A method for manufacturing a three-dimensional random undulating structural surface

Abstract

The present invention provides a method for fabricating a three-dimensional randomly undulating structural surface. Step 1: Using the Monte Carlo method, a mathematical model of a two-dimensional randomly undulating structural surface is established. Harmonics of different wavelengths are superimposed to form a randomly undulating surface with varying degrees of undulation. Step 2: The resulting two-dimensional randomly undulating surface is modified into a curved solid, completing the three-dimensional solid modeling of the randomly undulating structural surface. Step 3: The solid model is fabricated using 3D printing technology. Step 4: The three-dimensional randomly undulating structural surface is molded based on the desired structural surface material. This method can quantitatively reflect the surface roughness and random undulation characteristics of actual underground engineering structures, effectively simplifying the fabrication of the randomly undulating structural surface and providing reliable support for fabricating the structural surface for experiments on soil-structure surface contact and shear properties.

Description

Technical Field

[0001] The invention belongs to the field of rock mechanics and engineering technology, and in particular is a method for manufacturing a three-dimensional randomly undulating structural surface. Background Art

[0002] The properties and shear mechanical characteristics of the soil-structure interface are the prerequisites and foundation for solving and analyzing the interaction between soil and underground structures in practical engineering projects. The roughness of the structural surface significantly influences the shear mechanical properties of the soil-structure interface. However, existing research generally uses regular serrated or trapezoidal surfaces to approximate the structural surface. Less consideration is given to the roughness and random fluctuations of the exterior surfaces of cast-in-place concrete structures such as bored piles, underground diaphragm walls, and shaft linings. This, to a certain extent, restricts the understanding of the soil-structure interface contact and shear properties in practical engineering projects.

[0003] Therefore, there is an urgent need to provide a method that can effectively quantify the roughness of the structural surface and its random undulation characteristics, while simplifying the difficulty of making random undulating structural surfaces, so as to provide effective guarantees for the fabrication of structural surfaces in soil-structural surface contact properties, shear mechanical properties specimen tests, and model tests. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the present invention provides a method for producing a three-dimensional randomly undulating structural surface. This method can quantitatively reflect the roughness of the outer surface of an actual underground engineering structure and its random undulation characteristics, effectively simplify the difficulty of producing the randomly undulating structural surface, and provide reliable and efficient structural surface production support for experiments on soil-structure surface contact and shear properties.

[0005] In order to achieve the above object, the present invention provides a method for manufacturing a three-dimensional random undulating structure surface, which specifically comprises the following steps:

[0006] Step 1: Based on the Monte Carlo method, a mathematical model of a two-dimensional random undulating structure surface is established, and random undulating surfaces with different degrees of undulation are formed by superimposing harmonics of different wavelengths;

[0007] S10: According to formula (1), the power spectrum density of the two-dimensional rough surface is obtained The Monte Carlo method is used to filter the harmonic function using the power spectrum density function in the frequency domain;

[0008]

[0009] Where δ is the root mean square height, l x With l y are the relevant lengths in the x and y directions; and are the discrete wave numbers in the x and y directions respectively; L x With L yare the lengths of the two-dimensional randomly undulating rough surface in the x and y directions; m = -M / 2+1, ..., M / 2, n = -N / 2+1, ..., N / 2, where M and N are the numbers of Gaussian distribution discrete points generated by the two-dimensional randomly undulating rough surface in the x and y directions, respectively;

[0010] S11: Obtain the height of each point on the two-dimensional random undulating rough surface according to formula (2), so as to obtain the two-dimensional random undulating rough surface by using inverse fast Fourier transform;

[0011]

[0012] Where x m =mΔx and y n =nΔy is the coordinate value of the point; Δx and Δy are the distances between two adjacent points; is the Fourier transform pair, Among them, N(0,1) represents a random number with Gaussian distribution;

[0013] Step 2: Modify the formed two-dimensional random undulating surface into a curved surface entity, and complete the three-dimensional random undulating structural surface entity modeling;

[0014] S20: encrypting and smoothing the node coordinates of the generated two-dimensional random undulating rough surface to obtain a two-dimensional random undulating smooth surface;

[0015] S21: Reconstruct a two-dimensional random undulating smooth surface into a curved solid;

[0016] S22: Establish a three-dimensional random undulating structural surface solid model;

[0017] Step 3: Complete the production of the physical model based on 3D printing technology;

[0018] A three-dimensional solid model with a randomly undulating surface structure is printed using a 3D printer;

