Near-field dynamics modeling method of lattice material sandwich structure for heat conduction problem

Abstract

The invention discloses a near-field dynamics modeling method of a lattice material sandwich structure for solving the heat conduction problem. The method mainly comprises the steps that a three-dimensional model and a discrete model of the lattice material sandwich structure are established; the total number of mass points is obtained after discretization, the total step number is calculated, and the time step length is defined; the radius of the near-field influence range of each particle is initialized; calculating the micro heat conductivity coefficient of the key; updating boundary conditions; starting numerical integration calculation in a particle near field range; calculating the state of a key around the mass point and the heat flux density; judging whether heat flux density superposition of all keys around the mass point is traversed or not; updating the temperature of each particle; judging whether all the mass points are traversed or not; judging whether all calculation time steps are completed or not; and after calculation is finished, outputting a result. The method provided by the invention is convenient in modeling and high in calculation efficiency and precision, can effectively process the discontinuity and multi-scale effect in the material, adapts to a complex geometric structure, and can accurately predict the heat conduction behavior of the sandwich structure of the dot matrix material.

Description

Technical Field

[0001] The invention relates to the field of heat conduction system design and manufacturing, and in particular to a peridynamic modeling method of a lattice material sandwich structure for heat conduction problems. Background Art

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

[0003] The current modeling method is mainly based on the theory of continuum mechanics, but this method has limitations when dealing with the problem of heat conduction in lattice material sandwich structures. Traditional methods are difficult to accurately describe the discontinuity, multi-scale effects and complex geometric structures inside the material, which limits the understanding and prediction of the heat conduction behavior of lattice material sandwich structures. Existing methods have problems such as high modeling difficulty, grid dependence, and low calculation efficiency and accuracy of heat conduction in lattice material sandwich structures. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a peridynamic modeling method for a lattice material sandwich structure for heat conduction problems. The modeling method provided by the present invention has the characteristics of convenient modeling, high calculation efficiency and accuracy, can effectively deal with the discontinuity and multi-scale effects inside the material, and can adapt to complex geometric structures. It can accurately predict the heat conduction behavior of the lattice material sandwich structure. The specific scheme is as follows:

[0005] A peridynamic modeling method for a lattice material sandwich structure for heat conduction problems, the method mainly comprising the following steps:

[0006] S1. Establish a three-dimensional model of the sandwich structure of lattice materials;

[0007] The rod elements of the lattice material are represented by straight lines, and the skin of the sandwich structure is represented by planes;

[0008] S2, establish a discrete model;

[0009] Firstly, the lattice cell nodes of the lattice material in the sandwich are discretized into a series of mass points, which are connected by rod elements, and the mass and volume of the rod elements are evenly distributed at the mass points at both ends;

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

[0011]

[0012] Where: n is the number of rods connected to node i, l ij 、r ij are the length of the bar element and the cross-sectional radius between nodes i and j, respectively, and ρ is the material density;

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

[0014] S3. Discretize the skin of the sandwich structure into a uniformly distributed square grid with a side length of Δx. The particles are distributed at the center of the square grid. The volume V of each material point is i and mass m i That is, the mass and volume of the grid at the corresponding position, which is calculated as follows:

[0015] V i =hΔx 2 , m i =ρV i

[0016] In the equation: h is the skin thickness;

[0017] The total number of particles obtained after discretization is n p , and define the total number of steps n for program calculation t , define the time step Δt;

[0018] S4, initialize the radius δ of the near field influence range of each particle, and set each particle x i and other particles x in its near field j Establish a "bond", and the distance between the two ends of the "bond" is the "bond length ξ ij , determine the number of bonds around each particle as n b(i) The particles include lattice structure particles, masking points

[0019] The influence radius of the particle of the lattice structure is the points around the particle that are directly connected by rod elements, and each rod element becomes a "key";

[0020] The radius of the influence range of the mask point is δ=3Δx, and other particles x within this range j With particle x i A "bond" is formed between them;

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

[0022] S5, calculate the PD micro thermal conductivity 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 of the skin;

[0024] Among them, the "bond" formed by the rod elements in the lattice structure is calculated according to one-dimensional heat conduction:

[0025]

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

[0027]

[0028] The "bond" between the lattice material particles and the cover leather points is calculated by 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 rod element, and h is the thickness of the structural skin;

[0031] S6. Initialize the temperature T(x) of each particle at step n=1 according to the initial conditions. i ,0);

[0032] S7, update the time step and enter the calculation of the n+1th time step, 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 "key" 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 mass x i The temperature gradient on the surrounding "bonds" is calculated as follows:

[0039]

[0040] S12, determine whether to traverse the particle x iAll surrounding keys, if j <n b(i) , then j=j+1, return to step 11, otherwise continue to the next step;

[0041] S13, the particle x i The heat flux density on all surrounding "bonds" is superimposed to update the particle x i The total heat flux received is calculated as follows:

[0042]

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

[0044]

[0045] S15, determine whether to traverse all particles, if i <n p , then i=i+1, return to step 10, otherwise continue to the next step;

[0046] S16, determine whether all calculation steps are completed, if n <n t , then n=n+1, return to step 6, otherwise continue to the next step;

[0047] S17. Calculation is completed and the result is output.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. The method provided by the present invention can accurately describe the discontinuity inside the material, while also considering the influence of multi-scale effects and complex geometric structures, and can accurately and efficiently calculate the heat conduction problems of complex structures.

