Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas...Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.展开更多
Recently,HUGY has become quite popular in the Chinese market.The character can been seen everywhere,from its emojis,memes,cartoon stories,and art toys,to T-shirts,candies,garments.HUGY is a cartoon of a cute puppy,who...Recently,HUGY has become quite popular in the Chinese market.The character can been seen everywhere,from its emojis,memes,cartoon stories,and art toys,to T-shirts,candies,garments.HUGY is a cartoon of a cute puppy,who is always smiling widely and reaching out his arms,ready to hug you.We invited the character’s creator,Lina Ju for an interview.Lina Ju comes from South Korea but has been working in China for 10 years.She is the chief designer of GENMEC,a trendy brand belonging to Sums Model,a company based in the south of China.展开更多
The purpose of this article is to discuss the proper method for Chinese digital animation character design on the foundation of certain cultural elements. The method used in this study is known as comparative analysis...The purpose of this article is to discuss the proper method for Chinese digital animation character design on the foundation of certain cultural elements. The method used in this study is known as comparative analysis of Disney and Japanese animation styles in action, appearance, facial expression and voice design. These dynamic factors are the best carrier of the animation spirit and native culture, so it is important to take the dynamic factors into account when producing the digital animation, and it will be an excellent starting point to innovate Chinese digital animation.展开更多
Optimizing Flow Path Design(FPD)is a popular research area in transportation system design,but its application to Overhead Transportation Systems(OTSs)has been limited.This study focuses on optimizing a double-spine f...Optimizing Flow Path Design(FPD)is a popular research area in transportation system design,but its application to Overhead Transportation Systems(OTSs)has been limited.This study focuses on optimizing a double-spine flow path design for OTSs with 10 stations by minimizing the total travel distance for both loaded and empty flows.We employ transportation methods,specifically the North-West Corner and Stepping-Stone methods,to determine empty vehicle travel flows.Additionally,the Tabu Search(TS)algorithm is applied to branch the 10 stations into two main layout branches.The results obtained from our proposed method demonstrate a reduction in the objective function value compared to the initial feasible solution.Furthermore,we explore howchanges in the parameters of the TS algorithm affect the optimal result.We validate the feasibility of our approach by comparing it with relevant literature and conducting additional tests on layouts with 20 and 30 stations.展开更多
Chinese mythology with its profound cultural asserts and the unconstrained imagination is an indispensable factor in animation creation.The rich resources of myth in ancient China provided a broad space for the creati...Chinese mythology with its profound cultural asserts and the unconstrained imagination is an indispensable factor in animation creation.The rich resources of myth in ancient China provided a broad space for the creation of animation film and inherited a long ethnic culture.Firstly,the study creates an animation mythological character design model according to the literature review to provide the operational theory for animation design,which consists of three main parts:central idea,research method,and conceptual model.Secondly,the research sums up the animation character creative process framework through the case of Shisa with the specific ideas of creative design.Four steps are used to design a mythological character:set a scenario(illustration),tell a story(interpretation),write a script(reaction),and design a character(reflection).It has analyzed how to integrate the information about the mythology and stimulate the designers’creative imagination in the animation character design in order to create the artworks with unique oriental charm.展开更多
The quality and safety of residents’water rely heavily on the design of municipal water supply and drainage pipes.Therefore,this paper aims to enhance the optimization of municipal water supply and drainage pipe desi...The quality and safety of residents’water rely heavily on the design of municipal water supply and drainage pipes.Therefore,this paper aims to enhance the optimization of municipal water supply and drainage pipe design by focusing on design requirements,principles,and key elements.Drawing from relevant design optimization experiences,technology advancements,and optimization measures,the research will analyze and consolidate the essential aspects of municipal water supply and drainage pipe design.The goal is to fundamentally elevate the quality standards of these designs,ensuring they meet the criteria for engineering project excellence.Through this comprehensive approach,we aim to contribute to the improvement and sustainability of water supply and drainage systems,safeguarding the well-being of residents.展开更多