[0019] Step 4: According to the actual requirements of the structural surface material, a three-dimensional random undulating structural surface is produced by casting;

[0020] S40: first spraying a release agent on the upper surface of the 3D printed three-dimensional solid model and the inner side of the matching mold, and then assembling the two to form an integral structure;

[0021] S41: Using the 3D printed three-dimensional solid model as the mold base, pour an appropriate amount of solidifying material into the mold and pour it onto the upper part of the three-dimensional solid model, then vibrate and compact it. At the same time, ensure that the solidifying material is evenly filled to the set height of the mold;

[0022] S42: Curing is performed according to the requirements of the solidified material, and demoulding is performed after the curing is completed to obtain a three-dimensional random undulating structural surface solid model of the underground structure formed by the required solidified material.

[0023] Furthermore, in order to have a reasonable degree of roughness on the rough surface, in S10, δ = 0.5λ, l x =1.0λ,l y =1.0λ.

[0024] Furthermore, in order to facilitate the process of establishing the mathematical model, in step one, the mathematical model of the two-dimensional random undulating structural surface is established using Matlab.

[0025] Furthermore, in order to obtain the three-dimensional random undulating structural surface solid model quickly and conveniently, in step 4 S41 , the solidifying material is one of concrete, mortar or cement paste.

[0026] Furthermore, in order to conveniently and quickly realize the encryption and smoothing of the node coordinates of the random undulating rough surface, in step 2 S20, the node coordinates of the random undulating rough surface generated by Matlab are imported into Meshlab, and Meshlab is used to encrypt and smooth the mesh.

[0027] Furthermore, in order to facilitate the reconstruction of the two-dimensional random undulating smooth surface into a curved surface entity, in step 2 S21 , Geomagic Studio is used for editing to reconstruct the two-dimensional random undulating smooth surface into an editable curved surface entity.

[0028] Furthermore, in order to quickly and accurately manufacture a three-dimensional random undulating structural surface solid model, in step 2 S22 , a three-dimensional random undulating structural surface solid model is established using Solidworks.

[0029] In the present invention, a mathematical model of a two-dimensional random undulating structural surface is established based on the Monte Carlo method, and a random undulating surface with different undulation degrees is formed by superimposing harmonics of different wavelengths, so that a two-dimensional random undulating surface can be obtained more accurately; the node coordinates of the two-dimensional random undulating rough surface are first encrypted and smoothed to obtain a two-dimensional random undulating smooth surface, and then reconstructed into a curved surface entity, so that a three-dimensional undulating structural surface entity model can be obtained quickly and accurately; the three-dimensional undulating structural surface entity mold is printed using 3D printing technology, so that the three-dimensional random undulating structural surface entity model can be quickly and accurately constructed, and at the same time, the construction cost can be effectively saved. First, a release agent is sprayed on the inner side of the mold, and then the mold base is assembled, which can facilitate subsequent demoulding operations. The printed three-dimensional entity model is assembled in the mold as the mold base, and then a solid material is poured on the upper part. After solidification, the mold is demoulded to conveniently obtain a solid mold that conforms to the three-dimensional random undulating structural surface of the underground structure. The method of the present invention is simple and efficient, with low production cost and high production efficiency. It can quantify the random characteristics of structural surface roughness, fully consider the influence of different undulation degrees on the characteristics of the structural surface, and can conveniently adjust the shape and size of the structural surface according to needs, thereby effectively promoting the in-depth development of quantitative research on the morphological characteristics of random undulating structural surfaces, and can more accurately provide effective technical guarantees for the production of structural surfaces in soil-structural surface contact properties, shear mechanical properties sample tests and model tests, which helps to accurately reveal the mechanical mechanism of random undulating structural surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart for making a random undulating structural surface in the present invention;

[0031] Figure 2 Schematic diagram of a two-dimensional random undulating rough surface in the present invention;

[0032] Figure 3 It is a schematic diagram of the three-dimensional random undulating structure surface mold in the present invention.

[0033] In the figure: 1. 3D solid model, 2. Curing material, 3. Mold. DETAILED DESCRIPTION

[0034] The present invention will be further described below with reference to the accompanying drawings.

