Evaluation and analysis method for wind-induced response of tree

Abstract

The invention provides a tree wind-induced response evaluation and analysis method, and relates to the technical field of disaster prevention and reduction engineering, and the method comprises the steps: carrying out the construction of a geometric model for a target tree; on the basis of the geometric model, CFD analog simulation is carried out, and wind pressure time history data and crown load data of CFD grid points of the branches under different wind field conditions are obtained; finite element mesh generation is carried out on the geometric model, a finite element model is constructed, and mesh unit types in the model comprise hexahedron units, tetrahedron units and wedge-shaped units; the branch wind pressure time history data and the crown load data are mapped to the surface of a finite element model, structural finite element analysis is carried out, and cloud chart data of stress and displacement of the target tree changing along with time under different wind field conditions are obtained; and carrying out wind-induced response analysis and wind resistance evaluation on the target tree based on the cloud picture data and the wind-induced damage criterion of the tree. According to the technical scheme, a scientific basis can be provided for understanding the response behavior of the target tree under the strong wind condition.

Description

Technical Field

[0001] This application relates to the field of disaster prevention and mitigation engineering technology, specifically to an assessment and analysis method for the wind-induced response of trees. Background Technology

[0002] In recent years, with the intensification of global climate change, strong monsoons, typhoons, tornadoes, downbursts, and other severe convective weather events have become more frequent, posing serious challenges to the ecological environment and urban safety. Against this backdrop, trees, due to their relatively fragile structure, are highly susceptible to root collapse and branch breakage when encountering strong winds, which not only damages the natural environment but also poses a potential threat to human society. Therefore, scientifically and rationally assessing the wind-induced response patterns and wind resistance capabilities of trees under strong wind conditions has become a crucial issue that urgently needs to be addressed in the field of disaster prevention and mitigation engineering.

[0003] The response of objects (such as buildings and trees) in a wind field is related to both their aerodynamic and dynamic effects, and the fluid-structure interaction (FSI) between the two influences their wind-induced response. Existing technologies, such as Chinese patent application CN202110439793.7, propose a wind resistance analysis method for building structures considering bidirectional FSI effects, providing theoretical support for wind-resistant design in the building field. However, compared to buildings, trees have more complex geometries, such as complex trunks, branches, and dense leaf distribution. These characteristics make the FSI behavior of trees in a wind field more complex. Therefore, the bidirectional FSI analysis method proposed in the aforementioned patent is inefficient for analyzing the wind-induced response of trees, making it difficult to effectively assess the wind resistance performance of trees.

[0004] Therefore, developing a wind-induced response assessment method that can effectively address the complex morphological characteristics of trees has become an important task in the field of disaster prevention and mitigation engineering. Summary of the Invention

[0005] To at least partially overcome the problems existing in related technologies, embodiments of this application provide a method for evaluating and analyzing the wind-induced response of trees, which employs numerical simulation combined with specific data processing methods to effectively achieve the analysis and evaluation of the wind-induced response of trees.

[0006] This application provides a method for evaluating and analyzing the wind-induced response of trees in some embodiments, the method comprising: A geometric model is constructed for the target tree to obtain a first model representing the geometric morphological information of the tree. Based on the first model, CFD simulation was performed to obtain wind pressure time history data and canopy load data of each CFD grid point on the branch surface in the model under different atmospheric boundary layer wind field conditions. The first model is meshed using finite element methods based on the morphological characteristics of the trees. A second model for finite element analysis is constructed by combining the mechanical performance parameters of the target trees. The mesh element types in the second model include hexahedral elements, tetrahedral elements, and wedge elements. Based on the spatial location matching relationship, the wind pressure time history data and crown load data of each CFD grid point on the branch surface are mapped to the surface of the second model, and structural finite element analysis is performed accordingly to obtain cloud map data characterizing the stress and displacement of the target tree under different wind field conditions over time. Based on the cloud map data and the tree wind-induced damage judgment criteria, the wind-induced response assessment and analysis of the target trees are carried out.

[0007] In one possible implementation, the process of mapping the wind pressure time history data of each CFD grid point on the branch surface to the second model surface includes the following allocation process for each grid point in each CFD grid point: Based on the spatial coordinates of the CFD grid point and the spatial coordinates of each grid cell, the spatial range is filtered and the plane normalized normal vector is verified to determine the proposed grid surface for the CFD grid point. When there is only one proposed grid surface, the proposed grid surface is determined as the grid surface for the CFD grid point; when there are multiple proposed grid surfaces, the grid surface for the CFD grid point is determined from each of the proposed grid surfaces by area verification.

[0008] In one possible implementation, the spatial range filtering is performed based on the following expression: Where x, y, and z represent the coordinate values ​​of the CFD grid points in space along each direction. and These correspond to the minimum and maximum values ​​of the x-axis coordinates of the mesh surface. and These correspond to the minimum and maximum values ​​of the y-axis coordinates of the mesh surface. and These correspond to the minimum and maximum values ​​of the z-axis coordinate of the mesh surface. This indicates the coordinate tolerance set based on the grid surface size.

[0009] In one possible implementation, the plane normalized normal vector verification includes performing the following verification process for each mesh face selected based on the spatial range: Calculate the normalized normal vector of the mesh surface based on the coordinates of its three vertices; The distance from the CFD grid point to the grid surface is determined by multiplying the normalized normal vector with the direction vector formed by connecting the CFD grid point to any vertex of the grid surface. The verification is confirmed to be successful when the distance is less than or equal to the fixed distance tolerance.

