A rapid analysis method for complex drainage path roof surface

Abstract

The application provides a kind of complex drainage path roof surface drainage rapid analysis method, based on dynamic relaxation method, rainfall is dispersed from two dimensions of time and space into the position information of equal time step of particle on curved surface under the action of gravity.For the roof with complex drainage path, the slope of each place on the drainage path is different, the position of particle at the next time step is solved based on unbalanced force, and the motion trajectory of particle at each random position from initial position to the lowest point of roof surface under the action of gravity is obtained by iterative solution.The method can greatly reduce the time consumed by drainage analysis, facilitate the conceptual evaluation of drainage performance of roof structure design scheme with complex drainage path, especially for the roof structure composed of cable membrane system, in the case of mutual influence between structure performance and drainage performance, the method can quickly evaluate the drainage feasibility, greatly improve the design efficiency.

Description

Technical Field

[0001] This invention relates to the field of large-span spatial structure design and discloses a rapid drainage analysis method for complex drainage path roof surfaces. Background Technology

[0002] The efficient structural stress distribution of large-span cable-net structures often results in roofs that appear light and transparent. However, as a flexible structural system, cable-net structures deform more significantly under variable loads compared to traditional steel roofs. Membrane materials, also flexible, are increasingly being used as cladding materials in large-span cable-net structures due to their adaptability to large deformations. Membrane structures provide stiffness through prestressed curvature between boundaries with elevation differences; their shape is closely related to the magnitude of the prestress, the configuration of the boundaries, and the stiffness of the boundaries. As architects' aesthetic demands for roof designs continue to increase, the membrane shapes of roofs are becoming increasingly complex. This leads to increasingly complex drainage paths. However, computational fluid dynamics (CFD) analysis of drainage requires a very large amount of computation and takes a very long time. It is generally only suitable for verifying the designed roof membrane shape after the structural design is completed, and is not suitable for the design phase where multiple rounds of rapid assessment of drainage feasibility are needed. When designing cable-membrane structures, the roof drainage capacity can often only be qualitatively judged based on experience. Currently, there is no method for rapid analysis and evaluation of roof drainage.

[0003] The dynamic relaxation method discretizes the vibration process of a spatially discretized structural system in time, tracking the vibration process point by point (spatially) and step by step (temporally) to achieve specific computational analysis objectives. Since the dynamic relaxation method does not require calculating the total stiffness matrix or solving the stiffness equations in each iteration, the total computational workload and memory usage are less than those of the commonly used finite element method. Furthermore, the movement of rainwater on the curved surface of a roof can be viewed as the process of rainwater moving from a non-equilibrium position to its equilibrium position under the action of external forces, which is similar to the iterative principle of the dynamic relaxation method.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a rapid analysis method for drainage of complex drainage paths on curved roof surfaces, so as to shorten the analysis time and improve design efficiency.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a rapid drainage analysis method for complex drainage paths on curved roof surfaces, including:

[0008] S1: Establish a model of the roof surface to be simulated, and obtain the project location's temperature per unit time based on historical meteorological data. The rainfall data, multiplied by the projected area of ​​the roof's curved surface, yields the rainfall per unit time. The total volume of rainfall within And calculate the total mass of rainfall falling within the curved surface area per unit time. ;

[0009] S2: Total mass of rainfall per unit time Discretized The mass of an individual arranged on the curved surface according to the principle of uniform distribution density and random position is... particles, The particles remain in close contact with the curved surface.

[0010] S3: Apply gravity to all particles, and record the time as... ,particle The position is Based on the improved dynamic relaxation method and the particle's position on the curved surface, the particle is obtained. Unbalanced forces Under the action of this unbalanced force, The position of the particle at the time step ,in :

[0011]

[0012] in It is the acceleration due to gravity. Let be the angle between the surface normal at the particle's location and the direction of gravity. The coefficient of friction for the roof surface is approximately 0.013 for metal roofs and approximately 0.025 for PTFE roofs.

