Optimal Material Distribution Research Articles

Design of metamaterial-based heat manipulators using isogeometric level-set topology optimization

We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.

A novel design of multifunctional offshore floating platform structure based on topology optimization

Floating platforms are an economical option for offshore energy harvesting in deep water sea. Lightweight design and structural stability are most important concerns in the design of floating foundations under the premise of ensuring load-bearing capacity. Topology optimization has proven to be a successful method for determining the optimal material distribution with the desired stiffness, strength, and robustness of the subjected design structure. In this paper, a novel lightweight multifunctional offshore floating platform design is proposed utilizing the density-based topology optimization method for the combined utilization of wind-solar-wave energy. Firstly, based on the extreme sea conditions in the South China Sea, the minimum compliance subject to the prescribed volume percentage is formulated and an innovative platform structure is carried out by interoperating the variable density method in the ANSYS AQWA module. Secondly, the optimized floating platform structure was strength-checked based on the maximum von Mises stresses under extreme loading conditions specified in the DNV code. The total mass of the novel optimized structure is 40.82% of the primary structure. Moreover, the platform stiffness and durability have been significantly enhanced.

Improving the manufacturing of 3D printed insoles through a combined experimental and topology optimization approach

This study integrates additive manufacturing and advanced engineering to produce lightweight, mechanically suitable insoles. The research combines experimental data and computational techniques to enhance the manufacturing process. Through mechanical testing and computational homogenization, an alternative infill pattern is identified, allowing for faster printing. Topology optimization, based on Finite Element analysis, determines an optimal material distribution for the forefoot. Validation analyses confirm the structural performance of the optimized shape. Thanks to this procedure, a time reduction up to 50% can be expected. This approach allows for an efficient and sustainable alternative for the production of insoles.

Optimization of gearbox housing shape for agricultural UTV using structural–acoustic coupled analysis

In this study, gearbox radiated noise was successfully reduced through housing shape optimization. First, dynamic and structural–acoustic coupled analysis models of an agricultural UTV gearbox were developed. Then, the test equipment was configured to match that of the simulation model, and a test was conducted. The analysis and test results showed errors within 0.1 dB for vibration and 0.2 dB(A) for noise, indicating that the models were reliable. The housing design was then optimized using topology optimization based on the developed structural–acoustic coupling analysis model. The sound pressure level around the housing was used as an objective function for topology optimization. The optimal distribution of materials for the housing was also derived to reduce the radiated noise. Lastly, the housing rib was designed based on the optimization result, and an improvement in the radiated noise by approximately 2.43 dB(A) was confirmed in the operation area.

Implementation of multi-sensors for the measurement of pneumatically conveyed particles

Due to the complex flow state of pneumatically conveyed particles and the influence of the conveying conditions, existing measurement techniques have limitations in detecting the dynamic parameters of full-sections particles in large-scale pipelines. In order to further study and realize the measurement of local parameters of particles in pneumatic conveying pipelines, as well as to provide basic data for full-sections measurement, optimize material distribution and reduce energy consumption. Combined with electrostatic induction and piezoelectric effect, an invasive multi-sensors fusion measurement device was designed to measure local parameters such as particle velocity and mass flow rate in different areas of circular pipelines.

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal C 1 continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.

Fiber reinforced additive manufacturing: structurally motivated print orientation and sequential topology optimization of anisotropic material

PurposeFiber reinforced additive manufacturing (FRAM) is an emerging technology that combines additive manufacturing and composite materials. As a result, design freedom offered by the manufacturing process can be leveraged in design optimization. The purpose of the study is to propose a novel method that improves structural performance by optimizing 3D print orientation of FRAM components.Design/methodology/approachThis work proposes a two-part design optimization method that optimizes 3D global print orientation and topology of a component to improve a structural objective function. The method considers two classes of design variables: (1) print orientation design variables and (2) density-based topology design variables. Print orientation design variables determine a unique 3D print orientation to influence anisotropic material properties. Topology optimization determines an optimal distribution of material within the optimized print orientation.FindingsTwo academic examples are used to demonstrate basic behavior of the method in tension and shear. Print orientation and sequential topology optimization improve structural compliance by 90% and 58%, respectively. An industry-level example, an aerospace component, is optimized. The proposed method is used to achieve an 11% and 15% reduction of structural compliance compared to alternative FRAM designs. In addition, compliance is reduced by 43% compared to an equal-mass aluminum design.Originality/valueCurrent research surrounding FRAM focuses on the manufacturing process and neglects opportunities to leverage design freedom provided by FRAM. Previous FRAM optimization methods only optimize fiber orientation within a 2D plane and do not establish an optimized 3D print orientation, neglecting exploration of the entire orientation design space.