[0010] In one possible implementation, the area method verification includes performing the following verification process for each of the proposed grid surfaces: Calculate and determine the area vector of the mesh surface, and calculate and determine the projected area vector of the CFD mesh point to each edge of the mesh surface; The verification is considered successful when the directions of each projected area vector are consistent with those of the area vector, and the difference between the total area of ​​each projected area vector and the area of ​​the area vector is less than or equal to the area tolerance.

[0011] In one possible implementation, both the area tolerance and the coordinate tolerance are set in an incremental sequence.

[0012] In one possible implementation, the canopy load data consists of the resultant force and moment time history data of the surface of each sub-region of the canopy; the process of mapping the canopy load data to the surface of the second model includes the following allocation processing for the resultant force and moment time history data of each sub-region: Create a reference point at the geometric center of the tree branch model corresponding to the sub-region, and establish the correspondence between the reference point and the grid cells within a predetermined radius. Associate the resultant force and moment time history data of the sub-region with the corresponding grid cells.

[0013] In one possible implementation, the finite element mesh is generated using the following partitioning strategy: hexahedral elements are used for the trunk of the tree, wedge-shaped elements are used for the branches, and tetrahedral elements are used for the connection between the trunk and the branches.

[0014] In one possible implementation, during the CFD simulation process, a large eddy simulation turbulence model is used to simulate and reproduce the turbulent structure of the flow field around the trees, and the CDRFG method is used to generate atmospheric boundary layer turbulence.

[0015] In one possible implementation, the process of constructing the geometric model includes: The investigation aims to obtain information on the species and age of the target trees. Based on the species and age information, the geometric morphological parameters of the trees are calculated and determined using a priori formulas. These geometric morphological parameters include tree height, diameter at breast height (DBH), crown length at each height position, and crown radius. A geometric model is constructed based on the aforementioned geometric morphological parameters.

[0016] The tree wind-induced response evaluation and analysis method provided in this application, for a target tree, constructs a first model representing the tree's geometric morphology information to accurately reflect the tree's actual geometric characteristics. Based on this model, CFD simulation is performed to obtain wind pressure time history data and crown load data of each CFD grid point on the branch surface under different wind field conditions, providing solid data support for subsequent analysis. Furthermore, based on the tree's morphological characteristics, the first model is meshed using a finite element analysis framework. A second model is constructed using a combination of hexahedral, tetrahedral, and wedge-shaped mesh elements, combined with the mechanical performance parameters of the target tree. Based on spatial location matching relationships, the wind pressure time history data and crown load data of the branch CFD grid points are mapped onto the surface of the second model, and structural finite element analysis is performed accordingly. This approach, which combines CFD simulation with finite element simulation, improves the adaptability and flexibility of the model while ensuring the stability of numerical calculations. It can effectively obtain the changes in tree stress and displacement under different wind conditions, providing a scientific basis for understanding the response behavior of trees under strong wind conditions. This, in turn, provides strong support for identifying potential risk areas and formulating reasonable disaster prevention and mitigation measures in relevant disaster prevention and mitigation engineering applications.

[0017] Other advantages, objectives, and features of this application will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from an examination of the following, or may be learned from the practice of the invention. Attached Figure Description

[0018] The accompanying drawings are used to provide a further understanding of the technical solutions of this application or the prior art, and constitute a part of the specification. The drawings illustrating embodiments of this application, together with the embodiments of this application, are used to explain the technical solutions of this application, but do not constitute a limitation on the technical solutions of this application.

[0019] Figure 1 A flowchart illustrating a method for evaluating and analyzing the wind-induced response of trees according to an embodiment of this application; Figure 2 This is a schematic diagram illustrating a first model of Pinus sylvestris constructed in one embodiment of this application; Figure 3 This is a schematic diagram illustrating the CFD simulation computational domain and boundary conditions of the target tree in one embodiment of this application; Figure 4 This is a schematic diagram illustrating the mesh generation for a CFD simulation of a target tree in one embodiment of this application; Figure 5 This is a schematic diagram illustrating the scatter distribution of each sub-region of the model tree canopy in one embodiment of this application; Figure 6 This is a schematic diagram illustrating the boundary planes of the sub-regions of the model canopy in one embodiment of this application; Figure 7 This is a schematic diagram illustrating the mesh generation of the second model of Pinus sylvestris constructed in one embodiment of this application; Figure 8 This is a schematic diagram illustrating the process of allocating CFD mesh points and finite element mesh surfaces in one embodiment of this application; Figure 9 This illustration shows the positional relationship between CFD mesh points and finite element mesh surfaces in one embodiment of this application. Figure 1 ; Figure 10 This is a schematic diagram illustrating the triangular mesh surface of a finite element tetrahedral element in one embodiment of this application; Figure 11 This illustration shows the positional relationship between CFD mesh points and finite element mesh surfaces in one embodiment of this application. Figure 2 ; Figure 12 This illustration shows the positional relationship between CFD mesh points and finite element mesh surfaces in one embodiment of this application. Figure 3 ; Figure 13 This is a schematic diagram illustrating the stress cloud map data of a target tree in one embodiment of this application; Figure 14 This is a schematic diagram illustrating the displacement cloud map data of a target tree in one embodiment of this application; Figure 15 This is a schematic diagram of the distribution of bending moment and shear force along the trunk of the target tree in one embodiment of this application; Figure 16 This is a cloud map showing the maximum shear stress of a target tree in one embodiment of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be described in detail below. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] As described in the background section, scientifically and rationally assessing the wind-induced response and wind resistance of trees under strong wind conditions has become a crucial issue urgently needing resolution in the field of disaster prevention and mitigation engineering. The response of objects (such as buildings and trees) in a wind field is related to both their aerodynamic and dynamic effects, and the fluid-structure interaction (FSI) between these two effects influences their wind-induced response. Existing related technologies, such as Chinese patent application CN202110439793.7, propose a wind resistance analysis method for building structures considering bidirectional FSI effects, providing theoretical support for wind-resistant design in the building field. However, compared to buildings, trees have more complex geometric forms, such as complex crown structures and branch distributions. This makes it difficult to efficiently apply the FSI analysis method proposed in the aforementioned patent in analyzing the wind-induced response of trees, thus hindering the effective assessment of their wind resistance performance.