The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According t...The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.展开更多
Full face rock tunnel boring machine(TBM) has been widely used in hard rock tunnels, however, there are few published theory about cutter-head design, and the design criteria of cutter-head under complex geological ...Full face rock tunnel boring machine(TBM) has been widely used in hard rock tunnels, however, there are few published theory about cutter-head design, and the design criteria of cutter-head under complex geological is not clear yet. To deal with the complex relationship among geological parameters, cutter parameters, and operating parameters during tunneling processes, a cutter-head load model is established by using CSM(Colorado school of mines) prediction model. Force distribution on cutter-head under a certain geology is calculated with the new established load model, and result shows that inner cutters bear more force than outer cutters, combining with disc cutters abrasion; a general principle of disc cutters' layout design is proposed. Within the model, the relationship among rock uniaxial compressive strength(UCS), penetration and thrust on cutter-head are analyzed, and the results shows that with increasing penetration, cutter thrust increases, but the growth rate slows and higher penetration makes lower special energy(SE). Finally, a fitting mathematical model of ZT(ratio of cutter-head torque and thrust) and penetration is established, and verified by TB880 E, which can be used to direct how to set thrust and torque on cutter-head. When penetration is small, the cutter-head thrust is the main limiting factor in tunneling; when the penetration is large, cutter-head torque is the major limiting factor in tunneling. Based on the new cutter-head load model, thrust and torque characteristics of TBM further are researched and a new way for cutter-head layout design and TBM tunneling operations is proposed.展开更多
A two-phase approach is proposed to deal with the integration problem in theloop layout. Tabu search is applied to cell construction in phase 1 to minimize the inter-cell flow,and the heuristic for layout design is us...A two-phase approach is proposed to deal with the integration problem in theloop layout. Tabu search is applied to cell construction in phase 1 to minimize the inter-cell flow,and the heuristic for layout design is used as phase 2 to optimize the sum of intra-cell andinter-cell transportation cost. The final computational results demonstrate the validation of thetwo-phase approach.展开更多
The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure cons...The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.展开更多
The integrated layout problem in manufacturing Systems is investigated. Anintegrated model for Concurrent layout design of cells and flow paths is formulated. A hybridapproach combined an enhanced branch-and-bound alg...The integrated layout problem in manufacturing Systems is investigated. Anintegrated model for Concurrent layout design of cells and flow paths is formulated. A hybridapproach combined an enhanced branch-and-bound algorithm with a simulated annealing scheme isproposed to solve this problem. The integrated layout method is applied to re-layout the gear pumpshop of a medium-size manufacturer of hydraulic pieces. Results show that the proposed layout methodcan concurrently provide good solutions of the cell layouts and the flow path layouts.展开更多
Four-dimensional(4D)printing is an advanced form of three-dimensional(3D)printing with controllable and programmable shape transformation over time.Actuators are used as a controlling factor with multi-stage shape rec...Four-dimensional(4D)printing is an advanced form of three-dimensional(3D)printing with controllable and programmable shape transformation over time.Actuators are used as a controlling factor with multi-stage shape recovery,with emerging opportunities to customize the mechanical properties of bio-inspired structures.The print pattern of shape memory polymer(SMP)fbers strongly afects the achievable resolution,and consequently infuences several other physical and mechanical properties of fabricated actuators.However,the deformations of bio-inspired structures due to actuator layout are more complex because of the presence of the coupling of multi-directional strain.In this study,the initial structure was designed from closed-shell behavior and divided into a general unit and actuator unit,the latter responsible for driving the transformation.Mutual stress confrontation between the actuator and the general unit was considered in the layout thermodynamic model,in order to eliminate the transformation produced by the uncontrolled shape memory behavior of the general unit.Three critical and efective strategies for the layout design of actuators were proposed and then applied to achieve the desired accurate deformation of 3D-printed bilayer structures.Finally,the proposed approach was validated and adopted for fabricating a complex shell-like gripper structure.展开更多