Simultaneous optimal tri-directional distribution of material and porosity in functionally graded plates under free vibration

This paper for the first time attempts to find the simultaneously optimal three-dimensional distribution of porosity and material phases in functionally graded materials (FGMs) model that altogether maximize the natural frequency of porous FG plates. By using the same concept of non uniform rational B-splines (NURBS) based interpolation for the material distribution, the problem of finding the optimal porosity distribution is enabled. An upper bound of porosity is pointed out, which is necessary for considering the porosity design variables. Generalized shear deformation theory (GSDT) in the framework of isogeometric analysis (IGA) for free vibration analysis of the porous FG plates is verified with previous works. The findings are: in the optimal design of material only, the uniformly distributed pores have a neutral or detrimental effect on 4-side constrained plates but slightly increase the frequency for the cantilever plate; and with that same amount of porosity, the simultaneously optimal distributions of pores, similar to those in bio-materials or natural bones in the way that are most foam-like in the center or at the furthest from the boundaries, result in lighter yet of significantly elevated vibration frequency structures.

Topology Optimization using Nonlinear Finite Element Analysis

Topology optimization is a structural-mechanical investigation that structures optimization function values in an optimization iteration. Topology optimization with nonlinear static behavior is difficult due to several design considerations. Due of significant integrate distortion, low-density finite elements provide significant numerical challenges in the prevailing element density focused topology planning taking nonlinear dynamics under factor. Iterative procedures are used in the Bi-directional Evolutionary Structural Optimization (BESO) technique for reducing waste from a structure while concurrently adding efficient material using a finite element-based topology optimization strategy. Integrating the fully-connected Deep Neural Network (DNN) with the norm-level-set techniques yields a powerful method for optimizing structural topology. Hence, BESO-DNN has been designed spatial optimization of material distribution inside a specified area is the focus of topology optimization is a mathematical approach for minimizing a certain cost function while meeting a set of predefined restrictions. Topology optimization of geometrically non-linear systems is advantageous because of the solutions' lack of intermediate-density components and their great processing efficiency of high-resolution barrier representation can be effective. As a result, topology optimization is ensuring effective and providing fresh and efficient designs, understanding that outcomes needs an integration of credible decision-making, domain knowledge, and numerical analytic skills. The outcome of finite element analysis has to understand and anticipate an object's performance under various physical conditions using mathematical models, and testing.

Optimization of Material Distribution in Electrodes of Power Generating Devices: A Mixed Approach

Electrochemical devices are becoming increasingly common, and advanced optimization techniques are utilized to enhance their performance. Topology optimization [1, 2] is one such technique, and it is gaining more attention as a means of improving the performance of electrochemical device. Moreover, as fabrication technologies advance, electrodes with more complex structures are becoming feasible. Previous studies [3-5] have attempted to optimize the composition of various electrochemical devices, such as fuel cells and redox flow batteries, to improve overall cell performance. Using topology optimization methods, those research works seek heterogenous distribution of materials within the electrode design domain to increase the cell efficiency. Although the methods and procedures reported in those studies are promising, their optimization approach does not provide globally optimized results. This is due to the fact that those studies only focus on optimization in a specific horizontal or vertical direction on the polarization surface. In other words, their outputs are dependent on the point at which the optimization is performed.Power sources in electrochemical systems have an inherent optimal operating point that corresponds to the maximum output power. This presents an opportunity for a more comprehensive topology optimization strategy for power generating devices. This study introduces a novel approach called mixed topology optimization, which aims to enhance the efficiency of power sources by making simultaneous modifications to both the electrode structure and the operating conditions. The proposed strategy is self-directed and independent of the starting point. Given the highly nonlinear nature of electrochemical devices, such an approach is advantageous in identifying the globally optimized material distribution in a topologically optimized electrode. The proposed method is tested on a triple-phase electrode, and its superiority is compared with that of conventional approaches. Acknowledgment This work was partially supported by Grant-in-Aid for JSPS Fellows number 22J20603, JSPS KAKENHI Grant number 21H04540, and Research Strengthening Project of the Faculty of Engineering, King Mongkut's University of Technology Thonburi.

