Gray Elements Research Articles

An efficient volume-preserving binary filter for additive manufacturing in topology optimization

Topology optimization faces challenges concerning grey transition regions, manufacturability and computational efficiency. This article introduces an approach called the volume-preserving binary (VPB) filter. This novel sensitivity/density filter, based on a determinant-based matrix approach, efficiently detects grey elements and produces completely binary designs. The VPB filter addresses volume preservation by accurately expressing the volume-preserving condition, i.e. the volume before filtering equals the volume of solid materials after filtering. Comparison with other filtering methods, including the volume-preserving Heaviside filter and the Heaviside projection, illustrates the superior clarity and speed of the VPB filter. It reduces the number of iterations required for topology optimization, from hundreds or thousands to only tens of iterations, making it a promising solution for practical applications where manufacturability and computational efficiency are principal. Examples on compliance optimization, compliant mechanisms and heat conduction demonstrate the VPB filter's effectiveness in providing satisfactory solutions while perfectly preserving the length scale.

The nature gaze: Eye‐tracking experiment reveals well‐being benefits derived from directing visual attention towards elements of nature

Abstract The urban lifestyle has a profound effect on mental health, contributing significantly to the challenges faced by people who reside in urban areas. Growing empirical evidence underscores the potential of nature to alleviate these mental health burdens. However, we still lack understanding of which specific natural elements provide these benefits. Using eye‐tracking technology, we experimentally explored the relationships between intentional visual attention to natural (green) and human‐made (grey) elements in urban areas and their association with well‐being measures. Participants took a 45‐min outdoor walk that simulates a walk to and from work, in which we examined pre‐ and post‐measures of cognition, affect, anxiety and perceived restorativeness. Participants were prompted to direct their attention to green, grey or a mixture of both elements. By analysing participants' eye movements and patterns, we determined adherence to experimental conditions and related visual attention to natural elements. The experimental groups instructed to direct their visual attention to green, grey or a mix of both infrastructures exhibited differences in negative and positive affect, anxiety and perceived restorativeness, but not in cognition after a walk in an urban environment. The percentage of time spent viewing natural elements showed that people who focused more on green features reported a decrease in anxiety and higher perceived restorativeness. In contrast, those who spent more time viewing grey elements reported increased anxiety and lowered perceived restorativeness. The percentage of time viewing natural elements was not linked to affect or cognition. Viewing trees showed the strongest association with well‐being measures compared to other natural elements. Together, our results indicate that a simple behaviour change (directing visual attention to elements of nature instead of grey elements) can produce mental health benefits in the form of reducing anxiety and perceived restoration for people in urban areas. Thus, efforts to integrate nature, especially trees, in urban areas and promote city dwellers to visually interact with it during their daily routine can improve mental issues associated with urban lifestyle. Read the free Plain Language Summary for this article on the Journal blog.

Capturing residents’ perceptions of green spaces in densifying urban landscapes - The potentials of mental mapping

Understanding residents’ perceptions of green-blue infrastructure (GBI) is critical to ensure continued access to its associated benefits in growing and densifying urban landscapes. Physical availability and accessibility of green spaces alone do not directly translate to actual appreciation and use. Residents’ sense of place can determine if benefits from GBI are realized and how landscape changes may be perceived. In this study, set in sub-urban Stockholm, Sweden, we applied a mixed-methods approach combining mental mapping with follow-up interviews to investigate how such methodology can improve our understanding of residents’ perception of the recreational use of GBI. For the mental mapping exercise, participants drew, freehand, a map of appreciated neighborhood places for recreational purposes. Our results clearly show that mental mapping provides relevant information on individual and collective perceptions of recreational GBI, linkages between green-blue and gray infrastructure elements, and recreational hot-spots of importance to the local inhabitants. The unguided approach to welding local knowledge with spatial expressions makes the method well suited to contribute to a better understanding of plural senses of place with regards to the recreational use of GBI in rapidly urbanizing landscapes and an enhanced capacity to recognise locally appreciated recreational spaces in planning and practical management.

