Calculation method for local axis of spatial curved surface reticulated shell structural member

Abstract

The invention discloses a calculation method for a local axis of a spatial curved surface reticulated shell structural member, and the calculation method comprises the following steps: 1, obtaining a function of a spatial curved surface S, z = S (x, y); 2, for a component on the spatial curved surface reticulated shell, a starting point Pi and an end point Pj of the component are both located on a spatial curved surface S; 3, calculating the normal vector of the spatial curved surface S at the point Pi through a numerical method; and 4, averaging the normal vector of the spatial curved surface S at the starting point Pi position of the component and the normal vector of the spatial curved surface S at the end point Pj position of the component to obtain Vm. The spatial curved surface is an elementary spatial curved surface which can be expressed by an explicit function. A pure mathematical method is used for calculating the local axis of the spatial curved surface reticulated shell structural component, calculation is carried out through spatial analytic geometry, the local axis rotation angle, the local axial vector and the local axis plane of the component can be output, and the method is suitable for various local axis adjusting modes.

Description

Technical Field

[0001] The invention relates to the field of construction technology, in particular to a method for calculating the local axis of a spatial curved lattice shell structural component. Background Art

[0002] Since the 1990s, with the upgrading of computer technology, parametric design has gradually grown and developed in the field of architectural design.

[0003] Parametric design is a design process that automates the design process by programming the project itself as functions and procedures, modifying initial conditions and then calculating the project results through computer calculations. Parametric design is a feature of Revit Building and consists of two components: parametric primitives and a parametric modification engine. Revit Building primitives are represented as components, and differences between these components are reflected through parameter adjustments. Parameters contain all the information about the primitive as a digital building component. The parametric modification engine provides parameter change technology that allows any changes made to a building design or document to be automatically reflected in other related components. Using intelligent building components, views, and annotation symbols, each component is interconnected through a change propagation engine. Parametric changes caused by moving, deleting, or resizing a component will cause linked changes to the parameters of related components. Changes made in any view are parametrically and bidirectionally propagated to all views, ensuring consistency across all drawings, eliminating the need to modify each view individually. This improves work efficiency and quality.

[0004] Engineers mathematically model the project itself, programming its parameters as variables and the modeling process as functions. By adjusting these parameters, they automate the design process. This technology has evolved into a mature architectural design tool, particularly useful for modeling free-form surfaces, resulting in a vast number of curved spatial architectures. The various constraints established within the parametric model embody the designer's intent.

[0005] In traditional buildings, since the building floors, roofs, and vertical structures are all located in the orthogonal direction of the geodetic coordinate system, the primary and secondary axes of the cross-section of the structural components, also known as the strong and weak axes, are generally also set in the orthogonal direction of the geodetic coordinate system. However, in parametric spatial curved surface buildings, structural components are usually not located in the geoid horizontal plane, but are located at arbitrary positions in space. As a result, the axial force and bending moment directions of the components are located in arbitrary directions in space. In addition, the cross-sections of spatial lattice shell structural components are also diverse, with the most common ones being H-shaped, T-shaped, box-shaped, shuttle-shaped, and elliptical tube-shaped. These cross-sections all have strong and weak axes. When structural engineers are designing this type of building, they need to adjust the radial local axes of the components to align the axis of maximum strength of the cross-section with the direction of maximum bending moment, thereby maximizing the bending strength of the components and improving structural efficiency.

[0006] In previous design processes, due to the lack of a calculation method for the radial local axis of any component and the numerous structural components of spatial curved lattice shell structures, structural engineers often ignored the local axes of small-angle components during design and adjusted the local axes of large-angle components by "eyeballing," repeatedly trying to input the local axis angle until it was visually perpendicular to the spatial surface. This traditional design method is relatively crude, unable to perform fine-grained force adjustments, and prone to human errors and omissions. This results in low design efficiency and cannot guarantee the safety and economy of the structure. Therefore, a numerical calculation method and computer-aided system based on spatial analytical geometry are proposed here for adjusting the local axes of arbitrary spatial curved lattice shell structural components. Summary of the Invention

[0007] The purpose of the present invention is to provide a numerical calculation method and a computer-aided system based on spatial analytical geometry to solve the problems of too many structural components, easy omissions during design, long time for designers to adjust local axes, low precision, low design efficiency, and uncontrollable structural safety and economy.