[0022] Based on this, this application proposes an evaluation and analysis method for wind-induced response of trees, which adopts specific modeling and data processing methods to effectively realize the analysis and evaluation of wind-induced response of trees.

[0023] like Figure 1 As shown, in one embodiment, the tree wind-induced response evaluation and analysis method of this application includes: Step S110: Construct a geometric model for the target tree to obtain a first model representing the geometric morphological information of the tree; It is easy to understand that the target trees here refer to the trees to be evaluated and analyzed in reality. Their morphological and geometric dimensions can be obtained through relevant technical means, and the first model mentioned above can be constructed through geometric modeling. The technical means here may include actual field measurement, remote sensing measurement and image recognition, sampling test, etc. The constructed first model is a numerical geometric model used for engineering research. It can actually reflect the relevant characteristics of the objective research object for the research purpose.

[0024] Furthermore, based on existing tree modeling and relevant research on various trees in forestry science, for target trees with existing relevant modeling frameworks, the first model can be constructed based on these frameworks. Specifically, in this case, the above-mentioned geometric model construction process includes: The investigation obtains information on the species and age of the target trees. For example, based on the actual investigation, the species of the target trees is Scots pine, and the age is 5 years.

[0025] Furthermore, based on species and age information, the geometric morphological parameters of trees can be calculated and determined using prior formulas. These geometric morphological parameters include tree height, diameter at breast height (DBH), crown length at various height positions, and crown radius.

[0026] Specifically, taking a 5-year-old Pinus sylvestris as an example, the tree height parameters can be determined by fitting the following expression (prior formula) under the known modeling framework: (1) In expression (1), H represents the tree height parameter and t represents the tree age; thus, the tree height parameter of a 5-year-old Pinus sylvestris is determined to be 2 meters.

[0027] The chest diameter parameter can be determined by fitting the following expression based on the known modeling framework: (2) In expression (2), H represents the tree height parameter, and D represents the diameter at breast height parameter. This represents the reference coefficient of the model; based on this expression, the diameter at breast height (DBH) parameter of a 5-year-old Pinus sylvestris is determined to be 0.05 meters.

[0028] Based on the known modeling framework and actual surveys, with a crown length ratio of 80% and a crown spread rate of 0.4 times the tree height, the crown length and crown radius parameters at different locations on the outer contour of the crown can be determined by fitting the following piecewise parabolic function expression: (3) (4) In expressions (3) and (4), CL represents crown length, CR represents crown radius, LCR represents maximum crown radius, LCL represents maximum crown length, and I represents parameter variable; These represent model reference coefficients, such as the corresponding values ​​of 1.6679, 0.0385, 0.5459, and -3.68739.

[0029] In addition, to facilitate the construction of subsequent finite element analysis models, the mechanical performance parameters of trees can be determined based on the species information. The types of mechanical performance parameters here include shear modulus, Young's modulus, and the corresponding Poisson's ratio, etc.

[0030] Specifically, for example, the density of Scots pine can be determined to be 820 kg / m³ by consulting the "Timber Handbook". 3 However, given that trees are anisotropic materials, their mechanical properties differ in different directions. Therefore, in subsequent modeling, the longitudinal direction E needs to be considered. z Radial E ρ and tangential E T The Young's modulus was set to 8.8 GPa, 0.7744 GPa, and 0.3872 GPa, respectively, corresponding to Poisson's ratios. , , The values ​​are then taken as 0.35, 0.32, and 0.31 respectively; shear modulus , , The values ​​were set to 0.7543 GPa, 0.6255 GPa, and 0.0368 GPa, respectively.

[0031] Once the aforementioned tree geometric parameters are determined, a geometric model can be constructed based on these parameters. For example, in practical implementation, relevant 3D modeling software such as 3ds Max and Rhino can be used to construct the geometric model. Figure 2 As shown, this is a first model constructed in one embodiment, with the target tree being Pinus sylvestris.

[0032] Next, proceed to step S120, and perform CFD simulation based on the first model to obtain wind pressure time history data and canopy load data of each CFD grid point on the branch surface in the model under different atmospheric boundary layer wind field conditions.

[0033] Computational Fluid Dynamics (CFD) is a technique that uses numerical calculations and computer simulations to solve the governing equations of fluid flow, heat transfer, mass transfer, and related physical phenomena. It is a commonly used technique in the study of wind-induced effects. Its core principle is to discretize a continuous fluid system into a numerical grid and then use algorithms to approximate the solution of the governing equations to predict fluid behavior. The overall implementation process of CFD simulation in this application is similar to that in existing technologies; only the technical points closely related to the technical scenario of this application are briefly described here. Figure 3 The diagram shown is a schematic illustration of the CFD simulation computation domain and boundary conditions of the target tree in one embodiment of this application. During the CFD simulation process of this application, both the canopy and branches are subjected to wind loads. Considering the differences in their actual properties, different processing methods are adopted in this application to facilitate subsequent analysis and processing.

