A method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics

Abstract

The application discloses a near-field dynamic modeling method for a point array material sandwich structure for heat conduction problems, and mainly comprises the following steps: establishing a three-dimensional model of the point array material sandwich structure, and discretizing the model; obtaining the total number of particles after discretization, and simultaneously calculating the total step number and defining the time step; initializing the radius of the near-field influence range of each particle; calculating the micro-heat conduction coefficient of the "key"; updating the boundary condition; starting the numerical integration calculation in the near-field range of the particle; calculating the "key" state and heat flux density around the particle; judging whether the heat flux density superposition of all the keys around the particle is traversed; updating the temperature of each particle; judging whether all the particles are traversed; judging whether all the calculation steps are completed; and outputting the result after the calculation is completed. The method provided by the application is convenient for modeling, has high calculation efficiency and precision, can effectively process the non-continuity and multi-scale effect in the material, is suitable for complex geometric structures, and can accurately predict the heat conduction behavior of the point array material sandwich structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of heat conduction system design and manufacturing, and particularly relates to a near-field dynamics modeling method for a lattice material sandwich structure for a heat conduction problem. BACKGROUND

[0002] With the popularization of 3D printing technology, lattice material sandwich structures are increasingly widely used in the field of aerospace. Such structures not only have advantages such as ultra-low density, high specific strength, and energy absorption and buffering, but also can effectively reduce the weight of aircraft structures and improve overall performance due to their special periodic structural units. As the main load-bearing structure of an aircraft, the heat conduction characteristics of the lattice material sandwich structure under a thermal environment are a major challenge in structural design.

[0003] Current modeling methods are mainly based on continuum mechanics theory, but this method has limitations when dealing with heat conduction problems of lattice material sandwich structures. Traditional methods are difficult to accurately describe the discontinuity, multi-scale effects, and complex geometry of the material inside, limiting the understanding and prediction of the heat conduction behavior of the lattice material sandwich structure. The existing methods have the problems of large modeling difficulty, grid dependence, low calculation efficiency and accuracy of the lattice material sandwich structure heat conduction. SUMMARY

[0004] To solve the above technical problems, the present application provides a near-field dynamics modeling method for a lattice material sandwich structure for a heat conduction problem. The modeling method provided by the present application has the characteristics of convenient modeling, high calculation efficiency and accuracy, can effectively handle the discontinuity and multi-scale effects inside the material, and is suitable for complex geometry, can accurately predict the heat conduction behavior of the lattice material sandwich structure. The specific scheme is as follows:

[0005] A near-field dynamics modeling method for a lattice material sandwich structure for a heat conduction problem, the method mainly comprises the following steps:

[0006] S1, establishing a three-dimensional model of the lattice material sandwich structure;

[0007] The rod element of the lattice material is represented by a straight line, and the skin of the sandwich structure is represented by a plane;

[0008] S2, establishing a discrete model;

[0009] First, the lattice cell nodes in the interlayer are discretized into a series of particles, and the particles are connected by rod elements, and the mass and volume of the rod elements are evenly distributed at both ends of the particles;

[0010] Then, the particles at the ends of the rod elements are combined and merged according to the structure of the cell to form a discrete cell, and the volume V i and the mass mi For:

[0011]

[0012] In the formula: n is the number of bar elements connected to node i, l ij , r ij are the lengths and cross-sectional radii of the bar elements between nodes i and j, respectively, and p is the material density;

[0013] Finally, the vertices of adjacent cells are merged to form a complete lattice material structure;

[0014] S3, the skin of the sandwich structure is discretized into a uniform square grid with side length Δx, and the particles are distributed at the center of the square grid. The volume V i and mass m i of each particle are the mass and volume of the corresponding grid, and the calculation method is as follows:

[0015] V i = hΔx 2 , m i = pV i

[0016] is: h is the thickness of the skin;

[0017] After discretization, the total number of particles n p is obtained, and the total number of steps n t is defined by the program, and the time step Δt is defined;

[0018] S4, initialize the radius δ of the near-field influence range of each particle, and establish a "bond" between each particle x i and other particles x j within its near-field range. The distance between the two particles at the ends of the "bond" is the "bond" length ξ ij , and the number of bonds around each particle is n b(i) ; the particles include lattice structure particles, skin particles

[0019] Among them, the influence radius of the lattice structure particle is the particle around which is directly connected through the bar element. Each bar element becomes a "bond";

[0020] The radius of the influence range of the skin particle is δ = 3Δx, and a "bond" is formed between the other particle x j and the particle x i within this range;

[0021] The radius of the influence range of the lattice structure particle on the skin is δ = 3Δx;

[0022] S5, calculate the PD micro-heat conduction coefficient κ of the "bond";

[0023] The "bonds" include the "bonds" formed by the rod elements in the lattice structure, the "bonds" between the particles in the skin, and the "bonds" between the particles of the lattice material and the particles in the skin.