[0008] To achieve the above object, the present invention adopts the following technical solution: a method for calculating the local axis of a spatial curved lattice shell structure member, the calculation method comprising the following steps:

[0009] Step 1: Get the function of the space surface S, z = S (x, y);

[0010] Step 2: For the components on the space curved lattice shell, the starting point P i and the end point P j All are located on the spatial surface S;

[0011] Step 3: Calculate the spatial surface S in P by numerical method. i The normal vector of a point takes a minimum value:

[0012] △=1×10 -9 ;

[0013] Step 4: For the spatial surface S at the starting point P of the component i The normal vector of the position and the end point P of the component j The average of the normal vectors of the position is V m .

[0014] Furthermore, in step 1, the spatial surface is a spatial surface that can be expressed by an explicit function.

[0015] Furthermore, the space surface is an elementary space surface or a complex space surface.

[0016] Furthermore, the spatial curved surface is one of a cylindrical surface, an elliptical cylindrical surface, a spherical surface, an ellipsoidal surface, and a paraboloidal surface.

[0017] Furthermore, the spatial surface is a Bezier surface or a NURBS surface.

[0018] Furthermore, in step 1, the point P on the spatial surface S is obtained by inputting the x and y coordinates:

[0019]

[0020] Furthermore, in step 2, for the components on the space curved lattice shell, the starting point P i and the end point P j Both are located on the spatial surface S:

[0021]

[0022] According to the starting point P of the component axis i , end point P j , the component axial vector V0 can be calculated:

[0023]

[0024] Assume the initial normal vector V of the component n End point P n Share the same xy coordinates with the component starting point:

[0025]

[0026] According to the Pythagorean theorem, we can get:

[0027]

[0028] z can be found n ,Right now:

[0029]

[0030] The initial normal vector V of the component can be obtained n :

[0031]

[0032] Given the space surface equation:

[0033] z=S(x,y)

[0034] make:

[0035] F(x,y,z)=S(x,y)-z

[0036] but:

[0037]

[0038] Starting point P i For example, the space surface S passes through point P i The equation of the tangent plane is:

[0039] f x (x i ,y i )(xx i )+f y (x i ,y i )(yy i )-(zz i )=0

[0040] Then the space surface S passes through point P i The normal equation is:

[0041]

[0042] Further, in step three, according to the derivative definition:

[0043]

[0044] The space surface S can be calculated numerically at P i The normal vector of a point takes a minimum value:

[0045] △=1×10 -9 .

[0046] Further, in step four,

[0047]

[0048] Computable space surface S in P i The normal vector V of the point i :

[0049]

[0050] Similarly, the normal vector V of the space surface S at point Pj can be calculatedj :

[0051]

[0052] For the spatial surface S at the starting point P of the component i The normal vector of the position and the end point P of the component j The average of the normal vectors of the position is V m :

[0053]

[0054] Calculate the space vector V n 、V m The angle is the component torsion angle:

[0055]

[0056] Vm is the normal vector of the component, and the plane passing through Vn and Vm is the normal plane of the component.

[0057] Furthermore, in the finite element software, according to the different ways of adjusting the local axis of each software, the corresponding torsion angle, normal vector, and normal plane are selected to adjust the local axis of the component.

[0058] Furthermore, the programming part is completed using Matlab or AutoCAD software or Rhino software or Grasshopper software.

[0059] The beneficial effects of the present invention are reflected in: 1. The present invention uses pure mathematical methods to calculate the local axes of spatial curved lattice shell structure components, and uses spatial analytical geometry for calculation. It can output the component's local axis angle, local axis vector, and local axis plane, and is suitable for a variety of local axis adjustment methods.