[0034] Specifically, in order to reproduce the turbulent structure of the flow field around trees and obtain wind load information, this application uses a large eddy simulation (LES) turbulence model to simulate and reproduce the turbulent structure of the flow field around trees during the CFD simulation process. In the LES, the CDRFG (Consistent Discretizing Random Flow Generation) method is used to generate atmospheric boundary layer turbulence. That is, in the CFD simulation, the turbulent characteristics at the wind field inlet are adjusted by the CDRFG method to adjust the frequency distribution and correlation of the turbulence, so that the generated turbulent velocity field is closer to the real atmospheric turbulence characteristics in terms of frequency distribution and spatial correlation, so as to obtain subsequent wind pressure time history data based on the optimized turbulent inlet conditions.

[0035] In practice, the control equations for large eddy simulation are expressed as follows: (5) (6) In expressions (5) and (6), p and p represent the filtering speed and pressure, respectively. μ represents fluid density, and μ represents dynamic viscosity. This represents the subgrid scale (SGS) stress, which is smaller than the characteristic scale of the filter function.

[0036] SGS stress is modeled using the Smagorinsky model and can be determined by the following expression: (7) In expression (7), Represents the strain rate tensor. It is the turbulent viscosity coefficient. This indicates the trace of SGS stress.

[0037] The turbulent viscosity coefficient can be expressed as: (8) In expression (8), This represents the Smagorinsky constant, which is set to 0.13 here. The characteristic filter length is represented by the Van Driest attenuation function, which is used in the calculation to correct the near-surface SGS stress.

[0038] like Figure 4 The diagram shown is a schematic illustration of the mesh division for CFD simulation of a target tree in one embodiment of this application.

[0039] It should also be noted that in step S120, in order to facilitate subsequent analysis, the CFD simulation results of the branches can be post-processed to obtain the pressure values ​​of each grid point on the outer surface of the branches in the CFD model as a function of time, and output in the form of a txt document. The obtained data consists of 4 columns, namely the x-coordinate, y-coordinate and z-coordinate of the grid point, and the pressure value as a function of time.

[0040] On the other hand, regarding the tree canopy in CFD simulations, considering the characteristics of the technical scenario in this application, the tree canopy can be assumed to be a porous medium to achieve efficient simulation of the flow field around the forest belt. Accordingly, in the CFD simulation process, this application uses the Darcy-Forchheimer model to simulate the air-blocking effect of the forest belt canopy.

[0041] Specifically, based on the air obstruction effect of the forest canopy, a source term S needs to be added to the momentum equation. i According to the Darcy-Forchheimer model, the source term S... i The value can be determined based on the following expression: (9) In expression (9), D i F represents the viscous drag coefficient. i U represents the inertial drag coefficient; U represents the velocity. .

[0042] It should also be noted that when the Reynolds number exceeds 5000, the viscous drag coefficient is much smaller than the inertial drag coefficient, and the viscous loss term... This can be disregarded; at this point, this application will consider D. i The value is 0; inertial loss term Representing the drag per unit volume of the canopy region, F is used in this application. i The value is 1.2 in the three directions of i=x, y and z, which corresponds to the assumption that it is an isotropic porous medium.

[0043] In the technical scenario of this application, the load on the tree crown is transferred to the branches. In order to facilitate the subsequent finite element analysis and realize the effective transfer of the wind load on the tree crown to each branch, the tree crown part in the model is discretized into a spatial scatter set, and the spatial scatter points are divided into multiple sub-regions based on the specific branch distribution. Based on the minimum distance criterion, each scatter point is mapped to the nearest branch surface.

[0044] For example, in this embodiment, such as Figure 5 As shown, based on the actual branch distribution, a total of 6 types of scattered points were generated. Then, a plane fitting was performed on the boundaries of the scattered points in each sub-region, and the resulting fitted plane was used as the basis for canopy division, as shown below. Figure 6 The diagram shows the boundary planes between various types of scattered points (each sub-region), and their mathematical expression is shown in Table 1 below. In actual implementation, the above fitting can be achieved using MATLAB tools.

[0045] Table 1. List of Mathematical Expressions for Boundary Planes In the technical solution of this application, to facilitate the overall analysis, the wind load of each sub-region is set to be applied to the geometric center of the corresponding tree branch (tree branch model). During the CFD simulation, the equivalent load on the canopy of each sub-region in the wind field can be obtained by integrating the stress over the surface of the corresponding sub-region. The obtained data includes the resultant force components (Fx, Fy, Fz) and moment components (Mx, My, Mz) relative to the geometric center of the tree branch. It is easy to understand that these resultant force components and moment components are also time history data. These data, together with the wind pressure time history data of the CFD data points, constitute the load basis for the finite element analysis in the subsequent step S140.

[0046] like Figure 1 As shown, based on step S110, this application also includes step S130, which involves dividing the first model into finite element meshes under the finite element analysis framework based on the tree morphological characteristics, and constructing a second model for finite element analysis in combination with the mechanical performance parameters of the target tree.

[0047] In the scenario described in this application, the conversion of wind pressure into structural load is required during the wind-induced response study. To address this, and considering the specific characteristics of this application's scenario, a targeted meshing strategy was employed for the branch sections when constructing the second model for finite element analysis. This ensures effective conversion of wind pressure into structural load and avoids the problems mentioned in the background section.

[0048] Specifically, the following meshing strategy is adopted for finite element analysis: hexahedral elements are used for the tree trunk, wedge-shaped elements are used for the branches, and tetrahedral elements are used for the junction of the trunk and branches. Figure 7 As shown.