An ANN-BCMO Approach for Material Distribution Optimization of Bi-Directional Functionally Graded Nanocomposite Plates with Geometrically Nonlinear Behaviors

This study commences with the application of an efficient artificial neural network (ANN)-balancing composite motion optimization (BCMO) approach for finding the optimal material distribution of bi-directional functional graded nanocomposite (FGN) thin plates considering geometrically nonlinear behaviors. To this regard, an ANN-based surrogate model of the high-fidelity isogeometric analysis (IGA) of the geometrically nonlinear Kirchhoff–Love plates based on the Von Kármán nonlinearity theory is first constructed and then employed to predict the values of objectives and constraints required in the BCMO framework. The multi-mesh design approach is utilized to form two separate nonuniform rational B-spline meshes for optimal material distribution and analysis meshes. The unknown control point values of the design mesh are herein selected as the continuous design variables. This allows a possibility to fully explore the complex distribution of optimal material profiles without requiring a significant number of variables. Selected numerical examples with different plate geometries and loading conditions are presented to illustrate the merit features of the proposed approach. Obtained results reveal not only its high accuracy and significant efficiency compared with the conventional approach coupling the BCMO with IGA direct analysis but also the stable ability of the BCMO in finding global optimum material distributions in comparison with two commonly used metaheuristics algorithms, i.e., particle swarm optimization and genetic algorithm.

Optimization Model and Strategy for Dynamic Material Distribution Scheduling Based on Digital Twin: A Step towards Sustainable Manufacturing

In the quest for sustainable production, manufacturers are increasingly adopting mixed-flow production modes to meet diverse product demands, enabling small-batch production and ensuring swift delivery. A key aspect in this shift is optimizing material distribution scheduling to maintain smooth operations. However, traditional methods frequently encounter challenges due to outdated information tools, irrational task allocation, and suboptimal route planning. Such limitations often result in distribution disarray, unnecessary resource wastage, and general inefficiency, thereby hindering the economic and environmental sustainability of the manufacturing sector. Addressing these challenges, this study introduces a novel dynamic material distribution scheduling optimization model and strategy, leveraging digital twin (DT) technology. This proposed strategy aims to bolster cost-effectiveness while simultaneously supporting environmental sustainability. Our methodology includes developing a route optimization model that minimizes distribution costs, maximizes workstation satisfaction, and reduces carbon emissions. Additionally, we present a cloud–edge computing-based decision framework and explain the DT-based material distribution system’s components and operation. Furthermore, we designed a DT-based dynamic scheduling optimization mechanism, incorporating an improved ant colony optimization algorithm. Numerical experiments based on real data from a partner company revealed that the proposed material distribution scheduling model, strategy, and algorithm can reduce the manufacturer’s distribution operation costs, improve resource utilization, and reduce carbon emissions, thereby enhancing the manufacturer’s economic and environmental sustainability. This research offers innovative insights and perspectives that are crucial for advancing sustainable logistics management and intelligent algorithm design in analogous manufacturing scenarios.

Performance analysis and material distribution optimization for sound barriers using a semianalytical meshless method

AbstractWith the increase in car ownership, traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards. Noise reduction by sound barriers is a common protective measure used in this country and abroad. The acoustic performance of a sound barrier is highly dependent on its shape and material. In this paper, a semianalytical meshless Burton–Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers, and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method. The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition. The objective of optimization is to minimize the sound pressure in a given reference plane. The volume of the sound‐absorbing material is used as a constraint. The density of the nodes covered with the sound‐absorbing material is used as the design variable. The method of moving asymptotes was used to update the design variables. This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes. In addition, the approach also does not require the singular integral calculation in the boundary element method. The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.

A Versatile Topology-Optimized Compliant Actuator for Soft Robotic Gripper and Walking Robot.