[0050] 2. The calculation method provided by this technology does not rely on the grid, does not have the problem of grid sensitivity, and has the advantages of simple and efficient modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0052] Figure 1 A flowchart of the program provided by the present invention;

[0053] Figure 2 A schematic diagram of the discrete process of the lattice material provided by the present invention;

[0054] Figure 3This is a cloud diagram of the structural temperature distribution results calculated by the embodiment provided by the present invention.

[0055] Figure numerals: 1. Lattice material sandwich structure model; 2. Lattice material cell model; 3. Cell discrete model; 4. Sandwich structure discrete model; 5. Rod element discrete model; 6. Skin and interface discrete model.

[0056] Specific implementation methods

[0057] The present invention will be further described below in conjunction with the accompanying drawings. Example

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

[0059] S1. Establish a three-dimensional model of the sandwich structure of lattice materials;

[0060] The rod elements of the lattice material are represented by straight lines, and the structural skin is represented by planes;

[0061] The specimen size is 30mm×30mm×16mm, the cell structure of the lattice material is a regular rhombus dodecahedron, the unit cell size is 5mm×5mm×5mm, the diameter of the rod element constituting the cell body is 1mm, and the thickness of the skin on both sides is 0.5mm.

[0062] S2, establish a discrete model;

[0063] The lattice cell nodes of the lattice material in the interlayer are discretized into a series of material points. The material points are connected by rod elements. The mass and volume of the rod elements are evenly distributed at the material points at both ends. The material points at the ends of the rod elements are combined and merged according to the structure of the cell element to form a discrete cell. The volume of the merged particles is V i and mass m i for:

[0064]

[0065] Where: n is the number of rods connected to node i, l ij 、r ij are the length l of the rod element between nodes i and j respectively ij =2.5mm and cross-sectional radius r ij =0.5mm, material density ρ = 4430kg·m -3 ;

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

[0067] S3. Discretize the sandwich structure skin into a uniformly distributed square grid with a side length of Δx = 0.5 mm. The material points are distributed in the center of the square grid. The volume V of each material point is i and mass m i That is, the mass and volume of the grid at the corresponding position, which is calculated as follows:

[0068] V i =hΔx 2 , m i =ρV i

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

[0070] The total number of particles obtained after discretization is n p =8796, and define the total number of steps n for program calculation t =10, define the time step Δt=1;

[0071] S4, initialize the radius δ of the near field influence range of each material point, and set each particle x i and other particles x in its near field j Establish a "bond", and the distance between the two ends of the "bond" is the "bond length ξ ij , determine the number of bonds around each particle as nb ( i ) ;

[0072] Among them, the influence range of the lattice structure particle is the points around the particle that are directly connected by the rod elements, and each rod element becomes a "key";

[0073] The influence range of the mask point is δ = 3Δx. Other particles x within this range j With particle x i A "bond" is formed between them;

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

[0075] S5. Define the PD micro thermal conductivity κ of the “bond”;

[0076] Among them, the "bond" formed by the rod element in the lattice structure is calculated according to one-dimensional heat conduction:

[0077]

[0078] The "bonds" between particles in the skin are calculated using two-dimensional heat conduction:

[0079]

[0080] The "bond" between the lattice material particles and the leather surface points is calculated by three-dimensional heat conduction:

[0081]

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

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

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

[0085] S8, update the boundary conditions, calculate and update the temperature T(x i ,t)=100℃;

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

[0087] S10, start to enter the state calculation of the "key" around the particle i, starting from j=1;

[0088] S11. Calculate the heat flux density on the "key" as follows:

[0089] f(x j ,x i ,t)=κτ i,j

[0090] Among them, τ i,j For mass x i The temperature gradient on the surrounding "bonds" is calculated as follows:

[0091]

[0092] S12, determine whether to traverse the particle x i All surrounding keys, if j <n b (i), then j=j+1, return to step 11, otherwise proceed to the next step;

[0093] S13, the particle x i The heat flux density on all surrounding "bonds" is superimposed to update the particle x i The total heat flux received is calculated as follows:

[0094]

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

[0096]

[0097] The calculated structural temperature distribution result cloud diagram is as follows Figure 3 As shown;

[0098] S15, determine whether to traverse all particles, if i <n p , then i=i+1, return to step 10, otherwise continue to the next step;

[0099] S16, determine whether all calculation steps are completed, if n <n t , then n=n+1, return to step 6, otherwise continue to the next step;

[0100] S17. Calculation is completed and the result is output.