[0049] In practical implementation, the first model constructed above can be imported into the ABAQUS finite element software platform for mesh generation. As mentioned above, the mesh generation in this application refers to the branches and trunk. In practice, the mesh element size used in the finite element method is significantly larger than that in computational fluid dynamics (CFD). This difference allows the surface mesh elements of the finite element model to be reasonably used as the framework for subsequent analysis. Regarding the mesh generation strategy, for the trunk of the tree, considering its relatively regular geometric shape, the inventors selected hexahedral elements for fine meshing to ensure computational accuracy and effectively control computational costs. At the junction of the trunk and branches, due to the complex geometry and uneven stress distribution in this area, tetrahedral elements, which are more adaptable, are used to better capture local stress concentration phenomena. For the branches of the tree, wedge-shaped elements are used for meshing, taking into account their slender structural characteristics, thereby improving computational efficiency while ensuring computational accuracy.

[0050] In practical terms, since finite element analysis software such as ABAQUS does not directly provide a function for mesh surface numbering, this application uses mesh element numbering as an alternative. The specific operation is as follows: first, the mesh surfaces to be analyzed in the model are created as a surface set; then, code is written using the Python programming language to batch export the element numbers and their corresponding mesh node numbers (referring to the vertices of the elements), and then a complete analysis framework is constructed based on this data. It should be noted that in finite element software, element numbering for different components usually restarts, which requires explicit differentiation of elements for different components. Figure 7 Taking the example of the Pinus sylvestris branch and trunk model shown, this model contains one trunk and six branches. Based on the above meshing strategy and numbering rules, at least seven surface sets need to be created to correspond to each component; however, for the outer sides and top surfaces of each cylinder, such as Figure 7 As shown in Figure (a), they physically belong to the same component, but from the perspective of analytical requirements, they also need to be strictly distinguished, which further increases the required number of surface sets to 14; in addition, as Figure 7 As shown in Figure (c), on the outer surface of the tetrahedron of the tree trunk, some areas are covered by branches. To ensure the accuracy and rationality of the model, redundant mesh surfaces need to be removed. For this special case, a separate surface set needs to be created for each. This is how... Figure 7 The model configuration shown will ultimately create 16 surface sets for the Pinus sylvestris model.

[0051] Then, the mesh faces in the constructed model are numbered using Python programming. Specifically, Python indexing is used to establish the element numbers on the model surface and the mesh node numbers connected to those elements; subsequently, mesh nodes on the elements that do not belong to the surface are removed. After completing the above operations, the element numbers are used as mesh face numbers to generate a frame face file ('sur_mian.txt'). Each line in this frame face file contains: the Surf identifier, the mesh face number, and the mesh node number enclosed in square brackets, in the format: Surf identifier, mesh face number, [mesh node number]. At the same time, the coordinates of the selected mesh nodes are exported ('sur_node.txt'). The main purpose of this step is to determine the specific spatial location of each frame face based on the mesh node coordinates, thereby providing accurate spatial positioning information for further analysis and research.

[0052] After completing steps S120 and S130, step S140 can be performed. Based on the spatial location matching relationship, the wind pressure time history data and canopy load data of each CFD grid point on the branch surface are mapped to the surface of the second model. Based on this, structural finite element analysis is performed to obtain data on the stress and displacement of the second model under different wind field conditions, that is, cloud map data characterizing the stress and displacement of the target tree under different wind field conditions.

[0053] It is easy to understand that, since this application uses an improved branch model construction method in step S130, a corresponding mapping processing method is required to effectively realize the data mapping association and achieve the purpose of converting wind pressure into structural load. To facilitate understanding of the technical solution of this application, the mechanism and overall process involved in the mapping processing will be explained here first.

[0054] From a data processing perspective, the mapping aims to establish an index relationship between CFD mesh points and mesh surfaces within the finite element analysis framework, thereby enabling the calculation of mesh surface pressure. The overall approach is as follows: Figure 8 As shown, the first step is to filter the spatial range of the points to be assigned (CFD mesh points) based on their coordinates. This means that the coordinates of the points to be assigned in the x, y, and z directions must all satisfy the condition that they are greater than or equal to the minimum and less than or equal to the maximum coordinates in the plane. However, in the model construction of this application, as... Figure 9 As shown, the cylindrical surface is composed of multiple straight lines. Some data points may not fall completely on the plane. In such cases, spatial filtering can only roughly select multiple mesh surfaces that are close to the points to be assigned. Therefore, in the overall process, a normal vector verification method is set to further select a more matching mesh surface. Based on this, further considering the construction method of the second model in this application, for hexahedral element type mesh elements, the mesh facets formed on the outer surface are quadrilaterals. In this case, by using the above-mentioned spatial range filtering and normal vector verification method, the quadrilateral mesh facet into which the CFD mesh point falls can be uniquely determined (e.g., Figure 11 (as shown in the illustration). For tetrahedral and wedge-shaped mesh elements, the resulting mesh faces are triangular, especially as shown in the illustration. Figure 10 As shown, the tetrahedral mesh elements on the tree trunk, due to their location on a curved surface, exhibit slight folding, resulting in six vertices on their surface and forming multiple triangular mesh faces. In this case, the proposed mesh face allocation, determined using the aforementioned spatial range filtering and planar normalized normal vector verification method, still consists of multiple faces (e.g., ...). Figure 12 (As shown in the illustration). In the technical solution of this application, to ensure the effective implementation of finite element analysis, it is necessary to ensure that each CFD mesh point uniquely falls within a mesh surface. Therefore, for this situation, as shown in the illustration... Figure 8 As shown, this application further introduces an area method for verification to uniquely confirm the triangular grid surface into which the point to be assigned falls.

[0055] Based on the above technical approach, as a specific implementation method, the process of mapping the wind pressure time history data of each CFD grid point on the branch surface to the second model surface in this application includes the following allocation process for each grid point in each CFD grid point: Based on the spatial coordinates of the CFD grid point and the spatial coordinates of each grid cell, the spatial range is filtered and the plane normalized normal vector is verified to determine the proposed grid surface for the CFD grid point. When there is only one proposed grid surface, i.e., the shape is quadrilateral, the proposed grid surface is determined as the assigned grid surface for the CFD grid point. When there are multiple proposed grid surfaces, i.e., the shape is triangular, the assigned grid surface for the CFD grid point is determined from each proposed grid surface through the area method verification.

