Basketball motion worst working condition load model obtaining method and structure design method

Abstract

The invention discloses a method for obtaining a load model of the most unfavorable working condition of basketball sports, and the method comprises the steps: decomposing single-person basketball sports into five continuous stages according to the change characteristics of the load in the basketball running process, fitting the load curve of each stage by adopting a corresponding function, and building a single-person basketball sports load simplified model; setting simultaneous take-off of three persons in the center area under the basket in the basketball as the most unfavorable working condition, and establishing a load simplified model corresponding to the most unfavorable working condition of the basketball; and verifying the load simplified model corresponding to the most unfavorable working condition of the basketball. The invention further discloses a basketball venue structure design method. The method has the beneficial effects that a simplified load model of the most unfavorable working condition of the basketball is provided according to the load characteristics of the basketball, the structural dynamic response under the action of the basketball load can be predicted, and powerful support is provided for structural design and vibration comfort evaluation of a basketball venue.

Description

Technical Field

[0001] This invention relates to the field of building structure motion load analysis technology, specifically to a method for obtaining the most unfavorable load model for basketball and a structural design method. Background Technology

[0002] With the widespread development of national fitness activities, basketball, as a popular sport, is seeing an increasing number of indoor venues. As people's living standards improve and their pursuit of healthy lifestyles grows, indoor sports stadiums and multi-functional sports stadiums are gradually becoming a new trend in urban construction. These comprehensive buildings, in addition to their original office and conference functions, integrate sports venues for basketball, tennis, table tennis, and badminton, meeting the public's needs for sports, fitness, and sporting events. Currently, the structural design of such buildings often uses large-span floor slabs to provide the necessary space for sports fields. However, the human-induced loads generated by sports activities can lead to substandard structural vibration comfort and excessive indoor noise, causing not only discomfort but also potentially affecting the normal use of the building. Basketball is a highly popular sport in China, and among common sports, it is the most physically demanding, generating greater load intensity, which presents a challenge to the comfort evaluation of sports stadiums.

[0003] In current building structural design, most studies on indoor sports loads focus on relatively regular movements such as walking, running, and jumping. However, basketball, with its complex and varied technical movements, presents significant challenges for accurate measurement, resulting in relatively insufficient research on dynamic loads in basketball. In basketball, an athlete's weight, jump height, takeoff and landing speed, direction of movement, and coordinated movements among multiple players all affect the magnitude, direction, and distribution of the load. For example, during fast breaks, multiple rebounds, and close-quarters combat under the basket, multiple athletes may simultaneously push off the ground or land, generating a large instantaneous impact force. This corresponds to the most unfavorable working condition in basketball, producing an instantaneous impact load far exceeding that of a single movement. Existing load models struggle to simulate this basketball load, and current structural design also lacks load models specifically tailored to various sports.

[0004] In summary, existing research on indoor sports loads cannot reflect the complex load characteristics of basketball, and lacks simplified models that can accurately cover its most unfavorable working conditions. This makes it difficult to conduct targeted vibration comfort evaluation and optimization during the structural design phase of buildings, becoming a core technical bottleneck restricting the implementation of comprehensive sports venue functions and user experience. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for obtaining the most unfavorable load model for basketball sports and a structural design method, aiming to solve the technical problem that existing indoor sports load models cannot reflect the load characteristics of basketball sports.

[0006] The technical solution adopted in this invention is: a method for obtaining the most unfavorable load model for basketball, which includes the following steps: S1. Based on the load variation characteristics during basketball movement, the single-player basketball movement is decomposed into five continuous stages: the pre-jump power accumulation stage, the take-off stage, the flight stage, the landing impact stage, and the recovery static load stage. The corresponding functions are used to fit the load curves of each stage to establish a simplified load model for single-player basketball movement. S2. The most unfavorable working condition is to set the simultaneous jump of 3 people in the center area under the basket in basketball as the most unfavorable working condition, and to establish a simplified load model corresponding to the most unfavorable working condition in basketball. S3. Verify the simplified load model corresponding to the most unfavorable working condition for basketball.

[0007] According to the above scheme, the specific method of step S1 is as follows: S11. Determine the data collection targets based on the characteristics of the service recipients of the basketball court to be designed; S12. Have the data acquisition subject wear a plantar force measuring device to complete a specified basketball technique, collect plantar force time history data and generate a load curve; S13. Based on the slope inflection point, peak value, and contact and takeoff instant characteristics of the load curve, the single basketball movement is divided into five continuous stages using time boundary points t1, t2, t3, and t4: pre-jump power accumulation stage, takeoff stage, airborne stage, landing impact stage, and recovery static load stage. S14. A simplified load model for single-player basketball is obtained by fitting the load changes at each stage using piecewise functions.

[0008] According to the above scheme, in S14, the pre-jump power accumulation phase is fitted with a power function, the take-off phase is fitted with a linear function, the flight phase is set to a constant value of 0, the landing impact phase is fitted with a linear function, and the recovery static load phase is fitted with an exponential function.