[0060] 2. The present invention is implemented using the mathematical method of analytic geometry; it is applicable to any cross section; the perpendicular line can be directly obtained through mathematical calculation on the original space plane; and the result can be directly obtained through programming methods.

[0061] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The main purpose and other advantages of the present invention can be realized and obtained by the solutions particularly pointed out in the description. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The present invention will be further described in detail below with reference to the accompanying drawings.

[0063] Figure 1 A schematic diagram of the method of the present invention is provided;

[0064] Figure 2Schematic diagram of a cylinder, elliptical cylinder, sphere, ellipsoid, and paraboloid;

[0065] Figure 3 Schematic diagram of Bezier surface and NURBS surface;

[0066] Figure 4 is the rectangular coordinate diagram of Vn;

[0067] Figure 5 is a schematic diagram of the space surface s;

[0068] Figure 6 Schematic diagram of the spatial lattice shell structure L formed based on the spatial curved surface S;

[0069] Figure 7 Schematic diagram of the equation z=S(x,y) describing the spatial surface S.

[0070] Figure 8 Schematic diagram of V0 image.

[0071] Figure 9 Schematic diagram of the program code for calculating the component axis vector V0, the initial normal vector end point Pn, and the initial normal vector Vn.

[0072] Figure 10 Schematic diagram of Vn image.

[0073] Figure 11 To obtain the minimum value of 0.001, the spatial surface function z = S (x, y) is used to calculate the partial derivative and normal vector Vi at the starting point Pi of the component on the spatial surface S. The program code diagram is shown.

[0074] Figure 12 A schematic diagram of a Vi image.

[0075] Figure 13 Schematic diagram of the program code for calculating the partial derivative and normal vector Vj at the end point Pj of the component on the spatial surface S.

[0076] Figure 14 Schematic diagram of Vj image.

[0077] Figure 15 Schematic diagram of the program code for calculating the mean vector Vm.

[0078] Figure 16 Schematic diagram of the Vm image.

[0079] Figure 17 This is a schematic diagram of the program code for the calculation initial method.

[0080] Figure 18 This is a partial schematic diagram of the Beta angle calculation results.

[0081] Figure 19This is the schematic diagram before cross-section adjustment.

[0082] Figure 20 This is the schematic diagram after adjustment of the rectangular cross section.

[0083] Figure 21 This is a schematic diagram of the I-shaped section after adjustment.

[0084] Figure 22 This is a schematic diagram of the octagonal section after adjustment.

[0085] Figure 23 This is a schematic diagram of the three-dimensional modeling software AutoCAD in Example 2.

[0086] Figure 24 Schematic diagram of point selection for a rod in Example 2 Figure 1 .

[0087] Figure 25 Schematic diagram of the calculation component of Example 2 Figure 2 .

[0088] Figure 26 Schematic diagram of calculating the average vector in Example 2 Figure 3 .

[0089] Figure 27 Angle indication Figure 4 .

[0090] Figure 28 This is the schematic diagram before local axis adjustment.

[0091] Figure 29 This is a schematic diagram after local axis adjustment.

[0092] Figure 30 This is a schematic diagram of Example 3.

[0093] Figure 31 Schematic diagram of rod point selection in Example 3 Figure 1 .

[0094] Figure 32 Schematic diagram of point selection for a member Figure 2 .

[0095] Figure 33 Schematic diagram of the mean vector Vm.

[0096] Figure 34 Schematic diagram for calculating the angle between the initial normal vector and Vm. DETAILED DESCRIPTION

[0097] The present invention is realized by using the mathematical method of analytical geometry; the present invention is applicable to any cross section; the perpendicular line can be directly obtained by mathematical calculation on the original space plane; the present invention can directly obtain the result by programming method.