[0056] Furthermore, as a specific implementation method, spatial range filtering is performed based on the following expression: (10) (11) (12) In the above expressions (10)-(12), x, y, and z represent the coordinate values ​​of the CFD grid points in each direction in space. and This corresponds to the minimum and maximum values ​​of the x-axis coordinate of the mesh surface. For example, Here, x1, x2, and x3 represent the x-axis coordinates of points on the mesh surface; similarly, and These correspond to the minimum and maximum values ​​of the y-axis coordinates of the mesh surface. and These correspond to the minimum and maximum values ​​of the z-axis coordinate of the mesh surface. This indicates the coordinate tolerance set based on the grid surface size.

[0057] It should be noted that the coordinate tolerance settings mentioned above are a method to ensure the effectiveness of the filtering process. If it can be avoided... Figure 9 In some cases, no matching mesh surface can be found. Furthermore, to ensure the effectiveness of the filtering, for example, considering that the approximate element size of the finite element mesh is controlled at 0.0065 (meters), the coordinate tolerance can be set in an incremental sequence, such as setting the incremental sequence to 0, 1e-4, 1e-3. In the actual filtering process, for each CFD mesh point, the filtering is first performed based on the above expressions (10)-(12) with a coordinate tolerance of 0. For data points that have no filtering matching results, the filtering is performed again based on the above expressions (10)-(12) after the coordinate tolerance is increased. This process is repeated until all CFD mesh points have filtering matching results.

[0058] Based on the above technical approach, as a specific implementation method, for a CFD grid point, the plane normalized normal vector verification includes the following verification process for each grid surface selected from the spatial range: Calculate the normalized normal vector of the mesh surface based on the coordinates of its three vertices. Multiply the normalized normal vector by the direction vector formed by connecting the CFD mesh point to any vertex of the mesh surface to determine the distance from the CFD mesh point to the mesh surface. If the distance is less than or equal to a fixed distance tolerance, the verification is considered successful. For example, the fixed distance tolerance can be set to 1e-3. Specifically, the normalized normal vector can be determined based on the following expression: (13) (14) In expressions (13) and (14), Indicates the normal quantity. The corresponding normalized normal vector is represented by x1, y1, z1, which represent the values ​​of the coordinate axes of a vertex, and x2, y2, z2 and x4, y4, z4 are similar.

[0059] Based on the above technical ideas, as a specific implementation method, the area method verification in this application includes the following verification process for each grid surface in each proposed grid allocation: calculating and determining the area vector of the grid surface, and calculating and determining the projected area vector from the CFD grid point to each edge of the grid surface; when the direction of each projected area vector is consistent with the area vector, and the difference between the total area of ​​each projected area vector and the area of ​​the area vector is less than or equal to the area tolerance, the verification is determined to be successful. For example, such as Figure 12 As shown in the illustration, assuming the three vertices of the tetrahedral triangular mesh face are A, B, and C, and the mesh point is P, then the area vector S of triangle ABC is... ABC Let the area be AB×AC, and half its magnitude is the area of ​​the triangle. Then calculate the projected area vectors from point P to each side of the triangle: the area vector S1 of triangle PBC is BP×CP, the area vector S2 of triangle PCA is CP×AP, and the area vector S3 of triangle PAB is AP×BP. Finally, determine whether the directions of S1, S2, and S3 are perpendicular to the plane of triangle PBC. ABC Consistency, and S1+S2+S3 and S ABC The relationship between their areas. Considering the area tolerance caused by the cylindrical curved surface, if we assume the area tolerance is zero, then the judgment condition is: if S1·S ABC ≥0、S2·S ABC ≥0、S3·S ABC ≥0, and S1+S2+S3=S ABC If point P is inside triangle ABC, the verification is successful. It's also easy to understand that, similar to the coordinate tolerance setting method described above, the area tolerance can also be set using an incremental sequence, such as 0, 1e-18, 1e-21, and a similar progressive iterative method can be used to implement the area verification process, ensuring that each grid point is uniquely assigned to a specific triangular grid surface.

[0060] like Figure 8 As shown, after the points to be assigned are determined, an assignment result record is generated. This process is repeated until all CFD grid points have a defined associated grid surface. The assignment result records are then summarized to form a result data file. For example, in one embodiment, after all grid points are assigned, a result file ('sur_main-node.txt') is output, with the format: Surf identifier, grid surface number, [data point number]. In this result file, the number of data points within square brackets corresponding to a single grid surface may reach dozens or even hundreds.

[0061] Then, based on the pressure file (wind pressure time history data) of each data point obtained in step S120, the pressure values ​​of all data points under each grid surface at each time point can be averaged, and the result is the representative time history pressure value of that grid surface. This generates the pressure time history file ('sur_main-data.txt') corresponding to the grid surface, with the following format: Surf identifier, grid surface number, pressure at each time point.

[0062] As described in step S120 above, in addition to the wind load directly on the branches, there is also the load transmitted from the canopy to the branches. In this application, the wind load of each sub-region is set to be applied to the geometric center of the corresponding branch. As mentioned above, the canopy load data in this application is the resultant force and moment time history data of the surface of each sub-region of the canopy. Therefore, the resultant force components and moment components of the canopy of each sub-region obtained in step S120 need to be allocated based on this setting as follows. Specifically, in the process of mapping the canopy load data to the surface of the second model in this application, the following allocation process is performed on the resultant force and moment time history data of each sub-region: In finite element analysis software (such as Abaqus), a reference point is created at the geometric center of the tree model corresponding to the sub-region, and the correspondence between the reference point and the mesh element within a predetermined radius is established. The resultant force and moment time history data of the sub-region are associated with the corresponding mesh element to realize the transfer of load and motion.

