Method for calculating local bending properties of a plant leaf

Abstract

The present application relates to a kind of plant leaf local bending characteristic calculation method.The connecting place of plant leaf petiole and plant stem is fixed, the image of the state of plant leaf not under load and the image after bending deformation under load are shot, load is applied to the tip of plant leaf, and the profile and deflection characteristic of plant leaf bending deformation can be clearly seen in image.Requirement, select the section of which contribution information is wanted to be obtained, determine the length and position of selected section, and find the curve segment representing the same section on two deflection curves.Determine the coordinates and vectors of key points, calculate the oblique direction tangent direction of each key point on each deflection curve, rotate and smoothly connect each segment vector, and then approximately calculate the contribution degree.The leaf local bending contribution degree calculation method provided in the present application can quantitatively describe the characteristics of each part of leaf on bending deformation, and solves the problem that it is difficult to quantitatively express the difference between leaf bending deformation when studying the mechanical characteristics of different leaves.

Description

Technical Field

[0001] This invention relates to a method for calculating the local bending characteristics of plant leaves, particularly for the study of bending characteristics of leaves with a large length-to-width ratio, and belongs to the fields of biomechanics and plant phenotyping. Background Technology

[0002] Simplifying large aspect ratio components into beam models is a common practice in engineering. This allows for rapid and convenient calculations while maintaining a certain level of accuracy, which is of great significance in engineering. This method is also widely used for slender plant leaves. Current methods for analyzing complex leaf structures include simplifying them into homogeneous beams, using numerical analysis, and using mechanical theory. Homogeneous beam models ignore non-uniformity and use various equivalent mechanical parameters for analysis. This is advantageous for focusing on the motion of a single point, but it has significant errors when studying the overall motion characteristics of the leaf. Numerical analysis methods, such as ANSYS, can effectively simulate the deformation characteristics of components when accurate mechanical parameters are obtained for each part. However, obtaining these mechanical parameters is often difficult, especially for naturally formed composite structures. Mechanical theory analysis only provides accurate solutions for structures with certain specific shapes, and it is difficult to draw conclusions applicable to engineering for complex, non-homogeneous structures. Therefore, how to provide a method for describing the bending behavior of crop leaves with large aspect ratios, reducing the tedious measurement of leaf mechanical parameters, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0003] The purpose of this invention is to describe the bending behavior characteristics of different parts of a leaf more accurately using less experimental data on the bending deformation of plant leaves. These characteristics are ultimately reflected in the influence on the leaf bending deflection. The invention also provides a method for calculating a parameter called contribution degree (Cd) that can be quantified and compared.

[0004] The contribution is defined as follows: the beam model undergoes bending deformation with a bending deflection of δ1. If a segment of the beam becomes rigid, and the bending deflection of the beam model becomes δ2, then:

[0005]

[0006] Contribution calculation treats the blade as a non-uniform beam model with initial bending, replacing one segment of the blade with a rigid section, and calculating the contribution of this segment. This is used to calculate the difference in bending deformation deflection when the deformable part is stiffened and subjected to the same load. When replacing the flexible segment with a rigid segment, care must be taken to ensure the smoothness of the connection. The blade's shape before deformation is assumed to be the shape when the blade is rigid; a rigid object will not deform under force and is called a rigid body. The deformed object reflects the deformation of a real object and is called a flexible body.

[0007] The length of the stiffening segment should generally not be too long, as a longer stiffening segment is more likely to affect the overall stress distribution. For research objects with greater flexibility, the stiffening segment should be relatively shorter. To reflect the difference in contribution of different segments of the entire leaf, the contribution is a function of the position and length of the stiffened part. The length and position of the segment directly affect the calculation results. Generally, a fixed length is chosen, and the position is changed to obtain the contribution of different segments on the same leaf. These limitations should be determined specifically according to the application of this method.

[0008] To calculate the contribution of the bent and deformed blade, an approximate calculation method includes the following steps:

[0009] 1) Fix the connection between the plant leaf petiole and the plant stem, and take images of the plant leaf in its unloaded state and after it has been subjected to load and bent deformation. The load is applied to the tip of the plant leaf, and the magnitude of the load is referenced to the typical load that a plant leaf experiences during rainfall, ranging from 50mg to 200mg. The images should clearly show the outline and deflection characteristics of the plant leaf bending deformation. Digitize the images before and after bending, and abstract the leaf into a deflection curve. The two deflection curves should be placed in the same coordinate system, with the same origin and direction of extension.