[0098] See also Figure 1 As shown, the specific steps are:

[0099] Step 1: Get the function of the space surface S, z = S (x, y);

[0100] For any space surface that can use the equation z = S (x, y) to describe the correspondence between points on the plane and coordinates, including elementary space surfaces that can be expressed by explicit functions, such as but not limited to cylinders, elliptical cylinders, spheres, ellipsoids, paraboloids, etc., such as Figure 2 As shown; also includes space surfaces that do not have explicit function expressions in computer graphics but can be calculated by computer programs, such as but not limited to Bezier surfaces, non-uniform rational B-spline (NURBS) surfaces, etc. Figure 3 As shown. Users can obtain point P on the spatial surface S by inputting x and y coordinates:

[0101]

[0102] Step 2: For the components on the space curved lattice shell, the starting point P i and the end point P j Both are located on the spatial surface S:

[0103]

[0104] According to the starting point P of the component axis i , end point P j , the component axial vector V0 can be calculated:

[0105]

[0106] Assume the initial normal vector V of the component n End point P n Share the same xy coordinates with the component starting point:

[0107]

[0108] According to the Pythagorean theorem, we can get:

[0109]

[0110] z can be found n ,Right now:

[0111]

[0112] The initial normal vector V of the component can be obtained n :

[0113]

[0114] See also Figure 4 shown.

[0115] Step 3: Given the space surface equation:

[0116] z=S(x,y)

[0117] make:

[0118] f(x,y,z)=S(x,y)-z

[0119] but:

[0120]

[0121]

[0122] Starting point P i For example, the space surface S passes through point P i The equation of the tangent plane is:

[0123] f x (x i ,y i )(xx i )+f y (x i ,y i )(yy i )-(zz i )=0

[0124] Then the space surface S passes through point P i The normal equation is:

[0125]

[0126] According to the definition of derivative:

[0127]

[0128] The space surface S can be calculated numerically at P i The normal vector of a point takes a minimum value:

[0129] △=1×10 -9

[0130] (This minimum value can be 1, 0.01, 0.001, etc., and can be selected according to the specific engineering accuracy. It is not a fixed value) Then:

[0131]

[0132] Computable space surface S in P i The normal vector V of the point i :

[0133]

[0134]

[0135] Step 4: For the spatial surface S at the starting point P of the component i The normal vector of the position and the end point P of the component j The average of the normal vectors of the position is V m :

[0136]

[0137] Calculate the space vector V n 、V m The angle is the component torsion angle:

[0138]

[0139] Vm is the normal vector of the component, and the plane passing through Vn and Vm is the normal plane of the component.

[0140] In finite element software, according to the different ways of adjusting local axes in each software, the corresponding torsion angle, normal vector, and normal plane method are selected to adjust the local axis of the component.

[0141] This method can be implemented by programming or by using various tools provided by existing commercial software.

[0142] Example 1: Using Matlab programming to demonstrate the specific implementation process of this patent

[0143] Step 1: For the space surface S that can be described by the function z = S (x, y) and the lattice shell structure L formed based on the space surface S, you can draw an image in Matlab (or other programming languages): Figure 5 、 Figure 6 shown.

[0144] The equation describing the space surface S is z=S(x, y) Figure 7 As shown:

[0145] Step 2: The starting point x, y, z coordinates and the ending point x, y, z coordinates of the components in the spatial lattice shell structure L are shown in the following table. The x, V, and z coordinates are only partially shown:

[0146]

[0147] The code for extracting point coordinates is as follows;

[0148] load pt;

[0149] pts = table2array(pt);

[0150] xi=pts(:,1);

[0151] yi=pts(:,2);

[0152] zi=pts(:,3);

[0153] xj=pts(:,4);

[0154] yj=pts(:,5);

[0155] zj=pts(:,6);

[0156] Step 3: Calculate the component axis vector V0, the initial normal vector end point Pn, and the initial normal vector Vn. The program code is as follows: Figure 9 As shown in the figure, the above program code is the specific implementation of the formula in step 3. The data in step 2 can be processed by the above code to obtain the values ​​of V0 and VN. Due to the large amount of numerical calculations, listing them one by one will cause the text to be too long, and pure text data cannot intuitively display the calculation results. Therefore, the two sets of vectors V0 and VN are plotted in the form of images. The V0 image is shown in Figure 8, and the Vn image is shown in Figure 9. Figure 10 As shown;