[0063] Specifically, to ensure the realization of the association, the minimum value of the predetermined radius is related to the actual size of the finite element elements. For example, the minimum predetermined radius is 0.0065m.

[0064] After completing the data preparation for the above two aspects, structural finite element analysis can be carried out based on the second model. The technical implementation of this part is similar to the existing technology, and this application will only briefly describe it here.

[0065] In practice, existing finite element analysis software tools cannot create surfaces from meshed files using the traditional "findAt" search function. To address this issue, this application, during actual data import, first reads the surface names, element numbers, and node numbers from the previously exported 'sur_mian.txt' document. Then, it iterates through all elements located on the surface sets, creating sets of all element surfaces. Next, it iterates through these surface sets one by one, reading the node numbers on each set and comparing these numbers with the node number list in 'sur_node.txt' to determine the surface sets located on the outer surfaces of the model. Finally, it deletes surface sets that do not meet the criteria and renames the surface sets that do meet the criteria. The time-history pressure corresponding to each grid surface is then imported into the Abaqus software in the form of an amplitude table. The first column of the amplitude table represents time, and the second column corresponds to the pressure at the corresponding time point. To ensure that the pressure is accurately applied to the corresponding grid surface, the names of each amplitude table are matched one-to-one with the renamed grid surfaces in the surface set; furthermore, for grid elements with canopy load transfer, the corresponding resultant force component and moment component data are also associated. Then, in the Abaqus tool, the pressure variation between adjacent time points is configured as a linear slope, and the analysis step is selected as dynamic implicit analysis. After the analysis is completed, the stress and displacement contour plots of the second model over time under different wind speed conditions are obtained. For example, for the Pinus sylvestris model in this embodiment, the obtained stress and displacement contour plots are as follows: Figure 13 and Figure 14 As shown.

[0066] Based on step S140, step S150 is performed, which evaluates and analyzes the wind-induced response of the target tree based on the stress and displacement cloud map data and the tree wind-induced damage judgment criteria obtained in step S140.

[0067] In step S150, the wind-induced response assessment analysis can be conducted based on the wind-induced damage discrimination criteria in existing relevant forestry scientific research, so as to provide theoretical support for actual disaster prevention and mitigation.

[0068] A moment-based failure criterion can be adopted. This approach, mechanistically speaking, assumes that the wind-induced vibration of a tree as a whole primarily manifests as bending vibration along the windward direction. When the bending moment load on a certain section of the model exceeds its bending capacity, bending failure is determined for that section. The maximum bending moment of a tree typically occurs in the root or branch tip region; therefore, the failure bending moment at the root or branch tip section is used as the criterion for failure. If the maximum bending moment value of the section exceeds its failure bending moment, structural failure is determined. For example, the bending moment indicator function can be defined as: (15) In expression (15), I represents the bending moment indicator function, I<1 means the section is safe, and I>1 means the element fails; B is the maximum bending moment of the section; The failure bending moment of the section is denoted as .

[0069] Failure moment It can be determined based on the following expression according to the theory of material strength: (16) In expression (16), represents the material strength, and r represents the cross-sectional radius.

[0070] When applying this bending moment failure criterion, the failure bending moment at the root and branch ends is first calculated based on strength theory. Then, the bending moment at each key end face is obtained based on finite element analysis (e.g., ...). Figure 15 The blue arrow in the middle indicates the direction of the bending moment at the cross section. Finally, the damage status of the tree is determined based on the value of the bending moment indicator function.

[0071] If a failure criterion based on shear stress can be adopted, this approach posits that under wind load, the connection between the trunk and branches of a tree will experience significant shear stress, leading to shear failure. For *Pinus sylvestris*, referring to the *Timber Handbook*, this application uses the maximum shear stress (4.8 MPa) of *Pinus koraiensis*, a species with similar mechanical properties, as the maximum shear stress of the *Pinus sylvestris* trunk. The strength parameter of the primary branches is taken as 80% of the trunk strength parameter, i.e., 3.84 MPa. Furthermore, in one embodiment, the maximum shear stress contour map of the *Pinus sylvestris* model can be configured and output using Abaqus software, specifically as follows... Figure 16 As shown.

[0072] Furthermore, it is readily understood by those skilled in the art that, based on the analytical data obtained in step S140, other wind-induced damage discrimination criteria in forestry scientific research can also be used for relevant assessment and analysis studies, which will not be detailed here.

[0073] Based on the above embodiments, this application employs a combination of computational fluid dynamics (CFD) simulation and finite element numerical simulation to establish a unidirectional fluid-structure interaction numerical simulation method for the wind-induced response of trees under wind conditions. First, a real wind field environment is simulated using CFD to accurately calculate the wind force on the tree surface. Then, wind pressure data is imported into the finite element model to analyze the stress and deformation processes of the trunk and branches. By quantifying the stress and deformation trends of trees under different wind speeds, the characteristics of wind-induced damage to trees can be predicted and identified in advance, providing a scientific basis for taking early measures to reinforce and prune trees and reduce the risk of wind-induced damage.