Design of the multiphase material structures with mass, stiffness, stress, and dynamic criteria via a modified ordered SIMP topology optimization

This paper, a multi-material topology optimization method (MMTO) is presented for two-dimensional structures using modified ordered solid isotropic material with penalization (SIMP) under multiple constraints such as mass, stiffness, frequency, and stress. The element density is obtained by a density filtering and the Heaviside approximation, which are combined to avoid gray elements and numerical issues of stress. Effective improvement of multiphase material topology optimization was performed including the criteria for stiffness, stress, and free vibration. P-norm stress aggregation is employed to calculate the maximum von Mises stress and sensitivity of von Mises stress is formulated by the adjoint method. The natural frequency and stress constraints are solved simultaneously to enhance the stability and reduce the stress concentration of the optimized structures, which are not much covered in the literature. The multi-mode phenomenon in the eigenfrequency problem is treated by the simply proposed technique. Results indicate that the multi-material designs with multi-constraints can be illustrated and optimized effectively. The optimized topologies, for stress minimization, indicate that the maximum stress can be significantly reduced compared with compliance minimization. The maximum von Mises stress of the topological results considering the maximum stiffness with natural frequency and mass constraints is higher than that maximum stiffness with only mass constraints, which indicates that the optimized structure created considering the eigenvalues is safer. The proposed approach can obtain a reasonable result that effectively controls the stress level and reduces the stress concentration at the high stress regions of multi-phase material structures with multi-constraints. Benchmark numerical examples are presented to confirm the effectiveness of the presented method.

Fail-safe topology optimization for multiscale structures

This paper presents a novel fail-safe topology optimization method for multiscale structures. The partial damage of both macroscopic and microscopic scales is considered for structural design. To ensure precision, the effective elasticity tensor obtained by the homogenization method is fitted as a high-order polynomial function. Meanwhile, the simplified models of partially damaged truss-like microstructure are employed to reduce the computational cost and the difficulty of fitting. Moreover, Heaviside projection is applied to speed up the convergence and yield a relatively clear configuration. Three numerical examples are tested to demonstrate that the optimized multiscale structures successfully obtain comprehensive performances than optimized solid structures when appropriate microstructure configurations are chosen. Besides, multiscale structures are more self-supporting than solid structures and thus more suitable for additive manufacturing due to the large number of gray elements diffused.

Topology optimization of phononic crystal with prescribed band gaps

Phononic crystal, which can block the propagation of elastic waves in a certain frequency range, is widely used in acoustic devices, vibration reduction, and other fields. However, most of the previous studies on the design of phononic crystals only consider the problem of the maximum band gap of adjacent two orders and cannot give the design for a prescribed band gap, which is more applicability in practical engineering problems. To solve this issue, this study proposes a novel topology optimization method to realize the prescribed band gaps design of phononic crystal. Compared to the vibration structural design with prescribed band gaps, the difficulty of phononic crystals’ prescribed band gaps design lies in the correlation between stiffness matrix and wave vector, which is a typical eigenvalue problem with multi-class boundary conditions. Directly utilizing the frequency band constraints proposed by the authors in the previous papers may lead to numerical convergence difficulties. Thus an ipsilateral frequency constraint based on a modified Heaviside function is further proposed. Since the developed function is continuous and differentiable, the sensitivity of the constraint function can be derived for using the gradient-based optimization solver. Furthermore, in order to eliminate the checkerboard phenomena, grey elements and give the minimum size control in topology optimization, the “Robust formulation” is applied. Several numerical examples, including single-band gap and double-band gaps problems, are solved by the proposed method. The results validate the effectiveness of the developed method.

Reliability-based topology optimization for fundamental frequency maximization with frequency band constraints

Resonance can be avoided by preventing the structural natural frequencies from falling within the operating frequency range. However, structural natural frequencies are influenced by uncertain parameters, such as material properties and geometric sizes. Therefore, it is essential to consider these uncertainties during the conceptual design phase. To address this problem, a novel reliability-based eigenvalue topology optimization model under frequency-band constraints is established, in which the uncertainties of the material properties and structural size are considered. Owing to the high computational costs of dealing with frequency-band reliability constraints, a frequency-band constraint shifting method (FBCSM) is proposed to ease the heavy computational burden without sacrificing accuracy. In addition, the sensitivities of simple and multiple eigenfrequencies with respect to the design and random variables are derived. The “bound formulation” and “robust formulation” are used to reduce the gray elements and checkerboard phenomenon. Four examples are used to determine the effectiveness of the proposed reliability-based eigenvalue topology model and FBCSM. The results confirmed their superiority in terms of validity and efficiency.