[0157] Step 4: Take the minimum value 0.001 and use the spatial surface function z = S (x, y) to calculate the partial derivative and normal vector Vi on the spatial surface S at the starting point Pi of the component. The program code is as follows: Figure 11 As shown,

[0158] The above program code is the specific implementation of the formula in step 4. The data in step 3 can be processed by the above code to obtain the value of Vi. Due to the large amount of numerical calculations, listing them one by one will cause the text to be too long, and pure text data cannot intuitively display the calculation results. Therefore, the Vi vector is plotted in the form of an image. Vi is as follows Figure 11 shown.

[0159] Step 5: Use the same method to calculate the partial derivative and normal vector Vj at the component end point Pj on the spatial surface S. The program code is shown in Figure 13, and the Vj image is shown in Figure 14.

[0160] Step 6: Calculate the average vector Vm of Vi and Vj. The program code is as follows: Figure 15 As shown in the figure, the program code is the specific implementation of the formula in step 6. The data in steps 4 and 5 can be processed by the above code to obtain the value of Vm. Due to the large amount of numerical calculations, listing them one by one will cause the text to be too long, and pure text data cannot intuitively display the calculation results. Therefore, the Vi vector is plotted as an image, such as the Vm image. Figure 16 As shown;

[0161] Step 7: Calculate the angle between the initial normal vector and Vm. The program code is shown in Figure 17. The Beta angle calculation result is shown in Figure 17. Figure 18 The figure shown is only a part; in summary, there are 256 rods in this embodiment 1, and each rod corresponds to a Beta angle calculation result. Due to the large number of rods, not all calculation results are given, and only a part of the calculation results is shown.

[0162] In traditional design work, if the Beta angle of 256 rods needs to be adjusted, the designer needs to constantly try and find the angle by inputting numbers and visually observing whether the rod direction angle is perpendicular to the plane. If not, the designer needs to modify the numbers until an angle acceptable to the naked eye is obtained as the rod Beta angle. The Beta angle obtained by this method is very rough and has low precision. In addition, each rod needs to be tried 3 to 5 times. For 256 rods, the number of trials is large and the adjustment efficiency is very low. For large-scale station or airport projects, the number of rods exceeds hundreds of thousands. The trial and error method cannot traverse all rods and can only select some important rods for adjustment, while ignoring some less important rods with smaller Beta angles. The calculation results after such processing are relatively rough and do not meet the requirements of fine design.

[0163] By using the method provided by this patent, after forming the data in the above figure, the data can be directly copied and pasted into the finite element software. The Beta angle of the rod will be automatically adjusted without the need for trial and error. The calculation accuracy is high, the adjustment speed is fast, the operation is simple, and it can process massive amounts of data, allowing the design work to be completed efficiently.

[0164] Step 8: According to the local axis adjustment method provided by the finite element software, select the rotation angle Beta, normal vector Vm, and normal plane VmVn to adjust the local axis of the spatial lattice shell structure. For the rectangular section before and after adjustment, please refer to Figure 19 、 20 .

[0165] Adjusted I-section reference Figure 21 As shown, the adjusted octagonal cross-section reference Figure 22 shown.

[0166] Example 2: This example uses AutoCAD software to implement the implementation process.

[0167] Step 1: In the 3D modeling software AutoCAD, obtain the building space surface and space lattice shell and convert them into a computer model, as shown in FIG23;

[0168] Step 2: Taking a certain rod as an example, obtain the starting point Pi and the end point Pj of the rod in the computer system, as shown in FIG24;

[0169] Pi=(-4158.557,-8355.687,6666.667)

[0170] Pj=(-5092.631,-8444.027,5000.000)

[0171] Step 3: Calculate the component axis vector V0, the initial normal vector end point Pn, and the initial normal vector Vn:

[0172] V0=(-934.07,-88.34,-1666.67)