The remarkable interaction capabilities of soft robots within various environments have captured substantial attention from researchers. In recent years, bionics has provided a rich inspiration for the design of soft robots. Nevertheless, predicting the locomotion of soft actuators and determining material layouts solely based on intuition or experience remain a formidable challenge. Previous actuators predominantly targeted separate applications, leading to elevated costs and diminished interchangeability. The objective of this article is to extract the common requirements of diverse application domains and develop a versatile compliant actuator. A mathematical model of the compliant mechanism is proposed under the framework of topology optimization, resulting in an optimal distribution of both structure and material. Through comparison with empirical and semioptimal designs, the results show that the proposed versatile actuator has the advantages of both stiffness and flexibility. We propose an associative design strategy for soft grippers and walking robots. The soft gripper can perfectly complete adaptive grasping of objects with varying sizes, shapes, and masses. The successful in-water gripping experiment underscores the robust cross-medium operational capabilities of the soft gripper. Notably, our experimental results show that the walking robot can move quickly for 5 cycles in 8.25 s and can guarantee the control accuracy of continuous motion. Moreover, the robot swiftly switches walking directions within a mere 0.45 s. The optimization and design strategy presented in this article can furnish novel insights for shaping the next generation of soft robots.

Accelerating tri-directional material distribution optimization in functionally graded plates with an adaptive design control point variable selection

In this paper, the problem of optimizing tri-directional material distribution in functionally graded (FG) plates under static loads to minimize the compliance is studied. Generalized shear deformation theory (GSDT) in the framework of isogeometric analysis is employed as the analyzer for efficiency and accuracy, and a non-uniform rational B-spline function is used for depicting the material distribution. As the number of control points in fine 3D design meshes, i.e., the number of optimization variables, can be too large for an algorithm to find a practically feasible design, we propose an adaptive variable selection mechanism. It gradually selects control points at important regions as variables by considering neighbor material variance, hence accelerates the optimization process. Various plate geometries are considered to validate the present approach. The findings confirm that the design mesh should be fine, and that the proposed variable selection strategy enables the optimization algorithm to find much more refined designs even in cases of large dimensions while also reducing computation.

Multi-patch isogeometric material optimization of bi-directional functionally graded plates

This study investigates an effective design methodology for the optimal material distribution of bi-directional functionally graded plates (2D-FGPs) with complex shape. In mechanical analysis, a multi-patch isogeometric method is used to analyze the statics of 2D-FGP, which is based on the third-order shear deformation theory and Nitsche’s technology. This method can effectively avoid the use of duplicate nodes in the parameterization of IGA for complex shapes to obtain C1-continuity of 2D-FGPs. In the optimal design problem, we have constructed a rectangular material design mesh (RMDM) based on the shape of 2D-FGPs, which can map the material distribution on the surface of plate to achieve the implementation of the optimization process. This two-dimensional B-spline control points of RMDM are set as the design variable with mass reduction and the first-order natural frequency maximization as optimization objectives, and limited arbitrary deflection as constraint conditions. In addition, an improved multi-objective particle swarm optimization algorithm (IMOPSO) is used to obtain a series of Pareto optimization solutions that meet the needs of the designer. The validity and applicability of this innovative combination of multi-patch isogeometric analysis and IMOPSO are demonstrated through several numerical examples in integrated design. This approach further accomplishes the numerical unified CAD/CAE optimization design of 2D-FGPs across multiple non-smooth boundaries.

Structural Optimization of the Brake Pedal using Artificial Intelligence

In this study, weight reduction was performed on the brake pedal, which is one of the most important parts of the braking system, by using topology and shape optimi-zation, one of the structural optimization methods, respectively. The aim of the study is to develop an optimal design that reduces vehicle weight by finding the optimal material distribution for the brake pedal. The weight reduction process was carried out in two steps. In the first step, static analyses were performed on the starting brake pedal model. Later, topology optimization was performed for weight reduction pur-poses. After the topology optimization, new brake pedal design was created and weight reduction was performed. In the second step, shape optimization was per-formed using a genetic algorithm to obtain the optimal dimensions of the brake pedal. According to the optimization results, the weight of the design was reduced from 437 grams (g) to 326 grams (g) by topology optimization in the first step. So the new de-sign is 25.4% lighter compared to the first design. Later, as a result of shape optimiza-tion performed using a genetic algorithm, the weight was reduced from 326 g to 298 g and the optimal dimensions of the brake pedal were determined. Thus, with shape op-timization, a lighter brake pedal design of about 8.5% was achieved compared to to-pology optimization. As a result, the weight has been reduced from 437 g to 298 g, and the weight of the ideal brake pedal model is 31.8% lighter compared to the main model.