[0010] 2) Select the segment from which you want to obtain contribution information, determine the length and position of the selected segment, and find the curve segment representing the same segment on the two torsion curves.

[0011] 3) Determine the coordinates and vectors of key points. Find the rectangular coordinates of the starting and ending points of the part to be stiffened on the two deflection curves of the plant leaf before and after deformation. The starting point of the stiffened segment before deformation (x... 11 ,y 11 ) and endpoint (x) 12 ,y 12 ), the starting point of the stiffened segment after deformation (x) 21 ,y 21 ) and endpoint (x) 22 ,y 22 And establish vectors. This vector, pointing from the start to the end of the pre-deformation stiffened segment, is intended to represent the characteristic length of the pre-deformation stiffened segment. Using image processing methods, the midrib of the blade is digitized and its coordinates (x, y) are calculated on the pre-deformation deflection curve, and the coordinates of the deflection calculation point are extracted. 13 ,x 13 The deflection calculation point should be a pre-determined fixed point located at the blade tip and marked, such as with color, which makes image recognition methods particularly effective in tracking this point. The coordinates (x, y, y) of the deflection calculation point are then calculated on the deflection curve after deformation. 23 ,y 23and the vector from the end of the stiffened segment to the deflection calculation point This vector is composed of (x) 22 ,y 22 ) points to (x 23 ,y 23 ).

[0012] 4) To ensure the smoothness of the connection points when splicing the vector segments, i.e., to ensure the smoothness of the new curve formed after the segments are joined, it is necessary to calculate the tangent direction of the oblique line at each key point on each deflection curve. Calculate the angle θ1 between the tangents at the starting points of the rigid segments on the two deflection curves. Calculate the inclination of the ends of the rigid segments on the two deflection curves, the angle α1 between the tangent at the end point of the rigid segment before deformation and the horizontal direction, and the angle α2 between the tangent at the end point of the rigid segment after deformation and the horizontal direction.

[0013] 5) Rotate and smoothly connect the vector segments. Based on the angle θ1 calculated in step (4), rotate the vector segment before deformation calculated in step (3) counterclockwise. get calculate The vector makes an angle α0 with the horizontal direction. The tail is connected to the starting point (x) of the stiffened segment after deformation. 21 ,y 21 ) to obtain the new vector end coordinates (x 02 ,y 02 ) Calculate the tangent direction turning vector at the end point of the stiffened segment after deformation. The required angle β for the direction is β = α1 - θ1 - α2. (This refers to the vector...) By rotating synchronously by angle β, a new vector is obtained. vector The tail is attached to the coordinate (x) 02 ,y 02 On the x-axis, the coordinates of the new deflection curve deflection calculation point (x) are obtained. 03 ,y 03 ).

[0014] 6) The contribution can be approximated as:

[0015] The angles used in the calculation process are between -180° and 180°. The direction is defined as starting from the positive x-axis, with clockwise rotation being negative and counterclockwise rotation being positive. During the rotation, negative angle values ​​are rotated clockwise, and positive angle values ​​are rotated counterclockwise.

[0016] The method for calculating the contribution of local bending of blades provided in this application can quantitatively describe the characteristics of bending deformation of each part of the blade, and solves the problem that it is difficult to quantitatively represent the differences in bending deformation between blades when studying the mechanical properties of different blades. Attached Figure Description

[0017] Figure 1 A digital schematic diagram of the deflection curve of a solid blade provided for this invention.

[0018] Figure 2 A digital blade diagram provided as an example of the present invention.

[0019] Figure 3 A schematic diagram of key nodes and vectors of the deflection curve in the calculation method provided by this invention.

[0020] Figure 4 This is a schematic diagram of the splicing of the deflection curve and vector rotation provided by the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments, including the following steps:

[0023] 1) such as Figure 1 As shown, images of a fixed blade in its natural state and under stress and bending were captured in the same coordinate system. A load of 100 mg was applied to the tip of a blade that is 35 mm long and 20 mm wide at its widest point. The deflection curves y1(x) before deformation and y2(x) after deformation were extracted from the midrib of the blade in the images. The deflection curves were obtained by extracting several data points from the images, such as... Figure 2 As shown, the corresponding deflection curve is obtained by fitting the curve. Information extraction and curve fitting of the two images before and after blade deformation can yield the fitting results y1 and y2.