[0009] According to the above scheme, the simplified model of the load on a single basketball player is as follows: ; In the formula, The load value at time t is expressed in N. The variable is time, and the unit is seconds (s). The weight of the human body is expressed in N. , , and These represent the time boundary points of different stages in the simplified load model; when At that time, it belongs to the pre-jump power-building phase; when At that time, it belongs to the take-off phase; when At that time, it was in the air-lift phase; when At that time, it belongs to the impact phase upon landing; when At this time, it belongs to the static load recovery section; This represents the peak load during the take-off phase of the basketball's loading motion, expressed in N. This represents the peak load on the ground section, in N (N). The attenuation coefficient representing the peak value of the ground load; This represents the attenuation coefficient when returning to the static load range.

[0010] According to the above scheme, a1 and a2 are obtained using the least squares method. The specific method is as follows: First, take the attenuation segment data after t4, use the moving average method to process the noise, and then fit the processed data; Second, use the slope of the load curve to the left of t4 as a constraint condition to limit the slope of the starting point of the attenuation segment; Next, predict the initial values ​​of a1 and a2, construct the objective function of the least squares method to minimize the sum of the squared differences at each sampling time; Finally, solve the objective function and iterate repeatedly through the solver to obtain the optimal values ​​of a1 and a2.

[0011] According to the above scheme, in S13, t1 is the moment when the load in the pre-jump power-building phase reaches F1, t2 is the moment when the feet leave the ground and the load drops to 0, t3 is the moment when the feet touch the ground and the load begins to rise, and t4 is the moment when the load in the landing impact phase reaches F2.

[0012] According to the above scheme, the specific method for verifying the model is as follows: S31. Based on the design drawings, establish a local finite element model of the target basketball court. Use the fitted piecewise load function 3F(t) as a concentrated nodal force and apply it to the loading point in the finite element model of the target basketball court to predict the vertical acceleration response at the specified test point of the floor slab under the basketball motion load. S32. Conduct on-site testing at the target basketball court, arrange 3 testers matching the characteristics of the service object to perform a specified basketball action at the load loading point, and obtain the measured value of the vertical acceleration response of the floor slab at the specified test point during the entire movement process; S33. Compare the predicted and measured values ​​of the vertical acceleration response. If the relative error between the predicted and measured values ​​of the vertical acceleration response at each test point is ≤10%, the model is considered accurate. If the relative error between the predicted and measured values ​​exceeds 10%, the model is considered inaccurate.

[0013] This invention also employs a basketball court structure design method, which is as follows: Step 1: Based on the service characteristics of the basketball court to be designed, determine and obtain the appropriate simplified basketball load model 3F(t) using the method described in any one of claims 1 to 7. Step 2: Build a finite element model of the basketball court; Step 3: Apply the obtained simplified basketball load model 3F(t) to the three-second zone of the basketball court in the finite element model as a concentrated force load; Step 4: Extract the vertical acceleration response data of the specified test points, and determine whether the current structural design meets the vibration comfort requirements based on the corresponding limit requirements in the "Technical Standard for Vibration Comfort of Building Floor Structures". Step 5: If the judgment result meets the comfort requirements, the current finite element model can be used as the basic model for the design of the basketball court; if it does not meet the comfort requirements, the original finite element model needs to be optimized and adjusted.

[0014] According to the above scheme, in step five, after each round of optimization of the finite element model, the load conditions before optimization are used to recalculate in the optimized finite element model, and the comfort judgment process is repeated until the vibration comfort of the basketball court meets the specifications. Finally, the finite element model that meets the requirements is used as the basic model for the design of the basketball court.

[0015] According to the above scheme, in step four, the vertical acceleration limit in JGJ / T441-2019 "Technical Standard for Vibration Comfort of Building Floor Structures" is used to determine whether the vibration comfort requirements are met.

[0016] The beneficial effects of this invention are as follows: 1. This invention proposes a simplified load model for the most unfavorable working condition of basketball sports, which can predict the structural dynamic response under basketball load. It provides strong support for the structural design and vibration comfort assessment of basketball courts, solves the technical problem that existing indoor sports load models cannot reflect the characteristics of basketball sports load, and fills the gap in existing technology in basketball sports load models.

[0017] 2. This invention accurately captures the bi-peak impact characteristics under the most unfavorable conditions by segmenting and fitting key technical movements in basketball. Combined with the actual measurement and verification process, the accuracy of the model is ensured. It can reliably predict the structural dynamic response under basketball load, providing accurate data support for subsequent evaluation and design.

[0018] 3. The present invention can adjust parameters to adapt to the weight and movement characteristics of different athletes, and is applicable to basketball courts in various basketball venues and complex buildings. It does not require repeated model building for specific scenarios and has a wide range of applications. Attached Figure Description

[0019] Figure 1This is a flowchart of the present invention.