The layout and assembly of flexible cables play important roles in the design and development of complex electromechanical products.The rationality of cable layout design and the reliability of cable assembly greatly ...The layout and assembly of flexible cables play important roles in the design and development of complex electromechanical products.The rationality of cable layout design and the reliability of cable assembly greatly affect product quality.In this paper,we review the methods of cable layout design,cable assembly process planning,and cable assembly simulation.We first review research on flexible cable layout design(both interactive and automatic).Then,research on the cable assembly process planning,including cable assembly path and manipulation planning,is reviewed.Finally,cable assembly simulation is introduced,which includes general cable information,cable collision detection data,and cable assembly process modeling.Current problems and future research directions are summarized at the end of the paper.展开更多
It is important to improve residential thermal comfort in the high dense cities,in which wind environment is crucial.Waterside buildings take an advantage of micro-hydrological-climate in summer that should be used to...It is important to improve residential thermal comfort in the high dense cities,in which wind environment is crucial.Waterside buildings take an advantage of micro-hydrological-climate in summer that should be used to enhance residential thermal comfort especially in the subtropical region.In order to propose design approaches according to the outdoor thermal comfort of the waterside residential,a case study of Shenzhen She Kou residential district has been made.It focused on various factors that could have influence on wind environment for improving thermal comfort.Using wind velocity ratio(ΔRi)criterion,factors of building development volume,building direction and layout pattern,open space arrangement etc.have been broadly explored using FLUENT simulation.To planning parameters,the Floor Area Ratio(FAR)is significantly influence wind environment,the smaller FAR is better.To the vertical layout of the buildings,multi-storey layout and multi-storey&sub high-rise mixed layout would provide better wind environment.To the horizontal layout,the determinant is better than the peripheral.Other factors such as the buildings’direction towards the road,buildings’height,and open space setting,have influence on wind environment yet.In general,the more benefit of design layout for wind breezing,the better wind environment it could get.展开更多
From the perspective of humanized design concepts, humanized space design and behavioral psychological needs of users were re-interpreted and analyzed, basic elements and design principles of cultural plaza spatial la...From the perspective of humanized design concepts, humanized space design and behavioral psychological needs of users were re-interpreted and analyzed, basic elements and design principles of cultural plaza spatial layout were proposed. Particularly, application and role of humanized design in the spatial layout of cultural plaza was analyzed, on the basis of which humanized design objective and orientation for the sustainable development of cultural plaza was defined.展开更多
基金the National Natural Science Foundation of China and the Natural Science Foundation of Jiangsu Province.It was also supported in part by Young Elite Scientists Sponsorship Program by CAST.
文摘Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.
文摘Recently,HUGY has become quite popular in the Chinese market.The character can been seen everywhere,from its emojis,memes,cartoon stories,and art toys,to T-shirts,candies,garments.HUGY is a cartoon of a cute puppy,who is always smiling widely and reaching out his arms,ready to hug you.We invited the character’s creator,Lina Ju for an interview.Lina Ju comes from South Korea but has been working in China for 10 years.She is the chief designer of GENMEC,a trendy brand belonging to Sums Model,a company based in the south of China.
文摘The purpose of this article is to discuss the proper method for Chinese digital animation character design on the foundation of certain cultural elements. The method used in this study is known as comparative analysis of Disney and Japanese animation styles in action, appearance, facial expression and voice design. These dynamic factors are the best carrier of the animation spirit and native culture, so it is important to take the dynamic factors into account when producing the digital animation, and it will be an excellent starting point to innovate Chinese digital animation.
基金funded by Ho Chi Minh City University of Technology(HCMUT),VNU-HCM under Grant Number B2021-20-04.