[0024] y1(x) = -3.60375 × 10 -9 x 7 +4.20555×10 -7 x 6 -1.83661×10 -5 x 5 +3.53354×10 -4 x 4 -1.97×10 -3 x 3 -0.04805x 2 +0.50308x+0.04309;

[0025] y2(x)=-1.55975×10 -8 x 7 +1.44054×10 -6 x 6 -4.95522×10 -5 x 5 +7.25634×10 -4 x 4 -2.54×10 -3 x 3 -0.08107x 2 +0.62194x+0.03593.

[0026] 2) Select the segment whose contribution will be calculated as the stiffening segment. To achieve the effect of step (2), obtain curve segments representing the same segment on the two deflection curves. In the rectangular coordinate system, the same point on the blade has different coordinates before and after bending deformation, while in the arc length coordinate system, the same point on the blade has the same arc length coordinates before and after bending deformation. This can be verified in the neutral surface assumption of bending deformation. Since the blade is sufficiently flat, this error is ignored. Based on this, Figure 2 The diagram shows how the start and end points of the stiffened segment and the deflection calculation point can be represented by arc length coordinates s1, s2, and s3 on the deflection curve before bending. Using s1 = 9, s2 = 10, and s3 = 35 as a calculation example on the curve, their corresponding rectangular coordinates can be obtained. The starting point (x) of the stiffened segment before deformation... 11 ,y 11 ) = (8.800, 0.737), endpoint (x) 12 ,y 12 ) = (9.700, 0.476), establish a vector The calculation result of the deflection calculation point before deformation is denoted as (x) and points from the beginning of the stiffened segment before deformation to the end of the stiffened segment. 13 ,y 13 = (30.000, -13.608). In fact, all points on the two deflection curves can be represented by corresponding arc length coordinates, and the rectangular coordinates corresponding to the same arc length coordinates can be found on the two deflection curves before and after bending.

[0027] 3) Step (3) is performed using a coordinate transformation with the same arc length coordinates, such as... Figure 2 The right angle between the start and end points of the part to be stiffened is found on the blade deflection curve using the same arc length coordinates. Step (3) is then performed using this coordinate transformation with the same arc length coordinates. Figure 2 The method demonstrated here, which uses the same arc length coordinates to find the rectangular coordinates of the start and end points of the part requiring stiffening on the blade deflection curve, is... Figure 3 The starting point (x) of the stiffened segment after deformation is obtained by finding the corresponding arc length coordinates.21 ,y 21 ) = (8.600, -0.060), endpoint (x) 22 ,y 22 (9.500, -0.524). The deflection calculation point is also calculated using the same method. The location of the deflection calculation point after deformation can also be found on the deflection curve using the same arc length coordinates. Figure 3 The result of the deflection calculation point after deformation can be denoted as (x 23 ,y 23 = (25.3, -19.301), calculate the endpoint of the stiffened segment after deformation (x) 22 ,y 22 ) to the deflection calculation point after deformation (x) 23 ,y 23 ) vector

[0028] 4) In step (4), calculate the... Figure 3 The angle θ1 between the tangents at the starting point of the stiffened segment on the two deflection curves can be obtained by using the directional derivative (y′) of the starting point of the stiffened segment before deformation. 11 ,-1), the directional derivative of the stiffened segment at the starting point after deformation (y′) 21 ,-1). θ1 can be obtained by calculating the angle between the two directional derivatives, where y′ 11 =-0.266,y′ 21 = -0.483. Calculation yields θ1 = -10.854°. Using the same method, the inclination of the ends of the stiffened segments on the two deflection curves is calculated. The angle α1 between the tangent at the end of the stiffened segment before deformation and the horizontal direction is calculated to be -17.352°, and the angle α2 between the tangent at the end of the stiffened segment after deformation and the horizontal direction is -28.679°, where y′ 12 =-0.312,y′ 22 = -0.547.

[0029] 5) Step (5) Rotate and smoothly connect the vector segments. Figure 4 This can be used as a reference. Based on the angle θ1 calculated in step (4), rotate the vector of the stiffened segment before deformation calculated in step (3). get vector The tail is connected to the starting point (x) of the stiffened segment after deformation. 21 ,y 21 ) to obtain the new vector end coordinates (x 02 ,y 02 = (9.435, -0.486). Calculate the tangent direction turning vector at the end point of the stiffened segment after deformation. The required angle β for the direction is β = α2 - α1 - θ1 = -0.473°. (This refers to the vector...) By rotating synchronously by angle β, a new vector is obtained. vector The tail is attached to the coordinate (x) 02 ,y 02 On the x-axis, the coordinates of the new deflection curve deflection calculation point (x) are obtained. 03 ,y 03 ) = (25.389, -19.132), the result is as follows Figure 4 As shown.