[0020] Figure 2 This is a time-course diagram of plantar force in basketball techniques.

[0021] Figure 3 This is a comparison diagram of the load model obtained in this invention fitting the actual load time history.

[0022] Figure 4 A schematic diagram of the finite element model of the basketball court on the roof of the school's podium building.

[0023] Figure 5 This is a schematic diagram comparing the predicted and measured values ​​of the vertical acceleration of the floor slab in Example 1.

[0024] Figure 6 This is a schematic diagram comparing the vertical acceleration response spectrum of the floor slab in Example 1.

[0025] Figure 7 This is a schematic diagram showing the location of the load application point and the designated test point in Example 2.

[0026] Figure 8 This is a schematic diagram of the vertical acceleration response extracted from a test point in Example 2. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] In the description of the embodiments of this application, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application. In addition, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0029] In the description of the embodiments of this application, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application based on the specific circumstances.

[0030] In the embodiments of this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0031] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the embodiments of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples, without contradiction. Additionally, the term "a plurality of" indicates two or more.

[0032] A simplified calculation model for the most unfavorable load conditions in basketball is proposed. This method uses the physical characteristics of the foot force time history during basketball player movement as the basis for division, decomposes the movement into five continuous stages, and uses power functions, linear functions, dead load, linear functions and exponentially decaying superimposed static load functions to fit the load of the corresponding stage in turn, and finally superimposes them to obtain a simplified load model.

[0033] like Figure 1 The method shown is for obtaining the most unfavorable load model for basketball, and the method includes the following steps: S1. Based on the load variation characteristics during basketball movement, the single-player basketball movement is decomposed into five continuous stages: the pre-jump power accumulation stage, the take-off stage, the flight stage, the landing impact stage, and the recovery static load stage. The corresponding functions are used to fit the load curves of each stage to establish a simplified load model for single-player basketball movement. S2. The most unfavorable working condition is to set the simultaneous jump of 3 people in the center area under the basket in basketball as the most unfavorable working condition, and to establish a simplified load model corresponding to the most unfavorable working condition in basketball. S3. Verify the simplified load model corresponding to the most unfavorable working condition for basketball.

[0034] In this invention, S1 specifically includes the following steps: S1. Determine the data collection targets based on the service target characteristics of the basketball court to be designed. The service target characteristics include professional athletes corresponding to professional basketball courts, ordinary basketball enthusiasts and teenagers corresponding to public cultural and sports spaces, and students of the corresponding age group corresponding to primary and secondary school basketball courts. The weight, age, and exercise intensity of the data collection targets are matched with the service target characteristics.

[0035] In this invention, the data collection targets differ due to the varying characteristics of the venues serving different users. Professional basketball venues, serving professional athletes, require data collection from professional basketball players aged 20-35 with professional competition experience. Their weight must fall within the typical range for professional players (e.g., 80-110kg for males and 60-85kg for females), demonstrating high-intensity athletic ability. The impact load they experience upon landing better reflects the most unfavorable conditions in professional games, ensuring the collected load data perfectly matches the actual usage scenario of the venue. Public cultural and sports spaces, serving the general public and youth, require data collection from both ordinary basketball enthusiasts and youth groups. Ordinary enthusiasts should be aged 18-50 without professional sports background but with regular basketball habits, weighing between 50-90kg, and focusing on casual, competitive play. Youth groups should cover those aged 12-17, weighing 35-70kg, with a play style primarily based on basic techniques (such as dribbling and shooting), avoiding extreme high-intensity movements. The basketball courts in primary and secondary schools serve teenagers. Data collection targets students of the corresponding age groups. For primary school students, the data collection targets students aged 6-12 with a weight of 20-45kg. The range of motion is mainly low-intensity running, jumping, and basic shooting, with a low peak impact load. For junior high school students, the data collection targets students aged 13-15 with a weight of 40-65kg. The intensity of exercise is slightly higher, but it is still based on school sports activities, without high-intensity movements at the professional training level.

[0036] S12. Have the data acquisition subject wear a plantar force measuring device to complete a specified basketball technique, collect plantar force time history data and generate a load curve.

[0037] In this invention, the data acquisition subject (i.e., the test subject) wears force-measuring insoles (the plantar force measurement device uses Loadsol® wireless force-measuring insoles from Novel Inc., USA, with a force sensing range of 0-5000N and a sampling frequency set to 100Hz) and performs a specified basketball technique, thereby obtaining plantar force time-history data and plotting the corresponding load curve, such as... Figure 2 The image shows a typical load curve (the vertical axis corresponds to the normalized plantar force).