Controllable deformation design for 4D-printed active composite structure: Optimization, simulation, and experimental verification

Through integrating active composites and 4D printing techniques, active composites can achieve the pre-designed complex deformations. However, the tremendous design space of multiple materials brings the challenges of finding the optimum material distributions accurately, and the consistencies between simulated optimum results and actual experimental structures. Therefore, the controllable deformation design framework is proposed to guide the inverse design of 4D-printed active composite structure. The material properties of polylactic acid (PLA) and thermoplastic polyurethane (TPU) are tested and integrated into forward deformation analysis to improve the prediction accuracy of finite element analysis (FEA). An optimization integration framework with genetic algorithm is developed to optimize the material distribution and external displacement simultaneously to achieve the target deformation. Several voxelized beams and flower structures are used as engineering cases. The simulated and experimental deformation shapes and recovery shapes for the optimum structures are consistent with the target deformations. The mean squared errors (MSEs) of experimental shape and simulation shape are 0.62 mm and 0.27 mm for flower structures. These results show that the proposed methodology can obtain target deformation in simulation and experimental tests simultaneously, which can be applied into the flexible deformation design of complex active composite structures in the future.

Learning hyperparameter predictors for similarity-based multidisciplinary topology optimization

Topology optimization (TO) plays a significant role in industry by providing engineers with optimal material distributions based exclusively on the information about the design space and loading conditions. Such approaches are especially important for current multidisciplinary design tasks in industry, where the conflicting criteria often lead to very unintuitive solutions. Despite the progress in integrating manufacturing constraints into TO, one of the main factors restricting the use of TO in practice is the users’ limited control of the final material distribution. To address this problem, recently, a universal methodology for enforcing similarity to reference structures in various TO methods by applying scaling of elemental energies was proposed. The method, however, requires an expensive hyperparameter sampling, which involves running multiple TO processes to find the design of a given similarity to a reference structure. In this article, we propose a novel end-to-end approach for similarity-based TO, which integrates a machine learning model to predict the hyperparameters of the method, and provide the engineer, at minimal computational cost, with a design satisfying multidisciplinary criteria expressed by the similarity to a reference. The training set for the model is generated based on an academic linear elastic problem, but the model generalizes well to both nonlinear dynamic crash and industrial-scale TO problems. We show the latter by applying the proposed methodology to a real-world multidisciplinary TO problem of a car hood frame, which demonstrates the usefulness of the approach in industrial settings.

Employing additive manufacturing to create reusable TPU formworks for casting topologically optimized facade panels

Concrete is a building material with excellent structural qualities that can be molded into any shape. However, it is also responsible for approximately 8% of the world's total greenhouse gas emissions. There is a need to reduce material consumption during the design and construction of concrete structures. This research proposes a new manufacturing workflow for the design and fabrication of precast façade panels. Structural topology optimization (TO) is used to design perforated façade panels with optimized material distribution according to the panel's connection to a sub-structure. Structural simulations are conducted to validate the stiffness and strength of the TO panels. Finally, flexible Thermoplastic Polyurethane (TPU) molds are additively manufactured and repeatedly cast. The study results show that TO decreases the panels' volumes within a predefined WWR by anywhere from 23% to 30% of the total volume, while maintaining satisfactory structural performance. Additionally, the study demonstrates the potential of additively manufactured TPU molds for the repeatable casting of concrete while accommodating undercuts in the complex cast geometries. This study is novel as TO has not previously been used for designing façade panels. Furthermore, the use of 3D printed flexible molds made of TPU for repeatable casting of geometries is still in its early stages, with only one publication reporting the investigations at the time of writing this article. This workflow is innovative as a whole as it addresses material saving in the design phase through TO, as well as the creation of reusable 3D printed formworks in the fabrication phase.