[0101] Although the present invention has been disclosed as a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the above disclosed methods and technical contents without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention. The contents not described in detail in the specification of the present invention belong to the known technology of professional and technical personnel in this field.

Claims

1. A peridynamic modeling method for a lattice material sandwich structure for heat conduction problems, characterized in that , including the following steps: S1. Establish a three-dimensional model of the sandwich structure of lattice materials; The rod elements of the lattice material are represented by straight lines, and the skin of the sandwich structure is represented by planes; S2, establish a discrete model; Firstly, the lattice cell nodes of the lattice material in the sandwich are discretized into a series of mass points, which are connected by rod elements, and the mass and volume of the rod elements are evenly distributed at the mass points at both ends; Then, the particles at the ends of the rod element are combined and merged according to the structure of the cell to form a discrete cell. After merging, the particle volume V is obtained. i and mass m i ; Finally, the vertices of adjacent cells are merged to form a complete lattice material structure; S3. Discretize the skin of the sandwich structure into a uniformly distributed square grid with a side length of Δx. The particles are distributed at the center of the square grid. The volume V of each material point is i and mass m i That is, the mass and volume of the grid at the corresponding position; The total number of particles obtained after discretization is n p , and define the total number of steps n for program calculation t , define the time step Δt; S4, initialize the radius δ of the near field influence range of each particle, and set each particle x i and other particles x in its near field j Establish a "bond", the distance between the two ends of the "bond" is the "bond" length ξ ij , determine the number of bonds around each particle as n b(i) ; S5. Calculate the PD micro thermal conductivity κ of the "bond"; S6. Initialize the temperature T(x) of each particle at step n=1 according to the initial conditions. i ,0); S7, update the time step and enter the calculation of the n+1th time step, t=nΔt; S8, update the boundary conditions, calculate and update the temperature T(x i ,t); S9, start the numerical integration calculation within the near field of the particle, starting from i=1; S10, start to enter the state calculation of the "key" around the particle i, starting from j=1; S11. Calculate the heat flux density on the "key"; S12, determine whether to traverse the particle x i All surrounding keys, if j <n b(i) , then j=j+1, return to step 11, otherwise continue to the next step; S13, the particle x i The heat flux density on all surrounding "keys" is superimposed to update the particle x i The total heat flux received is calculated as follows: S14, update the temperature of each particle, the calculation method is as follows: S15, determine whether to traverse all particles, if i <n p , then i=i+1, return to step 10, otherwise continue to the next step; S16, determine whether all calculation steps are completed, if n <n t , then n=n+1, return to step 6, otherwise continue to the next step; S17. Calculation is completed and the result is output.

2. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 1, characterized in that: The particle volume V in step S2 i and mass m i The calculation is: Where: n is the number of rods connected to node i, l ij 、r ij are the length and cross-sectional radius of the bar element between nodes i and j respectively, and ρ is the material density.

3. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 1, characterized in that: The volume V of each material point described in step S3 i and mass m i The calculation is as follows: V i =hΔx 2 ,m i =ρV i Where: h is the skin thickness.

4. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 1, characterized in that: The particles in step S4 include mask points and lattice structure particles, wherein: The radius of the influence range of the particle of the lattice structure is the points around the particle that are directly connected by the rod elements, and each rod element becomes a "key"; The radius of the influence range of the mask point is δ=3Δx, and other particles x within this range j With particle x i A "bond" is formed between them; The radius of the influence range of the lattice structure particles on the skin is δ=3Δx.

5. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 1, characterized in that: The "bonds" described in step S5 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 of the skin.

6. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 5, characterized in that: The "bonds" formed by the rod elements in the lattice structure are calculated according to one-dimensional heat conduction: Where: k is the thermal conductivity of the material, A is the cross-sectional area of ​​the lattice material rod element, and h is the thickness of the structural skin.

7. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 5, characterized in that: The "bonds" between the particles in the skin are calculated by two-dimensional heat conduction: Where: k is the thermal conductivity of the material, A is the cross-sectional area of ​​the lattice material rod element, and h is the thickness of the structural skin.

8. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 5, characterized in that: The "bond" between the lattice material particles and the cover leather points is calculated by three-dimensional heat conduction: Where: k is the thermal conductivity of the material, A is the cross-sectional area of ​​the lattice material rod element, and h is the thickness of the structural skin.

9. The peridynamic modeling method of a lattice material sandwich structure for heat conduction problems according to claim 5, characterized in that: The heat flux density on the "key" in step S11 is calculated as follows: f(x j ,x i ,t)=ct i,j In the formula, τ i,j For mass x i The temperature gradient on the surrounding "keys".

10. A peridynamic modeling method for a lattice material sandwich structure for heat conduction problems according to claim 9, characterized in that: The τ in step S11 i,j For mass x i The temperature gradient on the surrounding "keys" is calculated as follows: Where ξ ij is the key length.

Images