[0038] S13. Based on the slope inflection point, peak value, and contact and lift-off characteristics of the load curve, the single-player basketball game is divided into five continuous stages using time division points t1, t2, t3, and t4: the pre-jump power-building stage, the take-off stage, the flight stage, the landing impact stage, and the static load recovery stage. Among them, t1 is the moment when the load reaches F1 in the pre-jump power-building stage, t2 is the moment when the foot leaves the ground and the load drops to 0, t3 is the moment when the foot touches the ground and the load begins to rise, and t4 is the moment when the load reaches F2 in the landing impact stage.

[0039] In this invention, the foot force time-course characteristics of various basketball techniques, such as a single three-step layup, a single jump shot, and a two- or three-person rebounding, are summarized. Based on the changing characteristics of the load curve, such as the slope inflection point, peak value, and contact / leap moment, the entire process of take-off-flight-landing in basketball is divided into five continuous stages. Each stage is further divided using four time boundary points t1, t2, t3, and t4. In other words, the time nodes are determined by the changing characteristics of the load curve, and then the time nodes are used as boundary points for modeling.

[0040] S14. A simplified load model for single-player basketball is obtained by fitting the load changes at each stage using piecewise functions: the pre-jump power function is used for the power-law function fitting, the take-off and landing function is used for the linear function fitting, the flight stage is set to a constant value of 0, the landing impact stage is used for the linear function fitting, and the static load recovery stage is used for the exponential function fitting.

[0041] In this invention, the weight of the test subject is assumed to be G, such as Figure 1As shown, segment AC of the load curve corresponds to the pre-jump power-building phase. Segment AC consists of segments AB and BC. Segment AB represents the process where the test subject slightly squats down, during which some of the force on the force-measuring insole is dissipated, resulting in a non-linear, slow decrease in load characteristics. Segment BC corresponds to the process where the test subject quickly pushes off the ground after a slow squat. During this phase, the test subject pushes off forcefully, causing the load on the force-measuring insole to rise rapidly and non-linearly. After reaching the first peak load F1, the test subject will be airborne in a very short time. Therefore, segment AC is the pre-jump power-building phase, the stage where the test subject prepares for the jump. The load curve is convex from bottom to top, with the load increasing non-linearly and accelerating. It rises slowly at the beginning and rapidly near t1, exhibiting a gradual increase followed by a steeper increase, and an overall convex shape. Therefore, combining the load curve characteristics of the pre-jump power storage phase, a power function is used to fit the load change of the pre-jump power storage phase. The exponent n controls the convexity and steepness of the later stage, so that the fitting remains monotonic and avoids overshoot, and the numerical value is stable and consistent with the observed "slow first and fast later" load pattern.

[0042] During the take-off phase, the load transitions from the first peak value F1 to zero load off the ground. This load change corresponds to segment CD of the load curve. Within this phase, the load change exhibits a near-linear decrease. Therefore, a linear function is used to fit a constant rate of descent (constant slope) unloading process, consistent with the "uniform unloading" load characteristic of this segment.

[0043] During the airborne phase, the feet are completely off the ground, and the vertical reaction force exerted by the ground on the feet is zero. The load change during this process corresponds to segment DE of the load curve. The load is constant (usually taken as 0) during this stage, which conforms to the load time history characteristics.

[0044] Upon impact, the foot touches the ground, and the load rapidly increases, corresponding to segment EF of the load curve. During this phase, the load rises rapidly and almost linearly from 0 to the second peak value F2. Therefore, a linear function is used for fitting, and the constant slope of the linear function represents the rate of impact ascent.

[0045] The FI segment of the load curve corresponds to the static load recovery segment. After reaching the peak load F2, the load rapidly declines and asymptotically stabilizes at the shape of G. The FH segment represents the process of the test subject recovering to body weight after experiencing the maximum impact force on the sole of the foot upon landing. Point G represents the transfer of impact force from the heel to the forefoot. The heel initially contacts the ground, resulting in a large peak impact load. Subsequently, the center of gravity continues to descend, and the pressure transfers to the forefoot, forming a second peak. The HI segment represents the process of the test subject recovering to normal body weight after landing. The concave segment of the normalized plantar force is due to the fact that the test subject cushions some of the impact force through the knee upon landing, thus the plantar force shows a trend of first decreasing and then recovering to body weight. During this stage, the load curve exhibits the characteristics of rapid initial decline followed by slowing down, monotonically decaying, and converging to a constant. The exponential function possesses the characteristics of monotonically decaying and asymptotically stable limits, ensuring both the continuity of F(t4) = F2 and ensuring monotonicity, no negative bounce, and asymptote around G. With few parameters (only 'a' controls the decay rate), stable fitting, and insensitive to post-peak noise, it can accurately describe the load variation pattern of "rapid descent → slow convergence" in this segment.