Topology optimization of turbine disk considering maximum stress prediction and constraints

For the stress-constrained topology optimization of a turbine disk under centrifugal loads, the jagged boundaries of the mesh and the gray densities on the solid/void interfaces could make the calculated stress field inconsistent with the actual value. It may result in overestimating the maximum stress and thus affect the effectiveness of stress constraints. This paper proposes a new method for predicting the maximum stress to overcome the difficulty. In the process, a predicted density is newly defined to obtain stable boundaries with thin layers of gray elements, a transition factor is innovatively proposed to evaluate the effects of intermediate-density elements, two different stiffness penalty schemes are flexibly used to calculate the elastic modulus of elements, and a linear stress penalty is further adopted to relax the stress field of the structure. The proposed approach for predicting the maximum stress value is verified by the analysis of a structure with smooth boundaries and the topology optimization of a turbine disk. An updating scheme of the stress constraint in the topology optimization is also developed using the predicted maximum stress. Some key ingredients affecting the optimization results are discussed in detail. The results prove the effectiveness and efficacy of the proposed maximum stress prediction and developed stress constraint methods.

Material Design with Topology Optimization Based on the Neural Network

This paper describes a neural network (NN)-based topology optimization approach for designing microstructures. The design variables are the NN weights and biases used to describe the density field, which is independent of element meshes. The number of design variables and gray elements is reduced substantially, and no filtering is necessary. Three numerical examples are provided to demonstrate the efficacy of the proposed method, namely, maximum shear modulus, maximum bulk modulus, and negative Poisson’s ratio.

From urban greenspace to health behaviors: An ecosystem services-mediated perspective

Urban greenspace can provide important health benefits for urban residents, but knowledge about the potential mechanisms remains unclear, and it is challenging in promoting health behaviors through design and management practices. This study proposed a hypothetical model that assumed ecosystem services as mediating factors between urban greenspace and health behaviors. An urban park in Beijing was selected as a case area to test the hypothesis and identify the ecosystem services-mediated pathways. Results based on spatial explicit mapping and multivariate statistical analysis confirmed the hypothesis and showed that urban greenspaces contribute to health behaviors in varying degrees through the delivery of health behaviors-related ecosystem services. The promotion effect was mainly mediated by cultural services, which is much more obvious than regulating services. We identified the importance of different properties of inner urban greenspace in promoting health behaviors through ecosystem services-mediated pathways. Green elements, especially tree canopy shaded ground, were found to contribute the most to health behaviors in the pathways, and slightly higher than facilities and grey elements. To promote health benefits, the design and arrangement of facilities and grey elements in urban greenspace is suggested to be cooperated with green elements for enhancing multiple ecosystem services. The findings will enhance the understanding of potential theoretical pathways from urban greenspace to health benefits, and support health promotion-oriented design and management practices.

Hybrid Grey Wolf and Finite Element Method (GWO-FEM) Algorithm for Enhancing High Voltage Insulator String Performance in Wet Pollution Conditions

The presence of wet pollution on the upper surface of a string insulator increases the electric field on the insulator surface, especially at the triple junction (pin-cement, cement-porcelain) as well as at the surrounding air of the insulator. The rise of the electric field leads to the ionization of the air surrounding the insulator. This phenomenon, called corona discharge, is accompanied by several consequences that are harmful to the electricity transmission network, such as electromagnetic interferences, energy losses, visible light, audible noise, and the destruction of materials by erosion. If favorable conditions are gathered, it may even cause the flashover of the insulator. Designing an optimal insulator shape that reduces this electric field value at the triple junction will be an important achievement in enhancing the performance of electrical grids. The objective of this paper is to evolve a hybrid algorithm based on the GWO-FEM for optimizing the shape and the electrical performance of a string insulator. To achieve this purpose, this work is structured in four parts. First, modeling of the insulator string geometry is conducted in Comsol-multiphysics, then FEM computation of the electric field on the polluted surface of the string insulator is completed, and the maximum electric field value at the triple junction is saved as the fitness function that will be sent to the GWO algorithm to be optimized (minimized). The third part of the work is devoted to the coding of the constrained (electrical and geometrical constraints) GWO algorithm in a Matlab interface, and finally, coupling the GWO code with the FEM code. This study is achieved in wet polluted conditions. The results are given in both 2D and 3D representations. From the obtained results we can confirm that the developed GWO-FEM hybrid algorithm for optimizing insulator strings is a very promising tool for designing and enhancing the shape and the electrical performance of insulators.