[0024] The “bonds” formed by the rod elements in the lattice structure are calculated based on one-dimensional heat conduction:

[0025]

[0026] The "bonds" between the particles in the skin are calculated using two-dimensional heat conduction:

[0027]

[0028] The "bond" between the lattice material particles and the cover leather points is calculated based on three-dimensional heat conduction:

[0029]

[0030] Where: k is the thermal conductivity of the material, A is the cross-sectional area of ​​the lattice material element, and h is the thickness of the structural skin;

[0031] S6. Initialize the temperature T(x i ,0);

[0032] S7, update the time step and enter the n+1th time step calculation, t=nΔt;

[0033] S8, update the boundary conditions, calculate and update the temperature T(x i ,t);

[0034] S9, start the numerical integration calculation within the near field of the particle, starting from i=1;

[0035] S10, start to enter the state calculation of the "bond" around the particle i, starting from j=1;

[0036] S11. Calculate the heat flux density on the "key" as follows:

[0037] f(x j ,x i ,t)=κτ i,j

[0038] Among them, τ i,j For the particle x i The temperature gradient on the surrounding "bonds" is calculated as follows:

[0039]

[0040] S12, determine whether to traverse the particle x iAll the keys around j < n b(i) j = j + 1, return to step eleven, otherwise continue to the next step;

[0041] S13, superimpose the heat flow density on all the keys around the particle x i Update the total heat flow received by the particle x i The calculation method is as follows:

[0042]

[0043] S14, update the temperature of each particle, and the calculation method is as follows:

[0044]

[0045] S15, judge whether all particles are traversed, if i < n p i = i + 1, return to step ten, otherwise continue to the next step;

[0046] S16, judge whether all calculation time steps are completed, if n < n t n = n + 1, return to step six, otherwise continue to the next step;

[0047] S17, the calculation is completed, and the result is output.

[0048] Compared with the prior art, the beneficial effects obtained by the present application are:

[0049] 1、The method provided by the present application can accurately describe the discontinuity inside the material, and can also consider the influence of multi-scale effect and complex geometric structure, and can accurately and efficiently calculate the heat conduction problem of complex structure.

[0050] 2、The calculation method provided by the present application is not dependent on the grid, and there is no grid sensitivity problem, and has the advantages of simple and efficient modeling. DETAILED DESCRIPTION

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0052] Figure 1 The program flowchart provided by the present application;

[0053] Figure 2 The dot matrix material discrete process schematic diagram provided by the present application;

[0054] Figure 3The structural temperature distribution result cloud diagram calculated by the embodiment provided by the application.

[0055] Fig. 1 is a lattice material sandwich structure model; 2 is a lattice material cell model; 3 is a cell discrete model; 4 is a sandwich structure discrete model; 5 is a bar element discrete model; 6 is a skin and interface discrete model.

[0056] Specific implementation

[0057] The application will be further described below with reference to the drawings. Embodiment

[0058] As Figure 1 shown, the embodiment includes the following steps:

[0059] S1, establishing a three-dimensional model of the lattice material sandwich structure;

[0060] The bar element of the lattice material is represented by a straight line, and the structure skin is represented by a plane.

[0061] The specimen size is 30mm*30mm*16mm, the lattice material cell structure form is a regular dodecahedron, the cell size is 5mm*5mm*5mm, the bar element diameter constituting the cell is 1mm, and the thickness of the two side skins is 0.5mm.

[0062] S2, establishing a discrete model;

[0063] The lattice material lattice cell nodes in the sandwich are discretized into a series of material points, the material points are connected through the bar elements, the mass and volume of the bar elements are evenly distributed at the two ends of the material points, the material points at the ends of the bar elements are combined and merged according to the structure mode of the cell to form a discrete cell, and the volume V i and mass m i of the material points after merging are as follows:

[0064]

[0065] Wherein, n is the number of bar elements connected to the node i, l ij , r ij are the length l ij =2.5mm and the cross-sectional radius r ij =0.5mm of the bar element between the nodes i and j, and the material density p=4430kg·m -3 .

