Abstract Virtual testing and hybrid simulation have become an important trend in airplane design and validation. The traditional Testing Pyramid (or Building Block) approaches that emphasis on uniaxial coupon test and full structure certification test are being challenged. Researchers are trying to use advanced testing and simulation methods to replace the Testing Pyramid approach. Before physical testing, virtual testing can be conducted to simulate the physical test. Virtual model of the full testing system including controller, actuators, and fixtures can be constructed and validated. In this work, an example has been developed and validated to show the potentials of the virtual testing process. Hybrid simulation is an approach of analyzing an analysis model and physical structure integrated system under realistic loading conditions. Hybrid simulation combines the lab testing with numerical analysis to explore the benefits of both methodologies. In this study, a hybrid simulation for a simplified airplane wing was conducted to demonstrate the process. Virtual testing and hybrid simulation are alternative methods of Testing Pyramid approach. Full scale tests are still required for certification but the more that is known about the test article, the greater chances of success in the full-scale certification testing.
{"title":"Breaking the Testing Pyramid with Virtual Testing and Hybrid Simulation","authors":"S. You, X. Shawn Gao, A. Nelson","doi":"10.2478/fas-2019-0001","DOIUrl":"https://doi.org/10.2478/fas-2019-0001","url":null,"abstract":"Abstract Virtual testing and hybrid simulation have become an important trend in airplane design and validation. The traditional Testing Pyramid (or Building Block) approaches that emphasis on uniaxial coupon test and full structure certification test are being challenged. Researchers are trying to use advanced testing and simulation methods to replace the Testing Pyramid approach. Before physical testing, virtual testing can be conducted to simulate the physical test. Virtual model of the full testing system including controller, actuators, and fixtures can be constructed and validated. In this work, an example has been developed and validated to show the potentials of the virtual testing process. Hybrid simulation is an approach of analyzing an analysis model and physical structure integrated system under realistic loading conditions. Hybrid simulation combines the lab testing with numerical analysis to explore the benefits of both methodologies. In this study, a hybrid simulation for a simplified airplane wing was conducted to demonstrate the process. Virtual testing and hybrid simulation are alternative methods of Testing Pyramid approach. Full scale tests are still required for certification but the more that is known about the test article, the greater chances of success in the full-scale certification testing.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2019 1","pages":"1 - 10"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49354673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work, the compressive residual strength tests results, Compression After Impact (CAI), are presented. The specimens were made of carbon-epoxy prepreg E722-02 UHS 130-14. Two variants of specimens were tested: samples undamaged and samples with damage that was centrally introduced by a drop-weight impact, as per the ASTM D7136/7136M standard. An impactor with potential energy equal to 15J and the type of support required by the standard were used. The size of impacted damages, defined as an area of damage on a plane perpendicular to the impact direction, and the equivalent diameter were specified using the flash thermography method. The tests were performed using the fixtures manufactured according to the ASTM D7137/7137M standard. The specimens were compressed to determine the residual strength. This value was afterwards used to specify the force levels for the fatigue tests. The fatigue tests were carried out under force control – with a sinusoidal shape, stress ratio R equal to 0.1 and frequency f 1Hz. Maximum force in a loading cycle Pmax was being increased after each thousand of cycles N until its value was close to the residual strength determined in the previously mentioned tests. In this work, the following relationships were presented: force-displacement P-δ for both static and fatigue tests and displacement-loading cycles δ-N for fatigue tests. A method of conducting the fatigue tests of CFRP composite was proposed, in which both the CAI specimens and CAI fixture were used. This allowed researchers to accelerate making initial comparisons between the two groups of specimens with damages – grouped relative to the way of conditioning.