[0046] Therefore, the simplified model of the load on a single basketball player is as follows: ; In the formula, The load value at time t describes how the load changes over time, and the unit is N; The variable is time, and the unit is seconds (s). The weight of the human body is expressed in N. , , and These represent the time boundary points of different stages in the simplified load model; when At that time, it belongs to the pre-jump power-building phase; when At that time, it belongs to the take-off phase; when At that time, it was in the air-lift phase; when At that time, it belongs to the impact phase upon landing; when At this time, it belongs to the static load recovery section; This represents the peak load during the take-off phase of the basketball's loading motion, expressed in N. This represents the peak load on the ground section, in N (N). The attenuation coefficient (dimensionless) represents the attenuation coefficient of the peak ground load. At higher levels, the peak decays faster, the impact is greater, and the structural acceleration response is greater. This represents the attenuation coefficient (dimensionless) upon returning to the static load range. When the values ​​are larger, the recovery to the static load segment is faster. Both a1 and a2 are dimensionless attenuation coefficients. a1 controls the attenuation rate of the landing peak, and a2 controls the regression rate to the static load segment. Both are average values ​​obtained by fitting normalized plantar force data measured on-site using force-measuring insoles. a1 and a2 are obtained using the least squares method. Specifically: First, attenuation data after t4 is taken, and noise is processed using the moving average method, then the processed data is fitted. Second, the slope of the load curve to the left of t4 is used as a constraint to limit the slope of the attenuation segment's starting point. Next, the initial values ​​of a1 and a2 are predicted, and a least squares objective function is constructed to minimize the sum of the squared differences at each sampling time. Finally, the objective function is solved and iterated repeatedly using a solver to obtain the optimal values ​​of a1 and a2.

[0047] The parameters in this invention include t1, t2, t3, t4, F1, F2, a1, and a2. The measured parameters differ significantly between ordinary basketball enthusiasts and professional basketball players. F1 and F2 directly measure the load intensity during basketball activities. For ordinary basketball enthusiasts, F1 is typically between 1.5 and 2 times their body weight, and F2 can reach between 3.5 and 4.5 times their body weight. For well-trained professional basketball players, F1 can reach a load intensity of 2 to 3 times their body weight, and F2 can reach 4.5 to 6.5 times their body weight. Specific parameters need to be adjusted according to the athlete's athletic ability, weight, and exercise intensity.

[0048] In step S2 of this invention, the most unfavorable condition is defined as three people jumping simultaneously in the center area under the basket during basketball. The basketball load corresponding to this condition is simplified to the superposition of the foot force of the three athletes. The simplified load model corresponding to the most unfavorable condition of basketball is 3F(t).

[0049] In step S3 of this invention, the specific method for verifying the model is as follows: S31. Based on the design drawings, establish a local finite element model of the target basketball court. Use the fitted piecewise load function 3F(t) as a concentrated nodal force and apply it to the loading point in the finite element model of the target basketball court (that is, the corresponding position of the three-second zone of the basketball court in the finite element model). Predict the vertical acceleration response at the specified test point of the floor slab under the action of basketball motion load. S32. Conduct on-site testing at the target basketball court, arrange 3 testers matching the characteristics of the service object to perform a specified basketball action at the load loading point, and obtain the measured value of the vertical acceleration response of the floor slab at the specified test point (consistent with the test point position in the numerical simulation) during the entire movement process; S33. Compare the predicted and measured values ​​of the vertical acceleration response to verify the accuracy of the simplified basketball load model. The specific method is as follows: If the relative error between the predicted and measured values ​​of the vertical acceleration response at each test point is ≤10%, the model is considered accurate and can be used for subsequent structural design of the basketball court. If the relative error exceeds 10%, the model is considered inaccurate and the simplified load model needs to be corrected by adjusting the parameters F1, F2, and a1. The specific corrections to the simplified load model are as follows: When the measured value of the vertical acceleration response is significantly greater than the predicted value (error exceeding 10%), it indicates that the model's load strength is too low. F1 and F2 can be increased to improve the amplitude of the athlete's landing load, while a1 can be increased to increase the slope of the FH segment, enhancing the load impact and thus improving the model's accuracy. When the measured value of the vertical acceleration response is significantly less than the predicted value, it indicates that the model's load strength is too high. The values ​​of F1, F2, and a1 need to be decreased to correct the model's accuracy.

[0050] A method for designing the structure of a basketball court; Step 1: Based on the characteristics of the service objects of the basketball court to be designed, the appropriate simplified basketball load model 3F(t) is determined and obtained using the method described above, so as to provide load basis for subsequent dynamic response analysis; Step 2: Referring to existing technologies, construct a finite element model of the basketball court. The finite element model includes the floor slabs, frame beams, and lower-level columns of the floor where the basketball court is located. The floor slabs are simulated using SHELL181 elements, and the beams and columns are simulated using BEAM188 elements. The bottom of the columns is set as a fixed boundary. The specific technical details of the model construction will not be elaborated here. Step 3: Apply the obtained simplified basketball load model 3F(t) to the three-second zone of the basketball court in the finite element model as a concentrated force load; Step 4: After the load is applied, extract the vertical acceleration response data of the designated test point (such as the audience seating area), and determine whether the current structural design meets the vibration comfort requirements based on the corresponding vertical acceleration response limit requirements in the "Technical Standard for Vibration Comfort of Building Floor Structures". Step 5: If the judgment result meets the comfort requirements, the current finite element model can be used as the basic model for the design of the basketball court; if it does not meet the comfort requirements, the original finite element model needs to be optimized and adjusted. After each round of optimization, the load conditions before optimization are used to recalculate in the optimized finite element model, and the comfort judgment process is repeated until the vibration comfort of the basketball court meets the specifications. Finally, the finite element model that meets the requirements is used as the basic model for the design of the basketball court.