[0066] Finally, the vertices of adjacent cells are merged to form a complete lattice material structure, as shown in Figure 2 .

[0067] S3, the sandwich structure skin is discretized into a uniform distribution of square grid with side length Δx = 0.5mm, and the material points are distributed at the center of the square grid, and the volume V and mass m of each material point are calculated as follows: i and mass m i , which are the mass and volume of the corresponding position grid, and the calculation method is as follows:

[0068] V i = hΔx 2 , m i = ρV i

[0069] Wherein, the skin thickness h = 0.5mm;

[0070] After discretization, the total number of particles n p = 8796, and the total number of steps n t = 10 is defined, and the time step Δt = 1 is defined;

[0071] S4, initialize the radius δ of the near-field influence range of each material point, and establish a "bond" between each material point x i and other material points x j within its near-field range, and the distance between the two ends of the "bond" is the "bond" length ξ ij , and the number of bonds around each material point is determined as nb ( i ) ;

[0072] Wherein, the point array structure particle influence range is the particles directly connected by the beam element around the particle, and each beam element becomes a "bond";

[0073] The influence range of the skin particle is δ = 3Δx, and a "bond" is formed between other particles x j and the particle x i within this range;

[0074] The influence radius of the point array structure particle on the skin is δ = 3Δx;

[0075] S5, define the PD micro-heat conduction coefficient κ of the "bond";

[0076] Wherein, the "bond" formed by the beam element in the point array structure is calculated according to one-dimensional heat conduction:

[0077]

[0078] The "bond" between the particles in the skin is calculated according to two-dimensional heat conduction:

[0079]

[0080] The "bond" between the particles in the point array material and the skin is calculated according to three-dimensional heat conduction:

[0081]

[0082] Wherein, the thermal conductivity of the material k = 273 W / (m·K), the cross-sectional area of the lattice material rod element A = 0.785 mm 2 , the thickness of the structural skin h = 0.5 mm;

[0083] S6, according to the initial conditions, initialize the temperature of each particle T(x i ,0) = 20℃ at n = 1 step;

[0084] S7, update the time step, enter the n+1 time step calculation, t = nΔt;

[0085] S8, update the boundary condition, calculate and update the temperature of the boundary particle T(x i ,t) = 100℃ according to the boundary condition;

[0086] S9, start the numerical integration calculation in the near field range of the particle, start from i = 1;

[0087] S10, start the state calculation of the "bond" around the particle i, start from j = 1;

[0088] S11, calculate the heat flux density on the "bond", the calculation method is as follows:

[0089] f(x j ,x i ,t) = κτ i,j

[0090] Wherein, τ i,j is the temperature gradient on each "bond" around the particle x i , the calculation method is as follows:

[0091]

[0092] S12, judge whether all the bonds around the particle x i have been traversed, if j < n b (i), then j = j + 1, return to step eleven, otherwise continue to the next step;

[0093] S13, superimpose the heat flux density on all the "bonds" around the particle x i , update the total heat flux received by the particle x i , the calculation method is as follows:

[0094]

[0095] S14, update the temperature of each particle, the calculation method is as follows:

[0096]

[0097] The calculated structure temperature distribution result cloud map is shown as follows: Figure 3

[0098] S15, judging whether all the mass points are traversed, if i p , then i=i+1, returning to step ten, otherwise continuing to the next step;

[0099] S16, judging whether all the calculation time steps are completed, if n t , then n=n+1, returning to step six, otherwise continuing to the next step;

[0100] S17, the calculation is ended, and the result is outputted.

[0101] Although the present application has been disclosed with the above preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not depart from the technical solutions of the present application, belongs to the protection scope of the present application. The contents not described in detail in the present application specification are the known technology of the person skilled in the art.​