Infrared Small Target Detection by Modified Density Peaks Searching and Local Gray Difference

Infrared small target detection is a challenging task with important applications in the field of remote sensing. The idea of density peaks searching for infrared small target detection has been proved to be effective. However, if high-brightness clutter is close to the target, the distance from the target pixel to the surrounding density peak will be very small, which easily leads to missing detection. In this paper, a new detection method, named modified density peaks searching and local gray difference (MDPS-LGD), is proposed. First, a local heterogeneity indicator is used as the density to suppress high-brightness clutter, and an iterative search is adopted to improve the efficiency in the process of searching for density peaks. Following this, a local feature descriptor named the local gray difference indicator (LGD) is proposed according to the local features of the target. In order to highlight the target, we extract the core area of the density peak by a random walker (RW) algorithm, and take the maximum response of the minimum gray difference element in the core region as the LGD of the density peak. Finally, targets are extracted using an adaptive threshold. Extensive experimental evaluation results in various real datasets demonstrate that our method outperforms state-of-the-art algorithms in both background suppression and target detection.

Topology optimization of bi‐material curved shell structures for minimizing time‐domain sound radiation

AbstractSo far, the research on topology optimization against noise has mainly addressed frequency‐domain problems, while time‐domain analysis is also widely used in practical engineering. Nonetheless, the topology optimization work on the latter was rarely reported due to its complexity. This article presents a new topology optimization scheme of bi‐material curved shell structure to reduce the time‐domain noise generated by transient vibration. A finite element formulation for an eight‐node curved shell element is presented. The Newmark integral method is employed to calculate transient responses, and the obtained results are input into the time‐domain boundary element method to predict transient sound pressure. In the optimization model, the volumetric densities of material in a bi‐material interpolation model constructed by the solid isotropic material with penalization model are chosen as the design variables; the time integral of the squared sound pressure on structural surfaces or prescribed reference points in acoustic medium over a specified time interval of interest is taken as the objective function; and the constraint on material volume is considered. A volume‐preserving Heaviside penalization is introduced to suppress gray elements. Furthermore, the calculation of time‐domain sound radiation sensitivity is transformed into the following two processes: (a) the derivation of transient response based on the Newmark integral method; (b) the derivation of transient sound pressure based on the discrete time‐domain boundary integral equation. Numerical examples demonstrate the validity of the approach proposed in this article. The influences of volume‐preserving Heaviside penalization, volume constraint, loading position and form, and selection of objective function on the optimal design are discussed.

Green, hybrid, or grey disaster risk reduction measures: What shapes public preferences for nature-based solutions?

Nature-based solutions (NbS) contrast with grey infrastructure measures to reduce risk from natural hazards. Using natural and sustainable measures (green) or combining green with grey elements (hybrid) can provide important co-benefits beyond risk reduction. Thanks to their co-benefits and flexibility across a range of possible climate change futures, NbS are sometimes referred to as 'win-win' or 'no-regret' measures. The success of NbS and associated projects often relies on the public for co-creation, co-implementation, and long-term sustainable use, monitoring, and management. However, the relative importance of NbS benefits is defined by the perceptions and underlying values of stakeholders with potentially divergent interests.It is unclear what measures at-risk individuals may prefer on the green-hybrid-grey spectrum and what shapes their preferences, including perceived benefits and potential regret. Identifying public (mis)perceptions, expectations, objectives, and what underlies these can inform communication and project framing, engagement, and ultimately increase public acceptance and continued uptake of NbS. We use citizen surveys at three distinct European sites where NbS are being planned and in-depth focus groups as a follow-up in the site at risk of landslides (Catterline, Scotland). Preferences and their drivers for measures on the green-hybrid-grey spectrum are assessed, focusing on public perceptions of NbS effectiveness, risk, and nature.We find that although wildlife habitat and aesthetics as co-benefits are important, reducing risk is of primary concern. Uncertainty in the strength and effectiveness of NbS, as one of 13 qualitative factors we identify, drives public preferences towards hybrid measures - seen as balancing green and grey trade-offs. Misperceptions and a demand for NbS information should be addressed with experiential learning, combined with transparent two-way communication of expectations. We urge caution and further research regarding emphasizing co-benefits and the 'natural' framing of NbS when risk reduction is the primary public objective.