文摘Optimizing Flow Path Design(FPD)is a popular research area in transportation system design,but its application to Overhead Transportation Systems(OTSs)has been limited.This study focuses on optimizing a double-spine flow path design for OTSs with 10 stations by minimizing the total travel distance for both loaded and empty flows.We employ transportation methods,specifically the North-West Corner and Stepping-Stone methods,to determine empty vehicle travel flows.Additionally,the Tabu Search(TS)algorithm is applied to branch the 10 stations into two main layout branches.The results obtained from our proposed method demonstrate a reduction in the objective function value compared to the initial feasible solution.Furthermore,we explore howchanges in the parameters of the TS algorithm affect the optimal result.We validate the feasibility of our approach by comparing it with relevant literature and conducting additional tests on layouts with 20 and 30 stations.
文摘Chinese mythology with its profound cultural asserts and the unconstrained imagination is an indispensable factor in animation creation.The rich resources of myth in ancient China provided a broad space for the creation of animation film and inherited a long ethnic culture.Firstly,the study creates an animation mythological character design model according to the literature review to provide the operational theory for animation design,which consists of three main parts:central idea,research method,and conceptual model.Secondly,the research sums up the animation character creative process framework through the case of Shisa with the specific ideas of creative design.Four steps are used to design a mythological character:set a scenario(illustration),tell a story(interpretation),write a script(reaction),and design a character(reflection).It has analyzed how to integrate the information about the mythology and stimulate the designers’creative imagination in the animation character design in order to create the artworks with unique oriental charm.
文摘The quality and safety of residents’water rely heavily on the design of municipal water supply and drainage pipes.Therefore,this paper aims to enhance the optimization of municipal water supply and drainage pipe design by focusing on design requirements,principles,and key elements.Drawing from relevant design optimization experiences,technology advancements,and optimization measures,the research will analyze and consolidate the essential aspects of municipal water supply and drainage pipe design.The goal is to fundamentally elevate the quality standards of these designs,ensuring they meet the criteria for engineering project excellence.Through this comprehensive approach,we aim to contribute to the improvement and sustainability of water supply and drainage systems,safeguarding the well-being of residents.
文摘The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.
基金Supported by National Natural Science Foundation of China(Grant No.51275339)National Basic Research Program of China(973 Program,Grant No.2013CB035402)
文摘Full face rock tunnel boring machine(TBM) has been widely used in hard rock tunnels, however, there are few published theory about cutter-head design, and the design criteria of cutter-head under complex geological is not clear yet. To deal with the complex relationship among geological parameters, cutter parameters, and operating parameters during tunneling processes, a cutter-head load model is established by using CSM(Colorado school of mines) prediction model. Force distribution on cutter-head under a certain geology is calculated with the new established load model, and result shows that inner cutters bear more force than outer cutters, combining with disc cutters abrasion; a general principle of disc cutters' layout design is proposed. Within the model, the relationship among rock uniaxial compressive strength(UCS), penetration and thrust on cutter-head are analyzed, and the results shows that with increasing penetration, cutter thrust increases, but the growth rate slows and higher penetration makes lower special energy(SE). Finally, a fitting mathematical model of ZT(ratio of cutter-head torque and thrust) and penetration is established, and verified by TB880 E, which can be used to direct how to set thrust and torque on cutter-head. When penetration is small, the cutter-head thrust is the main limiting factor in tunneling; when the penetration is large, cutter-head torque is the major limiting factor in tunneling. Based on the new cutter-head load model, thrust and torque characteristics of TBM further are researched and a new way for cutter-head layout design and TBM tunneling operations is proposed.
基金This project is supported by National Natural Science Foundation of China (No.59889505, No.70071017).
文摘A two-phase approach is proposed to deal with the integration problem in theloop layout. Tabu search is applied to cell construction in phase 1 to minimize the inter-cell flow,and the heuristic for layout design is used as phase 2 to optimize the sum of intra-cell andinter-cell transportation cost. The final computational results demonstrate the validation of thetwo-phase approach.
基金supported by National Natural Science Foundation of China(Grants No.50875174,51175347)Innovation Program of Shanghai Municipal Education Commission(Grant No.13ZZ114)Capacity Building Project of Local University of Shanghai Municipal Science and Technology Commission(Grant No.13160502500)
文摘The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.