摘要本文介绍了冲击后压缩(Compression After Impact, CAI)残余抗压强度试验结果。样品采用碳-环氧预浸料E722-02 UHS 130-14制备。根据ASTM D7136/7136M标准，测试了两种不同的样品:未损坏的样品和由落锤撞击引起的损坏样品。使用了势能等于15J的冲击器和标准要求的支撑类型。用闪蒸热成像法确定了冲击损伤的大小，即垂直于冲击方向平面上的损伤区域，并确定了等效直径。试验使用按照ASTM D7137/7137M标准制造的夹具进行。试样被压缩以测定残余强度。该值随后用于指定疲劳试验的力水平。疲劳试验是在力控制下进行的-正弦形状，应力比R等于0.1，频率f为1Hz。加载周期内的最大力Pmax在每一千次循环N后增加，直到其值接近上述试验中确定的残余强度。在这项工作中，提出了以下关系:静力和疲劳试验的力-位移P-δ和疲劳试验的位移-加载周期δ-N。提出了一种采用CAI试样和CAI夹具进行CFRP复合材料疲劳试验的方法。这使得研究人员可以加快对两组损伤标本的初步比较——根据条件作用的方式进行分组。
{"title":"Comparative Study on Fatigue Life of CFRP Composites with Damages","authors":"Marta Baran, P. Synaszko, J. Lisiecki, S. Kłysz","doi":"10.2478/fas-2019-0004","DOIUrl":"https://doi.org/10.2478/fas-2019-0004","url":null,"abstract":"Abstract In this work, the compressive residual strength tests results, Compression After Impact (CAI), are presented. The specimens were made of carbon-epoxy prepreg E722-02 UHS 130-14. Two variants of specimens were tested: samples undamaged and samples with damage that was centrally introduced by a drop-weight impact, as per the ASTM D7136/7136M standard. An impactor with potential energy equal to 15J and the type of support required by the standard were used. The size of impacted damages, defined as an area of damage on a plane perpendicular to the impact direction, and the equivalent diameter were specified using the flash thermography method. The tests were performed using the fixtures manufactured according to the ASTM D7137/7137M standard. The specimens were compressed to determine the residual strength. This value was afterwards used to specify the force levels for the fatigue tests. The fatigue tests were carried out under force control – with a sinusoidal shape, stress ratio R equal to 0.1 and frequency f 1Hz. Maximum force in a loading cycle Pmax was being increased after each thousand of cycles N until its value was close to the residual strength determined in the previously mentioned tests. In this work, the following relationships were presented: force-displacement P-δ for both static and fatigue tests and displacement-loading cycles δ-N for fatigue tests. A method of conducting the fatigue tests of CFRP composite was proposed, in which both the CAI specimens and CAI fixture were used. This allowed researchers to accelerate making initial comparisons between the two groups of specimens with damages – grouped relative to the way of conditioning.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2019 1","pages":"28 - 38"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48841209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract From the safety point of view, one of the most important issues regarding aircraft operations is ensuring the durability of the structural components. Corrosion processes can have a significant effect on the integrity of structural materials and are usually associated with aircraft aging. Due to the variety of materials used, environments and loads impacting the planes, a wide range of different types of corrosion may occur in aircraft structures. The main aim of this study is to present some theoretical knowledge related to corrosion processes as well as problems of aircraft structures associated with corrosion occurrence. Firstly, the paper presents a brief overview of what corrosion is and what different types of corrosion are. Secondly, some selected aircraft failures caused by corrosion are shortly presented and discussed.
{"title":"Aircraft Corrosion – Review of Corrosion Processes and its Effects in Selected Cases","authors":"Magdalena Czaban","doi":"10.2478/fas-2018-0001","DOIUrl":"https://doi.org/10.2478/fas-2018-0001","url":null,"abstract":"Abstract From the safety point of view, one of the most important issues regarding aircraft operations is ensuring the durability of the structural components. Corrosion processes can have a significant effect on the integrity of structural materials and are usually associated with aircraft aging. Due to the variety of materials used, environments and loads impacting the planes, a wide range of different types of corrosion may occur in aircraft structures. The main aim of this study is to present some theoretical knowledge related to corrosion processes as well as problems of aircraft structures associated with corrosion occurrence. Firstly, the paper presents a brief overview of what corrosion is and what different types of corrosion are. Secondly, some selected aircraft failures caused by corrosion are shortly presented and discussed.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"20 - 5"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46514922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Computed tomography (CT) of aluminum welded joint specimen has been performed. On the tomographic cross sections some defects have been found. To verify them the metallography cross sections of welded has been done. It was found that selected defects are micro cracks.
{"title":"Verification of the Computed Tomography Results of Aluminum Alloy Welded Joint","authors":"Maciej Malicki, K. Sobczak","doi":"10.2478/fas-2018-0004","DOIUrl":"https://doi.org/10.2478/fas-2018-0004","url":null,"abstract":"Abstract Computed tomography (CT) of aluminum welded joint specimen has been performed. On the tomographic cross sections some defects have been found. To verify them the metallography cross sections of welded has been done. It was found that selected defects are micro cracks.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"47 - 52"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43896644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The authors of the paper presented some of the models describing the process of micro-cracks’ development. In this study, the process of a selected model of micro-cracking was analyzed. In the model it was assumed that the damage to the material has some “thermodynamic properties” or rather universal properties inherent in most complex systems. In order to calculate the long-term fatigue strength properties of a structure, it is important to have a good understanding of the distribution parameters of the number of defects of different sizes. A model was built using the entropy principle, which is effectively used to test complex systems that are difficult to formalize. As a result of many experimental studies it was found that the development of fatigue damage is closely related to the process of plastic deformation of the material at the contact point of local defects. The results of computer calculations and simulations led to the conclusions presented in the final part of this paper.