Claims

1. A method for near-field dynamics modeling of a lattice material sandwich structure for heat conduction problems, characterized by The method comprises the following steps: S1, establishing a three-dimensional model of the lattice material sandwich structure; The rod element of the lattice material is represented by a straight line, and the skin of the sandwich structure is represented by a plane; S2, establishing a discrete model; Firstly, the lattice cell nodes in the lattice material of the sandwich are discretized into a series of mass points, the mass points are connected through rod elements, and the mass and volume of the rod elements are evenly distributed in the mass points at both ends; Then the particles at the end of the bar element are combined to form a discrete cell according to the structure of the cell. After the combination, the volume V i and the mass m i of the particle are obtained. Finally, the vertices of adjacent cells are merged to form a complete lattice material structure; S3, the skin of the sandwich structure is discretized into a uniform distribution of square grids with side length Δx, and the mass points are distributed at the centers of the square grids. The volume V and mass m of each mass point are i i That is, the mass and volume of the corresponding position grid.​ After the discretization the total number of particles is n p The program calculates the total number of steps n t The time step Δt is defined; S4, initialize the radius δ of the near-field influence range of each particle, and determine the number of bonds n around each particle x i and other particles x in the near-field range of x j Establish a "bond", and the distance between the two particles at the ends of the "bond" is the "bond" length ξ ij , determine the number of bonds n around each particle b(i) ; S5, calculating the PD micro-heat conduction coefficient K of the "key"; S6、According to the initial conditions, initialize the temperature of each particle T(x,0) at the first step n = 1. i ,0) S7, updating the time step and entering the n+1 time step calculation, t=nΔt; S8, update the boundary conditions, calculate and update the temperature T(x i ,t) of the boundary particles according to the boundary conditions; S9, starting the numerical integration calculation in the near-field range of the mass point, starting from i=1; S10, starting the state calculation of the "key" around the mass point i, starting from j=1; S11, calculating the heat flux density on the "key"; S12, judging whether the mass point x is traversed i all the keys around, if j < n b(i) then j = j + 1, return to step 11, otherwise continue to the next step; S13, the heat flux on all "keys" around the particle x i The total heat flux received by the particle x is updated as follows: i The total heat flux received by the particle x is updated as follows: S14, updating the temperature of each mass point, and the calculation method is as follows: S15, judging whether all the mass points are traversed, if i < n p then i = i + 1, returning to step ten, otherwise, continuing the next step; S16, determine whether all calculation time steps are completed, if n < n t then n = n + 1, return to step six, otherwise continue to next step; S17, calculation is completed, and the results are output.

2. A method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 1, wherein, The volume V of the mass point in step S2 i and the mass m i are calculated as: where n is the number of bar elements connected to node i, l ij , r ij are the length and cross-sectional radius of the bar element between nodes i, j, respectively, and p is the material density.

3. A method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 1, wherein, The volume V of each of the material points described in step S3 i and the mass m i The calculation is as follows: V i = h Δx 2 , m i = p V i Wherein: h is the thickness of the skin.

4. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 1, wherein, Each mass point in step S4 includes a skin mass point and a lattice structure mass point, wherein, The influence range radius of the lattice structure mass point is the points directly connected around the mass point through the rod element, and each rod element becomes a "key"; The skin point influence range radius is δ = 3Δx, and other points x j form a "bond" with the point x i ; The influence range radius of the lattice structure mass point on the skin is δ=3Δx.

5. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 1, wherein, The "key" in step S5 includes the "key" formed by the rod element in the lattice structure, the "key" between the mass points in the skin, and the "key" between the mass points of the lattice material and the mass points of the skin.

6. A method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 5, wherein, The "key" formed by the rod element in the lattice structure is calculated according to one-dimensional heat conduction: Wherein: k is the thermal conductivity of the material, A is the cross-sectional area of the rod element of the lattice material, and h is the thickness of the structure skin.

7. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 5, wherein, The "key" between the mass points in the skin is calculated according to two-dimensional heat conduction: Wherein: k is the thermal conductivity of the material, A is the cross-sectional area of the rod element of the lattice material, and h is the thickness of the structure skin.

8. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 5, wherein, The "key" between the mass points of the lattice material and the mass points of the skin is calculated according to three-dimensional heat conduction: Wherein: k is the thermal conductivity of the material, A is the cross-sectional area of the rod element of the lattice material, and h is the thickness of the structure skin.

9. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 5, wherein, The calculation method of the heat flux density on the "key" in step S11 is as follows: f(x j ,x i ,t) = κτ i,j where τ i,j is the temperature gradient around each "bond" of the particle x i around each "bond" of the particle x 10. The method of modeling a lattice material sandwich structure for heat conduction problems using near-field dynamics according to claim 9, wherein, The τ i,j For the particle x i The temperature gradient on each "bond" around the particle x is calculated as follows: wherein ξ ij is "a bond".

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