基金This project is supported by National Natural Science Foundation of China (No.59990470)Doctoral Foundation of Ministry of Education, China(No.20010487024).
文摘The integrated layout problem in manufacturing Systems is investigated. Anintegrated model for Concurrent layout design of cells and flow paths is formulated. A hybridapproach combined an enhanced branch-and-bound algorithm with a simulated annealing scheme isproposed to solve this problem. The integrated layout method is applied to re-layout the gear pumpshop of a medium-size manufacturer of hydraulic pieces. Results show that the proposed layout methodcan concurrently provide good solutions of the cell layouts and the flow path layouts.
基金the National Natural Science Foundation of China(Nos.51805472,51775489,and 51975386)the Natural Science Foundation of Zhejiang Province,China(No.LZ21E050004).
文摘Four-dimensional(4D)printing is an advanced form of three-dimensional(3D)printing with controllable and programmable shape transformation over time.Actuators are used as a controlling factor with multi-stage shape recovery,with emerging opportunities to customize the mechanical properties of bio-inspired structures.The print pattern of shape memory polymer(SMP)fbers strongly afects the achievable resolution,and consequently infuences several other physical and mechanical properties of fabricated actuators.However,the deformations of bio-inspired structures due to actuator layout are more complex because of the presence of the coupling of multi-directional strain.In this study,the initial structure was designed from closed-shell behavior and divided into a general unit and actuator unit,the latter responsible for driving the transformation.Mutual stress confrontation between the actuator and the general unit was considered in the layout thermodynamic model,in order to eliminate the transformation produced by the uncontrolled shape memory behavior of the general unit.Three critical and efective strategies for the layout design of actuators were proposed and then applied to achieve the desired accurate deformation of 3D-printed bilayer structures.Finally,the proposed approach was validated and adopted for fabricating a complex shell-like gripper structure.
基金the National Defense Fundamental Research Foundation of China(JCKY2017204B502,JCKY2016204A502)and National Natural Science Foundation of China(51935003).
文摘The layout and assembly of flexible cables play important roles in the design and development of complex electromechanical products.The rationality of cable layout design and the reliability of cable assembly greatly affect product quality.In this paper,we review the methods of cable layout design,cable assembly process planning,and cable assembly simulation.We first review research on flexible cable layout design(both interactive and automatic).Then,research on the cable assembly process planning,including cable assembly path and manipulation planning,is reviewed.Finally,cable assembly simulation is introduced,which includes general cable information,cable collision detection data,and cable assembly process modeling.Current problems and future research directions are summarized at the end of the paper.
文摘It is important to improve residential thermal comfort in the high dense cities,in which wind environment is crucial.Waterside buildings take an advantage of micro-hydrological-climate in summer that should be used to enhance residential thermal comfort especially in the subtropical region.In order to propose design approaches according to the outdoor thermal comfort of the waterside residential,a case study of Shenzhen She Kou residential district has been made.It focused on various factors that could have influence on wind environment for improving thermal comfort.Using wind velocity ratio(ΔRi)criterion,factors of building development volume,building direction and layout pattern,open space arrangement etc.have been broadly explored using FLUENT simulation.To planning parameters,the Floor Area Ratio(FAR)is significantly influence wind environment,the smaller FAR is better.To the vertical layout of the buildings,multi-storey layout and multi-storey&sub high-rise mixed layout would provide better wind environment.To the horizontal layout,the determinant is better than the peripheral.Other factors such as the buildings’direction towards the road,buildings’height,and open space setting,have influence on wind environment yet.In general,the more benefit of design layout for wind breezing,the better wind environment it could get.
文摘From the perspective of humanized design concepts, humanized space design and behavioral psychological needs of users were re-interpreted and analyzed, basic elements and design principles of cultural plaza spatial layout were proposed. Particularly, application and role of humanized design in the spatial layout of cultural plaza was analyzed, on the basis of which humanized design objective and orientation for the sustainable development of cultural plaza was defined.