[0013]

[0014]

[0015]

[0016] Where t=0, ;

[0017] Find the particle position The closest point on the surface And calculate the distance between the particle's position and the nearest point. And compare the 2-norm of that distance. and ,in If the preset limit is... If the particle remains on the curved surface, proceed to the next step S4; otherwise, use... replace The particle's position at that moment is used to proceed to the next step, S4.

[0018] S4: Particle positions obtained from step S3 Determine whether the projection position of the particle on the ground plane (XY plane) is still within the projection range of the roof surface on the ground plane (XY plane). If so, proceed to the next step; otherwise, consider that the particle has left the surface, stop the iteration, and remove the particle from the model.

[0019] S5: Based on particle position Then, proceed to step S3 for the next iteration to recalculate the unbalanced forces acting on it. Determine the 2-norm of the unbalanced force. Is it less than ,in If the preset unbalanced force convergence limit is... Then consider particles Iterative convergence, stopping on the particle If the iteration continues, proceed to the next step S6; otherwise, return to step S3 and repeat steps S3 through S5.

[0020] S6: Calculate Particles Location With the lowest point of the surface Distance between :

[0021] ,

[0022] in, For particles X coordinate of position X coordinates of the lowest point of the surface The difference between them For particles Y-coordinate of position Y-coordinate of the lowest point of the surface The difference between them For particles Z-coordinate of position Z-coordinate of the lowest point of the surface The difference between them; judgment Is it less than ,in If the preset distance limit is met, Then consider particles Remove the particle from the model if it leaves the roof surface; otherwise, view the particle as a separate entity. The particle, located at the point of water accumulation on the roof, ceases to move and remains within the model.

[0023] S7: Repeat steps S3 to S5 until the unbalanced forces of all particles converge iteratively. The time taken at this point is... This yields the position information of all particles on the surface at each time step. The particle positions at each time step are superimposed and merged onto the same surface to obtain the particle distribution on the surface when the particles are in a steady state.

[0024] S8: By counting the number of particles in different regions of the surface, the particle distribution density of each region of the surface can be obtained. And the distribution status and quality of water accumulation.

[0025] Compared with traditional CFD-based drainage analysis methods, this invention can significantly reduce the time consumed in drainage analysis, and has the following characteristics and beneficial effects:

[0026] 1. Facilitates a quick conceptual assessment of the drainage performance of roof structure designs with complex drainage paths, while also providing values ​​for water accumulation loads.

[0027] 2. For structures sensitive to drainage, the load values ​​obtained through this invention can be input into the finite element model to obtain the structural deformation under the water accumulation load. Based on the deformation results, the roof surface is updated again and drainage simulation is performed to obtain a new water accumulation load. This step is repeated until the deviation of the obtained deformation results is less than a preset threshold, at which point the iteration ends. This iteration can obtain accurate water accumulation distribution and load values.

[0028] 3. For roof structures composed of cable-membrane systems, the prestress level affects the structural morphology and performance, and the structural morphology and performance may also affect the drainage performance. This method can quickly assess the drainage feasibility of different prestress level schemes and improve design efficiency. Attached Figure Description

[0029] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 The flowchart illustrates the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention.

[0031] Figure 2 This is a schematic diagram of step S2 of the rapid drainage analysis method for complex drainage paths on roof surfaces provided by the present invention, in which rainfall is discretized into particles and arranged on the surface.

[0032] Figure 3 A schematic diagram of the trajectory of a single particle on the curved surface obtained by the rapid drainage analysis method for complex drainage path roof surfaces provided by this invention.

[0033] Figure 4 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0034] Figure 5 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0035] Figure 6 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0036] Figure 7 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0037] Figure 8 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0038] Figure 9 The time step obtained by the rapid drainage analysis method for complex drainage paths on curved roof surfaces provided by this invention A schematic diagram of the position of the surface particles at a given time.