[0051] The finite element model that meets the requirements in this invention serves as the basic model for the design of the basketball court and is the core parameter basis for the formal design drawings.

[0052] In this invention, the specific optimization methods include: 1. Thickening the floor slab (the optimization range of thickening the floor slab needs to be controlled within 10%-20% of the original floor slab thickness), adding secondary beams or ribs, locally stiffening the three-second zone, optimizing the support method and layout, etc., to adjust the natural frequency of the floor slab so that it avoids the main frequency of the basketball load, reduces the risk of resonance between the load and the structure, and reduces the vibration response; 2. Adding additional vibration reduction measures such as floating floor slabs to enhance the vibration reduction capacity of the structure, weaken the vibration transmission, and improve the vibration comfort level of the venue.

[0053] Example 1 This embodiment targets the indoor basketball court scenario used by ordinary basketball enthusiasts, providing a basketball load model adapted to this scenario, and simultaneously offering a corresponding structural acceleration response prediction method, which can directly serve the structural design of such venues: Using the entire process from takeoff to landing as the time axis, a piecewise function is used to describe the load characteristics of each stage from takeoff to landing, establishing the basketball load, and conducting on-site measurements on an existing basketball court to verify the effectiveness of the simplified load model; a finite element model of the basketball court is established, and the aforementioned piecewise function load model is loaded into the corresponding basketball court activity area in the finite element model to predict the basketball court vibration under the most unfavorable working conditions, ensuring that the basketball court vibration comfort meets national standards. A method for obtaining a simplified calculation model of the most unfavorable working condition load for basketball sports, specifically including the following steps: S1. Establish a simplified model of the load on a single basketball.

[0054] The indoor basketball courts described in this embodiment are mostly used by ordinary basketball enthusiasts. Therefore, the data collection subjects (i.e., the test subjects) are aged 18-50, weigh between 50-90kg, have no history of sports injuries, can complete routine actions such as dribbling and stopping suddenly, and jumping in place, but have no professional training background.

[0055] This embodiment uses measured plantar force time history data to statistically analyze and calculate time parameters based on a model of an average basketball enthusiast. , , and and weight parameters The specific method is as follows: A field test was conducted on a basketball court on the roof of a building for ordinary basketball enthusiasts, collecting 220 sets of measured plantar force time history data. The specific method was as follows: test subjects wore force-measuring insoles (the plantar force measuring device used was the Loadsol® wireless force-measuring insole from Novel, USA, with a force sensing range of 0-5000N and a sampling frequency set to 100Hz) for data collection. The data collection subjects were ordinary basketball enthusiasts, and the test conditions included various basketball techniques such as a single three-step layup, a single jump shot, and two or three players rebounding. After removing outlier data, the least squares method was used to fit the parameters of the established piecewise load model segment by segment. The fitting effect of one typical load time history is shown below. Figure 3 As shown in Table 1, the relevant parameters of the simplified load model based on ordinary basketball enthusiasts were obtained statistically: t1=0.54 s, t2=0.72 s, t3=1.17 s, t4=1.24 s, F1=1670.09 N, F2=3137.97 N, a1=8.73, a2=0.50.

[0056] Table 1. Relevant parameters of the simplified load model in Example 1

[0057] Substituting the average value of the above parameters into the following five load functions, we obtain the load model for a single basketball game.

[0058] .

[0059] S2. Establish the load model 3F(t) corresponding to the most unfavorable working condition in basketball.

[0060] In this embodiment, the most unfavorable working condition in basketball is set as three people jumping simultaneously in the center area under the basket. The corresponding basketball load is simplified to the superposition of the foot force of the three athletes. At this time, the basketball load is 3F(t).

[0061] S3. Verify the load model.