{"title":"Accumulation of Fatigue Microdefects– Entropy Interpretation","authors":"K. Szafran, N. Delas","doi":"10.2478/fas-2018-0010","DOIUrl":"https://doi.org/10.2478/fas-2018-0010","url":null,"abstract":"Abstract The authors of the paper presented some of the models describing the process of micro-cracks’ development. In this study, the process of a selected model of micro-cracking was analyzed. In the model it was assumed that the damage to the material has some “thermodynamic properties” or rather universal properties inherent in most complex systems. In order to calculate the long-term fatigue strength properties of a structure, it is important to have a good understanding of the distribution parameters of the number of defects of different sizes. A model was built using the entropy principle, which is effectively used to test complex systems that are difficult to formalize. As a result of many experimental studies it was found that the development of fatigue damage is closely related to the process of plastic deformation of the material at the contact point of local defects. The results of computer calculations and simulations led to the conclusions presented in the final part of this paper.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"104 - 116"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42139608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Parachute systems are in widespread use in aviation. Up to now, parachutes are the most uncertain air vehicles because of their complex and unsteady opening characteristics, changes in geometry up to 30% and vulnerability from unsteady atmospheric turbulence. Fatigue is a problem that the designers of long living parachute systems need to cope with. Authors demonstrate complexity of parachute exploitation and means to lower opening forces and extend service life without influencing safety.
{"title":"Fatigue Degradation of the Structure of Parachute Systems","authors":"K. Szafran, Ireneusz Kramarski","doi":"10.2478/fas-2018-0009","DOIUrl":"https://doi.org/10.2478/fas-2018-0009","url":null,"abstract":"Abstract Parachute systems are in widespread use in aviation. Up to now, parachutes are the most uncertain air vehicles because of their complex and unsteady opening characteristics, changes in geometry up to 30% and vulnerability from unsteady atmospheric turbulence. Fatigue is a problem that the designers of long living parachute systems need to cope with. Authors demonstrate complexity of parachute exploitation and means to lower opening forces and extend service life without influencing safety.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"103 - 93"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/fas-2018-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41614760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Barely visible impact damage is one of the problems commonly occurring in composite elements during an aircraft operation. The authors described the mechanisms of impact damage formation and propagation in composite structures. The paper presents a performed analysis of an influence of impact parameters on the resulting damage, i.e. its detectability by means of visual observation as well as its extent determined based on ultrasonic tests results. The tests were conducted on the CFRP specimens with a wide range of impact damage cases obtained with combinations of variable impact energy and shapes of impactors. Additionally, an algorithm based on image processing and image analysis methods is proposed for the purpose of the effective evaluation of the ultrasonic data obtained.
{"title":"Evaluation of Impact Damage in Composite Structures Using Ultrasonic Testing","authors":"Angelika Wronkowicz-Katunin, K. Dragan","doi":"10.2478/fas-2018-0008","DOIUrl":"https://doi.org/10.2478/fas-2018-0008","url":null,"abstract":"Abstract Barely visible impact damage is one of the problems commonly occurring in composite elements during an aircraft operation. The authors described the mechanisms of impact damage formation and propagation in composite structures. The paper presents a performed analysis of an influence of impact parameters on the resulting damage, i.e. its detectability by means of visual observation as well as its extent determined based on ultrasonic tests results. The tests were conducted on the CFRP specimens with a wide range of impact damage cases obtained with combinations of variable impact energy and shapes of impactors. Additionally, an algorithm based on image processing and image analysis methods is proposed for the purpose of the effective evaluation of the ultrasonic data obtained.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"82 - 92"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46397393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Damage tolerance of composite aircraft structure is one of the main areas of research, important when a new product is being developed. There are a number of variables, such as damage characteristics (dent depth, delamination area) and loading parameters (load type, amplitude of cyclic loading, load sequence) that need to be investigated experimentally [1]. These tests of composite materials are usually performed at an element level and are carried out in order to validate the analytical model, developed to predict the full-scale component’s behaviour. The paper presents the results of compression testing of the [36/55/9] carbon fibre/epoxy laminate, manufactured with the Automated Fibre Placement technology (AFP) and subjected to static and fatigue loads. The laminate compression loading mode was achieved through sandwich 4-point flexure. At the stage of fatigue testing, two parameters were investigated: the damage size, simulated by the hole diameter and the fatigue load level. Based on the test results, the laminate fatigue load limit equal to 75% of the OHC failure load was evaluated. By collating the static and fatigue tests results, the damage tolerance characteristic of the considered laminate was created.
