performance evaluation method of the Internet of Things system based on the cloud model is proposed. The comprehensive evaluation of the reliability of the IoT system for the cloud model will be based on the AHP. Based on the combination of attribute decision-making methods, a comprehensive evaluation method based on indicators is proposed, and the system’s indicator model is established. The reliability of the Internet of Things system can be comprehensively evaluated by the value of the indicators. Secondly, the probability density function of tracking error is studied, and its optimal probability density distribution is given by optimal control. Based on the optimal probability density distribution, the performance evaluation index of the system is constructed. In order to compare the current probability density function with the reference probability density function, the tracking error function is first vector, then the performance evaluation index is constructed by gray correlation, and the general steps of performance evaluation based on this index are given. Finally, the effectiveness of the proposed system performance evaluation algorithm is verified by simulation comparison. The data processing and experimental simulation are used to achieve the purpose of evaluating the performance of the Internet of Things system.

Method for generating manufacturable, topology-optimized parts for Laminated Layer Manufacturing

The great flexibility provided by generative manufacturing offers immense potential for the structural component optimization. However, this freedom needs to be utilized by appropriate CAx tools. In this paper, we present a novel slicing method, enabling the automatic generation of topology-optimized Laminated Layer Manufacturing (LLM) parts. With this method a part of arbitrary shape can be automatically sliced and equipped with a uniform virtual grid that is suitable for manufacturing. The optimal density distribution is then mapped onto the individual slices and locally approximated through the introduction of variably shaped cavities. By using 3D modeling techniques all LLM sheets are modeled parametrically and assembled automatically. To verify the functionality of the presented method, it is applied to two practical parts and compared with a conventional topology optimization method.

Multi-lattice inner structures for high-strength and light-weight in metal selective laser melting process

Due to the development of additive manufacturing (AM), lattice structure which cannot be fabricated by the conventional manufacturing process or have shape restriction has attracted much attention. We propose a new lightweight design method using two types of lattice structures considering the manufacturability in the metal selective laser melting (SLM) and structural characteristics. Firstly, the specific procedure for the proposed design method is presented. In order to apply the two lattice structures, relative density criterion is derived by fabricating experiments using metal SLM process and analyzing geometry according to relative density. The optimal relative density distribution is calculated by performing the topology optimization with minimum relative density using a commercial software package. This proposed method is computationally and experimentally validated by a three-point bending test. Simultaneously, the same procedure is applied to uniform lattice for comparison with the proposed method. This proposed design has a 46% increase in stiffness, a relative flexural rigidity of 35% compared to the solid material, and has a deformation mode different from the uniform lattice. This design sets the standard for using two lattice structures and gives a new perspective on lightweight design with lattice structures.

Design and Optimization of Graded Cellular Structures With Triply Periodic Level Surface-Based Topological Shapes

Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.

3D topology optimization of continuous fiber-reinforced structures via natural evolution method

The method to optimize a topology of 3D continuous fiber-reinforced additively manufactured structures is discussed. The proposed method makes it possible to simultaneously search for density distribution and local reinforcement layup in 3D composite structures of transversely isotropic materials. The approach uses a dynamical systems method to find density distribution, combined with the method for rotation of reinforcement direction to align it in the direction of principal stresses with local minimum compliance. The algorithm is implemented as a built-in material model within Abaqus finite element suite. Both the optimal material density distribution and the distribution of fiber orientation vector are determined for three structural elements used as benchmarks: the bending of simply supported 2D beam under central point load, the loading of 3D cube by vertical load, and the bending of 3D cantilever beam.

Continuous graded Gyroid cellular structures fabricated by selective laser melting: Design, manufacturing and mechanical properties

Functional graded cellular materials (FGCMs) have attracted increasing attentions for their improved properties when compared to uniform cellular structures. In this work, graded Gyroid cellular structures (GCSs) with varying gradient directions were designed and manufactured via selective laser melting (SLM). As a reference, uniform structures were also manufactured. The surface morphology and mechanical response of these structures under compressive loads were investigated. Results indicate high manufacturability and repeatability of GCSs manufactured by SLM. Optimized density distribution gives these structures novel deformation and mechanical properties. GCSs with density gradient perpendicular to the loading direction exhibit deformation behaviours similar to uniform ones, while GCSs with the gradient parallel to the loading direction exhibit layer-by-layer deformation and collapse behaviour. A novel phenomenon of sub-layer collapses is found in GCSs with gradient parallel to the loading direction. Furthermore, mathematical models were developed to predict and customize the mechanical properties of graded cellular structures by optimizing the relative density of each layer. These significant findings illustrate that graded cellular structures have high application prospect in various industries, particularly given the fact that additive manufacturing has been an enabler of cellular structure fabrication.

Optimal orthotropy and density distribution of two-dimensional structures

Optimal orthotropy and density distribution of two-dimensional structures

Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation

Additive manufacturing (AM) is now capable of fabricating geometrically complex geometries such as a variable-density lattice structure. This ability to handle geometric complexity provides the designer an opportunity to rethink the design method. In this work, a novel topology optimization algorithm is proposed to design variable-density lattice infill to maximize the first eigenfrequency of the structure. To make the method efficient, the lattice infill is treated as a continuum material with equivalent elastic properties obtained from asymptotic homogenization (AH), and the topology optimization is employed to find the optimum density distribution of the lattice structure. Specifically, the AH method is employed to calculate the effective mechanical properties of a predefined lattice structure as a function of its relative densities. Once the optimal density distribution is obtained, a continuous mapping technique is used to convert the optimal density distribution into variable-density lattice structured design. Two three-dimensional (3D) examples are used to validate the proposed method, where the designs are printed by the EOS direct metal laser sintering (DMLS) process in Ti6Al4V. Experimental results obtained from dynamical testing of the printed samples and detailed simulation results are in good agreement with the homogenized model results, which demonstrates the accuracy and efficiency of the proposed method.

Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing

Lightweight cellular structure generation and topology optimization are common design methodologies in additive manufacturing. In this work, we present a novel optimization strategy for designing functionally graded cellular structures with desired mechanical properties. This approach is mainly by generating variable-density gyroid structure and then performing graded structure optimization. Firstly, the geometric properties of the original gyroid structures are analyzed, and the continuity and connectivity of the structures are optimized by adding a penalty function. Then, a homogenization method is used to obtain mechanical properties of gyroid-based cellular structures through a scaling law as a function of their relative densities. Secondly, the scaling law is added directly into the structure optimization algorithm to compute the optimal density distribution in part being optimized. Thirdly, the density mapping and interpolation approach are used to map the output of structure optimization into the parametric gyroid structure which results in an optimum lightweight lattice structure with uniformly varying densities across the design space. Lastly, the effectiveness and robustness of the optimized results are analyzed through finite element analysis and experiments.

On topology optimization and canonical duality method

Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the author, the linear knapsack problem can be solved analytically to obtain global optimal solution at each design iteration. Both uniqueness, existence, and NP-hardness are discussed. The novel CDT method for general topology optimization is refined and tested by both 2-D and 3-D benchmark problems. Numerical results show that without using filter and any other artificial technique, the CDT method can produce exactly 0-1 optimal density distribution with almost no checkerboard pattern. Its performance and novelty are compared with the popular SIMP and BESO approaches. Additionally, some mathematical and conceptual mistakes in literature are explicitly addressed. A brief review on the canonical duality theory for modeling multi-scale complex systems and for solving general nonconvex/discrete problems are given in Appendix. This paper demonstrates a simple truth: elegant designs come from correct model and theory.