Topology optimization of multimaterial distribution based on isogeometric boundary element and piecewise constant level set method

Based on isogeometric boundary element method (IGA BEM) and piecewise constant level set (PCLS) method, a new topology optimization approach is proposed to design the distribution of sound absorbing materials (SAMs) on structural surfaces. First, an efficient IGA BEM is developed with the combination of multipatch discretization and parallel CPU design. A complex submarine model comprising multiple non-uniform rational B-spline surfaces is built for engineering optimization design. Second, the PCLS method is applied to represent the multiple SAM domains without gray elements, and the sensitivities of the objective function with respect to PCLS functions are obtained using the adjoint variable method. Finally, the optimization algorithm based on PCLS method is improved by a novel penalty coefficient formulation and ordered volume constraints. The improved optimization algorithm can realize the control of multimaterial volume fractions and make the objective function steadily converge for different volume structures without the need to change any parameters. The accuracy, efficiency, and applicability of the proposed approach in engineering are demonstrated by several numerical examples.

A simple way to achieve black-and-white designs in topology optimization

In order to obtain crisp black-and-white designs, it is vital to use filtering techniques in density-based topology optimization. However, the applying of filters result in a large number of gray transition zones between the solid and void phases in the final designs. To solve this problem, a dynamic parameter tuning method is proposed in this paper. With the approach, the filter radius can be dynamically adjusted during the optimization process, thereby suppressing the gray elements in the final designs. The proposed method is tested by the classic MBB beam problems. The experimental results show that the proposed method can effectively inhibit the appearance of gray transition areas in the optimization results.

An Improved Topology Optimization Method for Suppressing Gray Elements

An Improved Topology Optimization Method for Suppressing Gray Elements

Topology optimization of vibrating structures with frequency band constraints

Engineering structures usually operate in some specific frequency bands. An effective way to avoid resonance is to shift the structure’s natural frequencies out of these frequency bands. However, in the optimization procedure, which frequency orders will fall into these bands are not known a priori. This makes it difficult to use the existing frequency constraint formulations, which require prescribed orders. For solving this issue, a novel formulation of the frequency band constraint based on a modified Heaviside function is proposed in this paper. The new formulation is continuous and differentiable; thus, the sensitivity of the constraint function can be derived and used in a gradient-based optimization method. Topology optimization for maximizing the structural fundamental frequency while circumventing the natural frequencies located in the working frequency bands is studied. For eliminating the frequently happened numerical problems in the natural frequency topology optimization process, including mode switching, checkerboard phenomena, and gray elements, the “bound formulation” and “robust formulation” are applied. Three numerical examples, including 2D and 3D problems, are solved by the proposed method. Frequency band gaps of the optimized results are obtained by considering the frequency band constraints, which validates the effectiveness of the developed method.

البنیة التحتیة الخضراء وتأثیرها على العمران Green Infrastructure and Its Impact on Urbanism