[0035] like Figures 1 to 3 As shown, a method for manufacturing a three-dimensional random undulating structural surface specifically includes the following steps:

[0036] Step 1: Based on the Monte Carlo method, a mathematical model of a two-dimensional random undulating structure surface is established, and random undulating surfaces with different degrees of undulation are formed by superimposing harmonics of different wavelengths;

[0037] S10: According to formula (1), the power spectrum density of the two-dimensional rough surface is obtained The Monte Carlo method is used to filter the harmonic function using the power spectrum density function in the frequency domain;

[0038]

[0039] Where δ is the root mean square height, l x With l y are the relevant lengths in the x and y directions; and are the discrete wave numbers in the x and y directions respectively; L x With L y is the length of the two-dimensional randomly undulating rough surface in the x-direction and the y-direction; m = -M / 2+1, ..., M / 2, n = -N / 2+1, ..., N / 2, M and N are the number of Gaussian distribution (normal distribution) discrete points generated by the two-dimensional randomly undulating rough surface in the x-direction and the y-direction respectively;

[0040] S11: Obtain the height of each point on the two-dimensional random undulating rough surface according to formula (2), so as to obtain the two-dimensional random undulating rough surface by using inverse fast Fourier transform;

[0041]

[0042] Where x m =mΔx and y n =nΔy is the coordinate value of the point; Δx and Δy are the distances between two adjacent points; is the Fourier transform pair, in, is the power spectral density of the two-dimensional rough surface; N(0,1) represents a random number of Gaussian distribution (normal distribution);

[0043] Step 2: Modify the formed two-dimensional random undulating surface into a curved surface entity, and complete the three-dimensional random undulating structural surface entity modeling;

[0044] S20: encrypting and smoothing the node coordinates of the generated two-dimensional random undulating rough surface to obtain a two-dimensional random undulating smooth surface;

[0045] S21: Reconstruct a two-dimensional random undulating smooth surface into a curved solid;

[0046] S22: Establish a three-dimensional random undulating structural surface solid model;

[0047] Step 3: Complete the production of the physical model based on 3D printing technology;

[0048] A three-dimensional solid model 1 having a randomly undulating structured surface is printed using a 3D printer;

[0049] Step 4: According to the actual requirements of the structural surface material, a three-dimensional random undulating structural surface is produced by casting;

[0050] S40: spraying a release agent on the upper surface of the 3D printed three-dimensional solid model 1 and the inner surface of the matching mold 3, and then assembling the two to form an integral structure;

[0051] S41: Using the 3D printed three-dimensional solid model 1 as the mold base, pour an appropriate amount of solidifying material 2 into the mold 3 and pour it onto the upper part of the three-dimensional solid model 1, then vibrate and compact it. At the same time, ensure that the solidifying material 2 is evenly filled to the set height of the mold 3;

[0052] S42: Curing is performed according to the requirements of the solidified material 2, and demoulding is performed after the curing is completed to obtain a three-dimensional random undulating structural surface solid model of the underground structure formed by the required solidified material 2.

[0053] In order to have a reasonable degree of roughness of the rough surface, in S10, δ = 0.5λ, l x =1.0λ,l y = 1.0λ, and a two-dimensional random undulating rough surface is obtained. Figure 2 The degree of undulation of a two-dimensional random undulating rough surface is determined by the parameters root mean square height δ and correlation length l x With l y The larger the root mean square height δ is, the greater the fluctuation of the rough surface is; the smaller the root mean square height δ is, the more severe the fluctuation of the rough surface in the horizontal direction is.

[0054] In order to facilitate the process of establishing mathematical modeling, in step one, Matlab is used to establish the mathematical modeling of the two-dimensional random undulating structural surface.

[0055] In order to obtain a three-dimensional random undulating structural surface entity model quickly and conveniently, in step 4 S41 , the solidifying material 2 is one of concrete, mortar or cement paste. Of course, it can also be other solidifying materials.

[0056] In order to conveniently and quickly realize the encryption and smoothing of the node coordinates of the random undulating rough surface, in step 2 S20, the node coordinates of the random undulating rough surface generated by Matlab are imported into Meshlab, and Meshlab is used to encrypt and smooth the mesh.

[0057] In order to conveniently reconstruct the two-dimensional random undulating smooth surface into a curved surface entity, in step S21 of step 2, Geomagic Studio is used for editing to reconstruct the two-dimensional random undulating smooth surface into an editable curved surface entity.

[0058] In order to quickly and accurately manufacture a three-dimensional random undulating structural surface solid model, in step 2 S22, a three-dimensional random undulating structural surface solid model is established using Solidworks, and the structural surface is edited as needed and can be cut into cylindrical or rectangular parallelepiped models of required sizes.