[0062] Based on the structural design drawings, a local finite element model was established for the floor slabs, frame beams, and lower-level columns of the corresponding floors of the existing podium roof basketball court, such as... Figure 4 As shown. In this embodiment, the floor slab is simulated using SHELL181 elements, and the beams and columns are simulated using BEAM188 elements. All column bases are set as fixed boundaries. To simplify the calculation and ensure consistency of material properties, the elastic modulus of the beams, columns, and floor slab are taken as 3.15 × 10⁴ MPa, Poisson's ratio as 0.2, and density as 2500 kg / m³. The piecewise load function 3F(t) obtained by fitting in step S2 is used as a concentrated nodal force applied to... Figure 4The finite element model shown uses loading points to predict the vertical acceleration response of the floor slab under basketball load. Furthermore, on-site testing was conducted at the basketball court, with three athletes performing specified basketball movements at the load application points, obtaining measured values ​​of the vertical acceleration response at designated test points (e.g., the stands). Comparing the predicted and measured values ​​verifies the effectiveness of the simplified basketball load model. Figure 5 As shown, the predicted peak vertical acceleration at a certain location is 0.776 m / s², while the measured peak is 0.818 m / s², with a relative error of 5.13% and a root mean square error in the time domain of approximately 2.97%. Further analysis of the predicted time history is as follows... Figure 6 The spectrum analysis shown (vertical axis represents acceleration amplitude) shows that the predicted amplitude values ​​at the first five natural frequencies of the model are in good agreement with the measured values, verifying the accuracy of the simplified basketball load model.

[0063] Example 2 This embodiment takes the structural design of a multi-functional indoor basketball court as an example and proposes a basketball court structural design method, specifically a finite element model optimization method in basketball court structural design. The method is as follows: 1. The target audience of a certain multi-functional indoor basketball court is the general public, so the data collection target for plantar force is ordinary basketball enthusiasts, and the simplified basketball load model obtained in Example 1 is adopted. 2. Establish a finite element model of the basketball court. The initial structural parameters and design of the model are as follows: C40 concrete main beams with sections of 600×800mm, 500×800mm, and 600×900mm; secondary beams with sections of 250×750mm, 300×750mm, and 450×800mm; C45 prestressed concrete floor slabs with a base thickness of 120mm (including a 20mm leveling layer); ordinary columns with sections of 900×900mm, 850×850mm, and 800×800mm; steel-concrete composite columns with a wall thickness of 40mm and a section of 800×800mm; and matching shear walls with a thickness of 350mm; the elastic modulus of concrete is 3.25-3.35×10⁻⁶. 4 N / mm² (scaled 1.2 times according to concrete structure design standards), Poisson's ratio 0.2, density 2500kg / m³, and overall damping ratio 1.0%; the floor slab is discretized using Shell181 shell elements, the main and secondary beams and truss beams as well as the vertical load-bearing columns are simulated using Beam188 spatial beam elements, the steel-concrete composite columns are constructed using layered composite section technology in conjunction with Solid185 solid elements, and all column bases are set as fixed boundaries.

[0064] 3. The simplified basketball load model 3F(t) obtained in Example 1 is applied as a concentrated force load to the three-second zone of the basketball court finite element model. The specific loading points are as follows: Figure 7 As shown; 4. After loading, extract test points (test points can be selected from the audience seating area, such as...). Figure 7 The vertical acceleration response amplitude of the floor slab at positions one through four (as shown in the diagram) is 1.04 m / s². 2 ,like Figure 8 As shown, upon comparison, this vertical acceleration amplitude does not meet the requirement of no more than 0.7 m / s² for indoor basketball courts as stipulated in JGJ / T441-2019 "Technical Standard for Vibration Comfort of Building Floor Structures". 2 Requirements; 5. To optimize the structural acceleration response to meet the design standards, a floating floor was added to the original finite element model of the basketball court. The basic parameters of the floating floor are shown in Table 2. The load conditions before optimization were used to calculate the load in the finite element model with the added floating floor. The final vertical acceleration response of the floor was 0.65 m / s², which meets the design requirements.

[0065] Table 2 Basic parameters of floating floor slabs

[0066] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0067] Finally, it should be noted that the above are merely preferred embodiments of this application and are not intended to limit this application. Although this application has been described in detail with reference to the embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. However, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for obtaining a worst case load model for basketball, characterized by, The method comprises the following steps: S1, according to the variation characteristics of the load in the basketball running process, the single basketball movement is divided into five continuous stages of jump preparation and power accumulation section, ground lifting and jumping section, flight section, landing impact section and static load recovery section, and the load curve of each stage is fitted by using the corresponding function respectively, and a single basketball movement load simplified model is established; S2, the simultaneous jumping of three people in the center area under the basket in the basketball movement is set as the most unfavorable working condition, and a load simplified model corresponding to the most unfavorable working condition of the basketball movement is established; S3, the load simplified model corresponding to the most unfavorable working condition of the basketball movement is verified.