[0173] Pn=(-4158.557,-8355.687,4471.821)

[0174] Vn=(934.074,88.340,-528.179) see 25;

[0175] Step 4: Take the minimum value 0.1 and use the AutoCAD software function to obtain the z coordinate of the point on the spatial surface S by inputting the x and y coordinates. The operation can be recorded as z = S (x, y). Calculate the partial derivative and normal vector on the spatial surface S at the starting point Pi of the component:

[0176] fx=[S(-4158.557+0.1,-8355.687)-S(-4158.557-0.1,-8355.687)] / (2×0.1)=1.533420

[0177] fy=[S(-4158.557,-8355.687+0.1)-S(-4158.557,-8355.687-0.1)] / (2×0.1)=3.081061

[0178] Vi=(1.533420,3.081061,-1)

[0179] Step 5: Use the same method to calculate the partial derivative and normal vector fx=1.506318 on the spatial surface S at the component end point Pj.

[0180] fy=2.497617

[0181] Vj=(1.506318,2.497617,-1)

[0182] Step 6: Calculate the average vector Vm of Vi and Vj: Vm = (1.519869, 2.789339, -1) Figure 26 shown.

[0183] Step 7: Calculate the angle between the initial normal vector and Vm: Beta = 52.011783°, see Figure 27 shown.

[0184] Step 8: According to the local axis adjustment method provided by the finite element software, select the rotation angle Beta, normal vector Vm, and normal plane VmVn to adjust the local axis of the spatial lattice shell structure. Figure 28 、 29 shown.

[0185] Example 3 is implemented using Rhino software.

[0186] Step 1: In the 3D modeling software Rhino, obtain the architectural space surface and space lattice shell and convert them into a computer model. Figure 30 shown.

[0187] Step 2: Taking a certain rod as an example, obtain the starting point Pi and end point Pj of the rod in the computer system:

[0188] Pi=(992.445157,913.293196,390.576742)

[0189] Pj=(-414.183922,2630.409618,-1515.672886) Figure 31 shown.

[0190] Step 3: Calculate the component axis vector V0, the initial normal vector end point Pn, and the initial normal vector Vn:

[0191] V0=(1406.629079,-1717.116422,1906.249628)

[0192] Pn=(-414.183922,2630.409618,2975.282386)

[0193] Vn=(-1406.629079,1717.116422,2584.705644), see Figure 32 .

[0194] Step 4: Using the Rhino software function, by inputting the xy coordinates, obtain the z coordinate of the point on the curved surface S. This operation can be expressed as the function z = S(x, y). Taking the minimum value of 0.001, calculate the partial derivative and normal vector Vi on the spatial surface S at the starting point Pi of the component:

[0195] fx=[S(992.445157+0.001,913.293196)-S(992.445157-0.001,913.293196)] / (2

[0196] × 0.001) = 2.666774

[0197] fy=[S(992.445157,913.293196+0.001)-S(992.445157,913.293196-0.001)] / (2

[0198] × 0.001) = 1.546125

[0199] Vi=(2.666774,1.546125,-1)

[0200] Step 5: Use the same method to calculate the partial derivative and normal vector of the component end point Pj on the spatial surface S.

[0201] Vj

[0202] fx=1.802196

[0203] fy=0

[0204] Vj=(1.802196,0,-1)

[0205] Step 6: Calculate the average vector Vm of Vi and Vj:

[0206] Vm=(2.234485,0.773062,-1) Figure 33 shown

[0207] Step 7: Calculate the angle between the initial normal vector and Vm:

[0208] Beta=120.20516° Figure 34 shown

[0209] Step 8: According to the local axis adjustment method provided by the finite element software, select the rotation angle Beta, normal vector Vm, and normal plane VmVn to adjust the local axis of the spatial lattice shell structure component.

[0210] This invention aims to address the complex, time-consuming, and low-precision calculations of local axes for spatial curved lattice shell components in practical applications. The number of rods used in practical applications or implementations is enormous, making it impossible to list them all. Each rod corresponds to a Beta angle calculation result, and since there are so many rods, the full calculation results are not presented. Only a portion of the results are shown here.