{"title":"Influence of the Fatigue Load Level and the Hole Diameter on the Laminate Structure’s Fatigue Performance","authors":"M. Zalewska","doi":"10.2478/fas-2018-0002","DOIUrl":"https://doi.org/10.2478/fas-2018-0002","url":null,"abstract":"Abstract Damage tolerance of composite aircraft structure is one of the main areas of research, important when a new product is being developed. There are a number of variables, such as damage characteristics (dent depth, delamination area) and loading parameters (load type, amplitude of cyclic loading, load sequence) that need to be investigated experimentally [1]. These tests of composite materials are usually performed at an element level and are carried out in order to validate the analytical model, developed to predict the full-scale component’s behaviour. The paper presents the results of compression testing of the [36/55/9] carbon fibre/epoxy laminate, manufactured with the Automated Fibre Placement technology (AFP) and subjected to static and fatigue loads. The laminate compression loading mode was achieved through sandwich 4-point flexure. At the stage of fatigue testing, two parameters were investigated: the damage size, simulated by the hole diameter and the fatigue load level. Based on the test results, the laminate fatigue load limit equal to 75% of the OHC failure load was evaluated. By collating the static and fatigue tests results, the damage tolerance characteristic of the considered laminate was created.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"21 - 30"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44271538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper presents a summary of non-destructive testing and evaluation (NDT&E) methods applied in inspections of structural aircraft components. This brief review covers the most commonly applied methods such as visual and penetrant inspections, tap-testing, eddy current inspections, shearography, thermography, acoustic emission testing, radiographic and tomographic inspections, and ultrasonic inspections. The general operating principles of these methods as well as their main advantages, limitations and application areas are described below.
{"title":"A Brief Review on NDT&E Methods For Structural Aircraft Components","authors":"Angelika Wronkowicz-Katunin","doi":"10.2478/fas-2018-0007","DOIUrl":"https://doi.org/10.2478/fas-2018-0007","url":null,"abstract":"Abstract The paper presents a summary of non-destructive testing and evaluation (NDT&E) methods applied in inspections of structural aircraft components. This brief review covers the most commonly applied methods such as visual and penetrant inspections, tap-testing, eddy current inspections, shearography, thermography, acoustic emission testing, radiographic and tomographic inspections, and ultrasonic inspections. The general operating principles of these methods as well as their main advantages, limitations and application areas are described below.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"73 - 81"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41620916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elżbieta Gadalińska, A. Baczmaňski, S. Wronski, M. Wróbel, Christian Scheffzük
Abstract The paper presents the results of diffraction stress measurement in Al/SiC composite and in 2124T6 aluminum alloy during the in situ tensile test. The main aim of the work is to observe the stress values for different stages of tensile test for the composite after applying two types of thermal treatment and for the alloy used as a matrix in this composite, to identify the type of hardening process. The experimental results were compared against the calculations results obtained from the self-consistent model developed by Baczmański [1] - [3] to gain the information about the micromechanical properties (critical resolved shear stress τcr and hardening parameter H) of the examined materials. This comparison allowed researchers to determine the role of reinforcement in the composite as well as the impact of the heat treatment on the hardening of the material.
{"title":"The Hardening in Alloys and Composites and Its Examination with a Diffraction and Self-Consistent Model","authors":"Elżbieta Gadalińska, A. Baczmaňski, S. Wronski, M. Wróbel, Christian Scheffzük","doi":"10.2478/fas-2018-0003","DOIUrl":"https://doi.org/10.2478/fas-2018-0003","url":null,"abstract":"Abstract The paper presents the results of diffraction stress measurement in Al/SiC composite and in 2124T6 aluminum alloy during the in situ tensile test. The main aim of the work is to observe the stress values for different stages of tensile test for the composite after applying two types of thermal treatment and for the alloy used as a matrix in this composite, to identify the type of hardening process. The experimental results were compared against the calculations results obtained from the self-consistent model developed by Baczmański [1] - [3] to gain the information about the micromechanical properties (critical resolved shear stress τcr and hardening parameter H) of the examined materials. This comparison allowed researchers to determine the role of reinforcement in the composite as well as the impact of the heat treatment on the hardening of the material.","PeriodicalId":37629,"journal":{"name":"Fatigue of Aircraft Structures","volume":"2018 1","pages":"31 - 46"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46231186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：