[0059] This method addresses the difficulties of fabricating random undulating structural surfaces and the difficulty in quantifying their roughness. Based on the Monte Carlo method, a two-dimensional mathematical model of the randomly undulating structural surface is established using Matlab software. A three-dimensional solid model is then produced using Geomagic Studio and Solidworks modeling software, along with 3D printing technology. Finally, a three-dimensional randomly undulating structural surface is produced using a reverse molding method using materials such as concrete and cement mortar. This method is simple and efficient in producing three-dimensional randomly undulating structural surfaces, capable of quantifying the random undulation characteristics of the exterior surface of actual underground engineering structures. The shape, size, and material of the structural surface can be adjusted according to actual needs, providing reliable and efficient support for fabricating structural surfaces for soil-structure contact and shear properties testing.

Claims

1. A method for producing a three-dimensional random undulating structure surface, characterized in that: The specific steps include: Step 1: Based on the Monte Carlo method, a mathematical model of a two-dimensional random undulating structure surface is established, and random undulating surfaces with different degrees of undulation are formed by superimposing harmonics of different wavelengths; S10: According to formula (1), the power spectrum density of the two-dimensional rough surface is obtained The Monte Carlo method is used to filter the harmonic function using the power spectrum density function in the frequency domain; Where δ is the root mean square height, l x With l y are the relevant lengths in the x and y directions; and are the discrete wave numbers in the x and y directions respectively; L x With L y are the lengths of the two-dimensional randomly undulating rough surface in the x and y directions; m = -M / 2+1, ..., M / 2, n = -N / 2+1, ..., N / 2, where M and N are the numbers of Gaussian distribution discrete points generated by the two-dimensional randomly undulating rough surface in the x and y directions, respectively; S11: Obtain the height of each point on the two-dimensional random undulating rough surface according to formula (2), so as to obtain the two-dimensional random undulating rough surface by using inverse fast Fourier transform; Where x m =mΔx and y n =nΔy is the coordinate value of the point; Δx and Δy are the distances between two adjacent points; is the Fourier transform pair, Among them, N(0,1) represents a random number with Gaussian distribution; Step 2: Modify the formed two-dimensional random undulating surface into a curved surface entity, and complete the three-dimensional random undulating structural surface entity modeling; S20: encrypting and smoothing the node coordinates of the generated two-dimensional random undulating rough surface to obtain a two-dimensional random undulating smooth surface; S21: Reconstruct a two-dimensional random undulating smooth surface into a curved solid; S22: Establish a three-dimensional random undulating structural surface solid model; Step 3: Complete the production of the physical model based on 3D printing technology; Printing a three-dimensional solid model with a randomly undulating surface structure using a 3D printer (1); Step 4: According to the actual requirements of the structural surface material, a three-dimensional random undulating structural surface is produced by casting; S40: spraying a release agent on the upper surface of the 3D printed three-dimensional solid model (1) and the inner surface of the matching mold (3), and then assembling the two to form an integral structure; S41: Using the 3D printed three-dimensional solid model (1) as the mold base, pour an appropriate amount of solidified material (2) into the mold (3) and pour it onto the upper part of the three-dimensional solid model (1), and then vibrate and compact it. At the same time, ensure that the solidified material (2) is evenly filled to the set height of the mold (3); S42: Curing is performed according to the requirements of the solidified material (2), and demoulding is performed after the curing is completed to obtain a three-dimensional random undulating structural surface solid model of the underground structure formed by the required solidified material (2).

2. The method for manufacturing a three-dimensional random undulating structure surface according to claim 1, characterized in that: In S10, δ = 0.5λ, l x = 1.0λ, l y = 1.0λ.

3. The method for manufacturing a three-dimensional random undulating structure surface according to claim 1 or 2, characterized in that: In step one, Matlab is used to establish a mathematical model of a two-dimensional random undulating structural surface.

4. The method for manufacturing a three-dimensional random undulating structure surface according to claim 3, characterized in that: In step 4 S41, the solidifying material (2) is one of concrete, mortar or cement paste.

5. The method for manufacturing a three-dimensional random undulating structure surface according to claim 4, characterized in that: In step 2, in S20 , the node coordinates of the random undulating rough surface generated by Matlab are imported into Meshlab, and the mesh is encrypted and smoothed using Meshlab.

6. The method for manufacturing a three-dimensional random undulating structure surface according to claim 5, characterized in that: In step 2, in S21 , Geomagic Studio is used for editing to reconstruct the two-dimensional random undulating smooth surface into an editable surface entity.

7. The method for manufacturing a three-dimensional random undulating structure surface according to claim 6, characterized in that: In step 2, in S22, a three-dimensional random undulating structural surface solid model is established using Solidworks.

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