مع التوسع العمرانی فی مدن العالم وزیادة الاقبال السکانی على المناطق الحضریة حیث زیادة الکثافة السکانیة والبنائیة، فقد أصبحت المدن الحضریة تستأثر بنسبة کبیرة من الطلب على الطاقة بهدف الاستخدامات المختلفة، کما أصبحت نسبة الانبعاثات والاکاسید الضارة الصادرة کبیرة بشکل یؤثر على تغیر المناخ ومن ثم صحة الانسان. خاصة مع استبدال الغطاء النباتی بالمبانی والاسطح الرمادیة وهو ما یؤثر بشکل کبیر على المناطق الحضریة وادائها البیئی، وکذا امتداداتها العمرانیة حیث التوسع العمرانی على الأرض الزراعیة ذات القیمة العالیة.لذا فقد اتجه البحث لدراسة احدى مبادی واعتبارات العمران الأخضر وهی البنیة التحتیة الخضراء والتی تمثل نظام لدعم الحیاة فی المدینة بما تشمله من شبکة مکونات بیئیة طبیعیة ومساحات خضراء تعمل على تحقیق الاستدامة العمرانیة وتحسین الأداء البیئی للعمران، حیث خفض الانبعاثات الضارة والحد من الاضطرابات والاضرار الناجمة عن تغیر المناخ والتقلیل من تأثیر الجزیرة الحراریة.حیث یهدف البحث للتوصل لمدى مساهمة البنیة التحتیة الخضراء فی تحسین أداء العمران وظیفیا وبیئیا واجتماعیا واقتصادیا، بالإضافة لتحقیق التکامل بین البنیة التحتیة الخضراء والبیئة المبنیة لتحقیق مبادئ الاستدامة وتوفیر نظام مترابط من المساحات الخضراء. حیث التوصل لاستراتیجیة لتخطیط البنیة التحتیة الخضراء بالمدن المصریة بما یعزز وظائفها ویحقق الاتزان البیئی ویوفر مبادئ الاستدامة لمستخدمیه.یتناول البحث دراسة البنیة التحتیة الخضراء أنواعها وانماطها المختلفة، بالإضافة لتناول وظائفها وفوائدها داخل العمران ودورها فی تحقیق الاحتیاجات والاعتبارات البیئیة والعمرانیة والاجتماعیة والایکولوجیة المختلفة، بالإضافة لدراسة تحلیلیة للبنیة التحتیة الخضراء ببعض المناطق العمرانیة بمدینة المنصورة خلال فترات زمنیة مختلفة وتحلیل مدى تأثیر تواجدها وانحصارها على شکل العمران ووظائفه وکذا سلوکه واداءه البیئی. للتوصل لعمران ایکولوجی قادر على التوائم مع التغیرات المختلفة. With the expansion in urban areas and the increase in population and building density, cities have become a large consumer of energy resources. Consequently, climate and human health are affected by the dramatic increase in harmful emissions. These emissions impact has become evident especially with the replacement of vegetation cover by buildings and gray roofs, which greatly affects urban areas and their environmental performance, as the urban expansion negatively influences the highly valuable agricultural lands.This research aims to find how the green infrastructure contributes to improving the urban performance: functionally, environmentally, socially, and economically. In addition to find how it integrates with the built environment to achieve the principles of sustainability and the provision of an interconnected green spaces system. Hence, a strategy is deduced for planning green infrastructure in Egyptian cities to enhance their functions, achieve environmental balance, and provide the principles of sustainability. In this research a study of the various types of green infrastructure is done. Also, the role of green infrastructure in achieving environmental, urban, and social considerations is studied. An analytical study of green infrastructure in some urban areas in Mansoura for different periods is analyzed. It is concluded that the integration between the green and gray infrastructure elements in urban areas and the connectivity of the green infrastructure network along the movement paths improves the performance of the green component of urban areas socially and environmentally, and strengthening the green economy, which is clear in the study samples in El Mansoura City.

Topology optimization of 2D in-plane single mass MEMS gyroscopes

In this paper, we apply the topology optimization method to the design of MEMS gyroscopes, with the aim of supporting traditional trial and error design procedures. Using deterministic, gradient-based mathematical programming, the approach is here applied to the design of 2D in-plane single mass MEMS gyroscopes. We first focus on a benchmark academic case, for which we present and compare three different formulations of the optimization problem, considering typical industrial requirements. These include the maximization of the response of the sensor’s structure to the external angular rate, target resonant frequencies and minimum or constrained material usage. Also, a minimum length scale is imposed to the geometric features in order to ensure manufacturability, and an explicit penalization of grey elements is proposed to improve convergence to black and white layouts. Once the suitability of the method has been assessed, the formulation associated with the lowest computational cost, i.e. the one considering static estimations of the resonant frequencies, is applied to the design of a real-world MEMS gyroscope, targeting different resonant frequencies.