[0039] Figure 10 This is a schematic diagram of the particle distribution results after superimposing the particle positions of each time step onto the same curved surface in the rapid drainage analysis method for complex drainage paths of roof surfaces provided by the present invention. Detailed Implementation

[0040] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0042] This invention provides a rapid drainage analysis method for roof surfaces with complex drainage paths. Based on the dynamic relaxation method, rainfall is discretized in both time and space dimensions into the positional information of particles under gravity on the surface at equal time steps. For roofs with complex drainage paths, the slope varies at different points along the path, resulting in different magnitudes of unbalanced forces on the particles at different slopes. The position of the particles at the next time step is determined based on these unbalanced forces. This iterative solution continues until the positions of all particles no longer change or they leave the surface. This state is considered as all particles leaving the roof and completing drainage. The resulting trajectory of particles at random positions moving from their initial positions to the lowest point of the roof surface under gravity is obtained. Figure 3 As shown, by superimposing the positions of particles at each time step, from the appearance of a particle to the cessation of particle iteration, the regional particle density of the entire roof swarm in a steady state can be obtained. In areas with gentler roof slopes, the water flow velocity is slower, corresponding to slower particle movement. After superposition, the number of particles in areas with gentle slopes will be greater, resulting in higher density. The water accumulation distribution when the roof water volume reaches a steady state can be obtained from the particle density distribution and particle weight. This method can significantly reduce the time consumed in drainage analysis, facilitating a rapid conceptual assessment of the drainage performance of roof structure designs with complex drainage paths. Especially for roof structures composed of cable-membrane systems, where structural performance and drainage performance are interdependent, this method can quickly assess drainage feasibility and greatly improve design efficiency.

[0043] Combination Figures 1 to 10 As shown, this embodiment provides a rapid drainage analysis method for complex drainage paths on curved roof surfaces, including:

[0044] S1: Establish a model of the roof surface to be simulated, and obtain the project location's temperature per unit time based on historical meteorological data. The rainfall data, multiplied by the projected area of ​​the roof's curved surface, yields the rainfall per unit time. The total volume of rainfall within And calculate the total mass of rainfall falling within the curved surface area per unit time. ;

[0045] S2: Total mass of rainfall per unit time Discretized The mass of an individual arranged on the curved surface according to the principle of uniform distribution density and random position is... particles, such as Figure 2 and Figure 4 As shown, The particles remain in close contact with the curved surface.

[0046] S3: Apply gravity to all particles, and record the time as... ,particle The position is Based on the improved dynamic relaxation method and the particle's position on the curved surface, the particle is obtained. Unbalanced forces Under the action of this unbalanced force, The position of the particle at the time step ,in :

[0047]

[0048] in It is the acceleration due to gravity. Let be the angle between the surface normal at the particle's location and the direction of gravity. The coefficient of friction for the roof surface is approximately 0.013 for metal roofs and approximately 0.025 for PTFE roofs.

[0049]

[0050]

[0051]

[0052] Where t=0, ;

[0053] Find the particle position The closest point on the surface And calculate the distance between the particle's position and the nearest point. And compare the 2-norm of that distance. and ,in If the preset limit is... If the particle remains on the curved surface, proceed to the next step S4; otherwise, use... replace The particle's position at that moment is used to proceed to the next step, S4.

[0054] S4: Particle positions obtained from step S3 Determine whether the projection position of the particle on the ground plane (XY plane) is still within the projection range of the roof surface on the ground plane (XY plane). If so, proceed to the next step; otherwise, consider that the particle has left the surface, stop the iteration, and remove the particle from the model.

[0055] S5: Based on particle position Then, proceed to step S3 for the next iteration to recalculate the unbalanced forces acting on it. Determine the 2-norm of the unbalanced force. Is it less than ,in If the preset unbalanced force convergence limit is... Then consider particles Iterative convergence, stopping on the particle If the iteration continues, proceed to the next step S6; otherwise, return to step S3 and repeat steps S3 through S5.