[0030] 6) The contribution can be approximated as:

[0031] The calculation results of the contribution are closely related to the curve fitting method and the method of calculating the arc length coordinates. This example is for reference only.

Claims

1. A method for calculating the local bending characteristics of plant leaves, characterized in that, The specific steps are as follows: 1) Fix the connection between the petiole of the plant leaf and the stem of the plant, and take pictures of the plant leaf in the state without load and after bending and deforming under load. The load is applied to the tip of the plant leaf. The images should clearly show the outline and deflection characteristics of the plant leaf bending and deformation. Digitize the pictures before and after bending, and abstract the leaf into a deflection curve. The two deflection curves should be placed in the same coordinate system with the same origin and direction of extension. 2) Select the segment from which you want to obtain contribution information, determine the length and position of the selected segment, and find the curve segment representing the same segment on the two torsion curves; 3) Determine the coordinates and vectors of key points. Find the rectangular coordinates of the start and end points of the part to be stiffened on the two deflection curves of the plant leaf before and after deformation. The starting point (x, y) of the stiffened segment before deformation is... 11 y 11 ) and endpoint (x) 12 y 12 ), the starting point of the stiffened segment after deformation (x) 21 y 21 ) and endpoint (x) 22 y 22 ); and establish vector The vector, pointing from the start point to the end point of the pre-deformation stiffened segment, is intended to represent the characteristic length of the pre-deformation stiffened segment. Using image processing methods, the blade midrib is digitized and its coordinates (x, y) are calculated on the pre-deformation deflection curve, and the coordinates of the deflection calculation point are extracted. 13 y 13 The deflection calculation point should be a pre-determined fixed point located at the blade tip and marked. The coordinates (x, y) of the deflection calculation point are then calculated on the deflection curve after deformation. 23 y 23 and the vector from the end of the stiffened segment to the deflection calculation point This vector is composed of (x) 22 y 22 ) points to (x 23 y 23 ); 4) To ensure the smoothness of the connection points when splicing each vector segment, that is, to ensure the smoothness of the new curve formed after the connection of each segment, it is necessary to calculate the oblique direction and tangent direction of each key point on each deflection curve, calculate the angle θ1 between the tangents at the starting point of the rigid segment on the two deflection curves, calculate the inclination of the end of the rigid segment on the two deflection curves, calculate the angle α1 between the tangent at the end point of the rigid segment before deformation and the horizontal direction, and calculate the angle α2 between the tangent at the end point of the rigid segment after deformation and the horizontal direction. 5) Rotate and smoothly connect the vector segments; based on the angle θ1 calculated in step (4), rotate the vector segment before deformation calculated in step (3) counterclockwise. get calculate The vector is at an angle α0 with the horizontal direction. The tail is connected to the starting point (x) of the stiffened segment after deformation. 21 y 21 ) to obtain the new vector end coordinates (x 02 y 02 ), calculate the tangent direction turning vector at the end point of the stiffened segment after deformation. The required angle β for the direction is α1 - θ1 - α2, which will be the vector. By rotating synchronously by angle β, a new vector is obtained. vector The tail is attached to the coordinate (x) 02 y 02 On the x-axis, the coordinates of the new deflection curve deflection calculation point (x) are obtained. 03 y 03 ); 6) The contribution can be approximated as:

2. The method for calculating the local bending characteristics of plant leaves as described in claim 1, characterized in that, In step 1), the load size is compared with the typical load that plant leaves experience during rainfall, which is 50 mg to 200 mg.

3. The method for calculating the local bending characteristics of plant leaves as described in claim 1, characterized in that, In step 2), the marking includes color marking.

4. The method for calculating the local bending characteristics of plant leaves as described in claim 1, characterized in that, The angles in the calculation process are between -180° and 180°. The direction is defined as starting from the positive x-axis, with clockwise rotation being negative and counterclockwise rotation being positive. During the rotation, negative angle values ​​are rotated clockwise and positive angle values ​​are rotated counterclockwise.

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