[0074] In terms of specific implementation, this application performs mesh generation of the first model under the finite element analysis framework based on the tree morphological characteristics. A second model is constructed using a combination of hexahedral, tetrahedral, and wedge-shaped meshes, which improves the model's adaptability and flexibility while enhancing computational stability, thus contributing to more reliable analysis results. Through spatial location matching and targeted data processing, wind pressure time history data from CFD mesh points can be effectively mapped onto the surface of the second model for structural finite element analysis. This allows for the acquisition of stress and displacement variations in trees under different wind conditions, effectively integrating the advantages of CFD and FEA, resulting in a highly efficient and accurate analysis process. Finally, the wind-induced response assessment of the target trees based on stress and displacement cloud map data provides a scientific basis for understanding tree behavior under strong wind conditions. In summary, this application solves the problem of traditional methods being unable to handle complex tree morphologies, significantly improving the accuracy and reliability of tree wind resistance performance assessment, and possesses significant theoretical value and practical application prospects.

[0075] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0076] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0077] It should be noted that in the description of this application, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, in the description of this application, unless otherwise stated, "a plurality of" means at least two.

[0078] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example 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.

[0079] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for evaluating and analyzing the wind-induced response of trees, characterized in that, include: A geometric model is constructed for the target tree to obtain a first model representing the geometric morphological information of the tree. Based on the first model, CFD simulation was performed to obtain wind pressure time history data and canopy load data of each CFD grid point on the branch surface in the model under different atmospheric boundary layer wind field conditions. The first model is meshed using finite element methods based on the morphological characteristics of the trees. A second model for finite element analysis is constructed by combining the mechanical performance parameters of the target trees. The mesh element types in the second model include hexahedral elements, tetrahedral elements, and wedge elements. Based on the spatial location matching relationship, the wind pressure time history data and crown load data of each CFD grid point on the branch surface are mapped to the surface of the second model, and structural finite element analysis is performed accordingly to obtain cloud map data characterizing the stress and displacement of the target tree under different wind field conditions over time. Based on the cloud map data and the tree wind-induced damage judgment criteria, the wind-induced response assessment and analysis of the target trees are carried out.

2. The method for evaluating and analyzing the wind-induced response of trees according to claim 1, wherein, The process of mapping the wind pressure time history data of each CFD grid point on the branch surface to the second model surface includes the following allocation process for each CFD grid point: Based on the spatial coordinates of the CFD grid point and the spatial coordinates of each grid cell, the spatial range is filtered and the plane normalized normal vector is verified to determine the proposed grid surface for the CFD grid point. When there is only one proposed grid surface, the proposed grid surface is determined as the grid surface for that CFD grid point; When there are multiple proposed grid surfaces, the assigned grid surface of the CFD grid point is determined from each of the proposed grid surfaces using the area method for verification.

3. The method for evaluating and analyzing the wind-induced response of trees according to claim 2, wherein, The spatial range filtering is performed based on the following expression: Where x, y, and z represent the coordinate values ​​of the CFD grid points in space along each direction. and These correspond to the minimum and maximum values ​​of the x-axis coordinates of the mesh surface. and These correspond to the minimum and maximum values ​​of the y-axis coordinates of the mesh surface. and These correspond to the minimum and maximum values ​​of the z-axis coordinate of the mesh surface. This indicates the coordinate tolerance set based on the grid surface size.

4. The method for evaluating and analyzing the wind-induced response of trees according to claim 3, wherein, The plane normalized normal vector verification includes performing the following verification process for each grid surface selected based on the spatial range: Calculate the normalized normal vector of the mesh surface based on the coordinates of its three vertices; The distance from the CFD grid point to the grid surface is determined by multiplying the normalized normal vector with the direction vector formed by connecting the CFD grid point to any vertex of the grid surface. The verification is confirmed to be successful when the distance is less than or equal to the fixed distance tolerance.

5. The method for evaluating and analyzing the wind-induced response of trees according to claim 3, wherein, The area method verification includes performing the following verification process for each of the proposed grid surfaces: Calculate and determine the area vector of the mesh surface, and calculate and determine the projected area vector of the CFD mesh point to each edge of the mesh surface; The verification is considered successful when the directions of each projected area vector are consistent with those of the area vector, and the difference between the total area of ​​each projected area vector and the area of ​​the area vector is less than or equal to the area tolerance.

6. The method for evaluating and analyzing the wind-induced response of trees according to claim 5, wherein, Both the area tolerance and the coordinate tolerance are set using an incremental sequence.

7. The method for evaluating and analyzing the wind-induced response of trees according to claim 1, wherein, The canopy load data consists of the resultant force and moment time history data of the surface of each sub-region of the canopy; the process of mapping the canopy load data to the surface of the second model includes the following allocation processing for the resultant force and moment time history data of each sub-region: Create a reference point at the geometric center of the tree branch model corresponding to the sub-region, and establish the correspondence between the reference point and the grid cells within a predetermined radius. Associate the resultant force and moment time history data of the sub-region with the corresponding grid cells.

8. The method for evaluating and analyzing the wind-induced response of trees according to claim 1, wherein, The following meshing strategy is used for the finite element meshing: hexahedral elements are used for the trunk of the tree, wedge-shaped elements are used for the branches, and tetrahedral elements are used for the connection between the trunk and the branches.

9. The method for evaluating and analyzing the wind-induced response of trees according to claim 1, wherein, In the CFD simulation process, the large eddy simulation turbulence model is used to simulate and reproduce the turbulent structure of the flow field around the trees, and the CDRFG method is used to generate atmospheric boundary layer turbulence.

10. The method for evaluating and analyzing the wind-induced response of trees according to claim 1, wherein, The process of constructing the geometric model includes: The investigation aims to obtain information on the species and age of the target trees. Based on the species and age information, the geometric morphological parameters of the trees are calculated and determined using a priori formulas. These geometric morphological parameters include tree height, diameter at breast height (DBH), crown length at each height position, and crown radius. A geometric model is constructed based on the aforementioned geometric morphological parameters.

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