[0056] S6: Calculate Particles Location With the lowest point of the surface Distance between :

[0057] ,

[0058] in, For particles X coordinate of position X coordinates of the lowest point of the surface The difference between them For particles Y-coordinate of position Y-coordinate of the lowest point of the surface The difference between them For particles Z-coordinate of position Z-coordinate of the lowest point of the surface The difference between them; judgment Is it less than ,in If the preset distance limit is met, Then consider particles Remove the particle from the model if it leaves the roof surface; otherwise, view the particle as a separate entity. The particles are located in the area where water accumulates on the roof and cannot be drained, so the particles remain in the model.

[0059] S7: Repeat steps S3 to S5 until the unbalanced forces of all particles converge iteratively. The time taken at this point is... This yields the position information of all particles on the surface at each time step. ,like Figures 5-9 As shown, the particle positions at each time step are superimposed and merged onto the same surface to obtain the particle distribution on the surface when the particles are in a steady state, as shown. Figure 10 As shown;

[0060] S8: By counting the number of particles in different regions of the surface, the particle distribution density of each region of the surface can be obtained. And the distribution status and quality of water accumulation.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapid analysis of complex drainage path roof surfaces, characterized by, Comprising: S1: Establish the model of the roof surface that needs to be simulated, and obtain the rainfall data of the project site per unit time based on historical meteorological data. Multiply the unit rainfall by the projected area of the roof surface to obtain the total rainfall volume per unit time within the surface range, and calculate the total mass of rainfall falling within the surface range per unit time. ;​​​ S2: the total mass of rainfall per unit time discretized into individual masses of particles, which move in close proximity to the surface. S3: Apply gravity to all particles, and record the time as... ,particle The position is Based on the improved dynamic relaxation method and the particle's position on the curved surface, the particle is obtained. Unbalanced forces Under the action of this unbalanced force, The position of the particle at the time step ,in : ； wherein g is the acceleration of gravity, is the angle between the normal to the surface at the position of the particle and the direction of the gravitational force, is the friction coefficient of the roof surface, which is approximated by 0.013 for a metal roof and by 0.025 for a PTFE roof; ； ； ； where t = 0, ; Find the particle position The nearest point on the curved surface Calculate the distance between the particle position and the nearest point And compare the 2-norm of the distance With Where Is a preset limit, if The particle is still on the curved surface, go to the next step S4, otherwise, replace With As the particle position at this moment, go to the next step S4 S4: the particle position obtained according to step S3 , judging whether the projection position of the particle on the horizontal plane is still within the projection range of the roof curve on the horizontal plane, if yes, entering the next step, otherwise, considering that the particle has left the curve, stopping iteration, and removing the particle from the model; S5: according to the particle position , re-entering the S3 step for the next iteration, re-computing the unbalanced force , judging the 2-norm of the unbalanced force whether it is less than , where is a preset unbalanced force convergence limit, if , the particle iteration is considered to be converged, stopping the iteration of the particle , and entering the next step S6; otherwise, returning to the S3 step and re-executing the S3 step to the S5 step; S6: Calculate Particles Location and the lowest point of the surface Distance between : , ； in, For particles X coordinate of position X coordinates of the lowest point of the surface The difference between them For particles Y-coordinate of position Y-coordinate of the lowest point of the surface The difference between them For particles Z-coordinate of position Z-coordinate of the lowest point of the surface The difference between them; judgment Is it less than ,in If the preset distance limit is met, Then consider particles Remove the particle from the model if it leaves the roof surface; otherwise, view the particle as a separate entity. The particles are located in the area where water accumulates on the roof and cannot be drained, so the particles remain in the model. S7: repeat steps S3 to S5 until the unbalanced force of all particles converges, and the time is recorded as , and the position information of each particle at each time step on the curved surface is obtained , and the particle distribution when the particles on the curved surface are in a steady state is obtained by superimposing and combining the particle positions at each time step on the same curved surface. S8: Count the number of particles in different regions on the curved surface, i.e. obtain the particle distribution density of each region on the curved surface and the water distribution state and distribution quality.

Images