2. The method for obtaining the most unfavorable load model for basketball as described in claim 1, characterized in that, The specific method of step S1 is: S11, determining the data collection object according to the service object characteristics of the basketball venue to be designed; S12, wearing the foot force measuring device to complete the specified basketball technical action, collecting the foot force time history data and generating the load curve; S13, according to the slope inflection point, peak value, contact and off ground instantaneous characteristics of the load curve, the single basketball movement is divided into five continuous stages of jump preparation and power accumulation section, ground lifting and jumping section, flight section, landing impact section and static load recovery section by using time division points t1, t2, t3 and t4; S14, the load variation of each stage is fitted by using the segmented function, and a single basketball movement load simplified model is obtained.

3. The method of claim 2, wherein the method further comprises: determining the load of the basketball game by using the load of the basketball game in the most unfavorable working condition. In S14, the jump preparation and power accumulation section is fitted by using a power function, the ground lifting and jumping section is fitted by using a linear function, the flight section takes a constant value 0, the landing impact section is fitted by using a linear function, and the static load recovery section is fitted by using an exponential function.

4. The method of claim 3, wherein the method further comprises: determining the load of the basketball game by using the obtained load model. The single basketball movement load simplified model is: ； In the formula, is the load value at time t, with units of N; is the time variable, with units of s; is the body's own gravity, with units of N; , , and respectively represent the time demarcation points of different stages of the load simplified model; when , it belongs to the pre-jump force storage segment; when , it belongs to the take-off segment; when , it belongs to the airborne segment; when , it belongs to the landing impact segment; when , it belongs to the static load recovery segment; represents the peak value of the take-off segment load in the basketball load movement process, with units of N; is the peak value of the landing segment load, with units of N; represents the decay coefficient of the landing load peak value; represents the decay coefficient of the static load recovery segment.

5. The method for obtaining the most unfavorable working condition load model of basketball movement according to claim 4, characterized in that, The acquisition of a1 and a2 adopts the least square method, and the specific method is: first, taking the decay section data after t4, the noise is processed by using the moving average method, and then the processed data is fitted; second, the slope of the load curve on the left side of t4 is used as a constraint condition to limit the slope of the starting point of the decay section; third, the initial values of a1 and a2 are predicted, the objective function of the least square method is constructed, and the sum of the squares of each sampling time is minimized; finally, the objective function is solved and iterated by using a solver, and finally the optimal values of a1 and a2 can be obtained.

6. The method of claim 4, wherein the method further comprises: determining the load of the basketball game by using the load of the basketball game in the most unfavorable working condition. In S13, t1 is the time when the load of the jump preparation and power accumulation section reaches F1, t2 is the time when the foot leaves the ground and the load drops to 0, t3 is the time when the foot touches the ground and the load begins to rise, and t4 is the time when the load of the landing impact section reaches F2.

7. The method of claim 4, wherein the method further comprises: determining the load of the basketball game by using the load of the basketball game in the most unfavorable working condition. The specific method for verifying the model is: S31, a local finite element model of the target basketball venue is established based on the design drawing, the segmented load function 3F(t) fitted is used as a concentrated node force, and is applied to the loading point in the finite element model of the target basketball court, and the predicted value of the vertical acceleration response of the specified test point of the floor under the basketball movement load is predicted; S32, on-site testing is carried out in the target basketball court, three testers matching the service object characteristics are arranged to perform specified basketball actions at the load loading point, and the measured value of the vertical acceleration response of the specified test point of the floor in the whole movement process is obtained. S33, compare the predicted value and the measured value of the vertical acceleration response, if the relative error of the predicted value and the measured value of the vertical acceleration response of each test point is less than or equal to 10%, it is determined that the model is accurate; if the relative error of the predicted value and the measured value exceeds 10%, it is determined that the model is inaccurate.

8. A method of designing a basketball venue structure, characterized by, The method is; Step one, based on the characteristics of the service object of the basketball venue to be designed, the method of any one of claims 1-7 is used to determine and obtain the adapted basketball load simplified model 3F(t); Step two, build a finite element model of the basketball venue; Step three, load the obtained basketball load simplified model 3F(t) in the form of concentrated force load on the three-second zone of the finite element model of the basketball venue; Step four, extract the vertical acceleration response data of the specified test point, and determine whether the current structure design meets the vibration comfort requirement according to the corresponding limit value requirement in the Technical Standard for Vibration Comfort of Building Floor Structure; Step five, if the determination result meets the comfort requirement, the current finite element model is used as the basic model for the design of the basketball venue; If the comfort requirement is not met, the original finite element model needs to be optimized and adjusted.

9. The method of designing a basketball arena structure of claim 8, wherein, In step five, after each round of optimization of the finite element model, the load loading condition before optimization is used to recalculate in the optimized finite element model, and the comfort determination process is repeated until the vibration comfort of the basketball venue meets the specification requirement, and finally the finite element model that meets the requirement is used as the basic model for the design of the basketball venue.

10. The method of designing a basketball arena structure of claim 8, wherein, In step four, whether the vibration comfort requirement is met is determined according to the corresponding vertical acceleration limit value in JGJ / T441-2019 Technical Standard for Vibration Comfort of Building Floor Structure.

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