[0211] In traditional design work, adjusting the Beta angle of a member requires designers to conduct continuous trial and error, and the calculated results are relatively rough and do not meet the requirements of fine design.

[0212] This method, after forming the data in the above figure, can directly copy the data and paste it into the finite element software. The Beta angle of the member will be automatically adjusted without trial and error. It has high calculation accuracy, fast adjustment speed, simple operation, and can process massive amounts of data, making the design work efficient.

[0213] It should be noted that the spatial surface is a spatial surface that can be expressed by an explicit function. In other words, the spatial surface is an elementary spatial surface or a complex spatial surface. In the embodiment, only three types of spatial surfaces are listed: ellipsoid, parabola, and NURBS. Of course, the spatial surfaces here are not limited to these, but any spatial surface that can be expressed by an explicit function is applicable to the present invention. Among them, cylindrical surfaces, ellipsoidal surfaces... these are elementary spatial surfaces, Bezier surfaces and NURBS surfaces are complex spatial surfaces, and these surfaces can be expressed by explicit functions. Figure 2 is an example of an elementary space surface, and Figure 03 is an example of a complex space surface.

Claims

1. The calculation method of the local axis of the spatial curved lattice shell structure is characterized by: The calculation method includes the following steps: Step 1: Get the function of the space surface S, z = S (x, y); Step 2: For the components on the space curved lattice shell, the starting point P i and the end point P j All are located on the spatial surface S; Step 3: Calculate the spatial surface S in P by numerical method. i The normal vector of a point takes a minimum value: △＝1×10 -9 ； Step 4: For the spatial surface S at the starting point P of the component i The normal vector of the position and the end point P of the component j The average of the normal vectors of the position is V m .

2. The calculation method according to claim 1, wherein: In step 1, the space surface is a space surface that can be expressed by an explicit function.

3. The calculation method according to claim 2, wherein: The space surface is an elementary space surface or a complex space surface.

4. The calculation method according to claim 1, wherein: In step 1, the point P on the spatial surface S is obtained by inputting the x and y coordinates:

5. The calculation method according to claim 1, wherein: In step 2, for the components on the space surface lattice shell, its starting point P i and the end point P j Both are located on the spatial surface S: According to the starting point P of the component axis i , end point P j , the component axial vector V0 can be calculated: Assume the initial normal vector V of the component n End point P n Share the same xy coordinates with the component starting point: According to the Pythagorean theorem, we can get: z can be found n ,Right now: The initial normal vector V of the component can be obtained n : Given the space surface equation: z=S(x,y) make: F(x,y,z)=S(x,y)-z but: Starting point P i For example, the space surface S passes through point P i The equation of the tangent plane is: f x (x i ,y i )(x-x i )+f y (x i ,y i )(y-y i )-(z-z i )=0 Then the space surface S passes through point P i The normal equation is:

6. The calculation method according to claim 1, wherein: In step 3, according to the derivative definition: The space surface S can be calculated numerically at P i The normal vector of a point takes a minimum value: △＝1×10 -9 。 7. The calculation method according to claim 1, wherein: In step four, Computable space surface S in P i The normal vector V of the point i : Similarly, the normal vector V of the space surface S at point Pj can be calculated j : For the spatial surface S at the starting point P of the component i The normal vector of the position and the end point P of the component j The average of the normal vectors of the position is V m : Calculate the space vector V n 、V m The angle is the component torsion angle: Vm is the normal vector of the component, and the plane passing through Vn and Vm is the normal plane of the component.

8. The calculation method according to claim 1, wherein: In finite element software, according to the different ways of adjusting local axes in each software, the corresponding torsion angle, normal vector, and normal plane method are selected to adjust the local axis of the component.

9. The calculation method according to claim 1, wherein: Use Matlab or AutoCAD software or Rhino software or Grasshopper software to complete the programming part.

Images