A method for studying the equivalent mechanical properties of propellants

Abstract

The invention discloses a method for studying the equivalent mechanical properties of a propellant, which belongs to the technical field of multi-scale modeling. The method comprises: inserting a cohesive force unit of zero thickness between a particle unit and a matrix unit of the propellant to form a micro-grid model; setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the micro-grid model; constructing a node displacement constraint relationship under periodic boundary conditions based on the original boundary nodes and the new boundary nodes of the propellant, and the boundary nodes of the cohesive force unit, and obtaining a corresponding constraint coefficient matrix based on the node displacement constraint relationship under periodic boundary conditions; constructing an overall stiffness matrix and a residual force matrix based on the constraint coefficient matrix; and carrying out a calculation of the equivalent mechanical properties of the propellant using a virtual unit method based on the overall stiffness matrix and the residual force matrix to obtain a calculation result of the equivalent mechanical properties of the propellant. The method can improve the accuracy of the study of the equivalent mechanical properties of the propellant.

Description

Technical Field

[0001] The invention relates to a method for studying the equivalent mechanical properties of a propellant, and belongs to the technical field of multi-scale modeling. Background Art

[0002] Analysis of the micromechanical properties of propellants is a key issue in the development of propellant formulations.

[0003] The virtual element method has a natural advantage in dealing with the real microscopic morphology of propellants by virtue of its characteristics of processing polygonal elements. In order to better simulate the mechanical behavior response of propellants, the computational model must consider the use of periodic boundary conditions.

[0004] The real mesoscopic model of propellant in the existing virtual element method does not take periodic boundary conditions into consideration and lacks a specific design method for periodic boundary conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a method for studying the equivalent mechanical properties of propellants. Compared with the real microscopic model of the propellant in the existing virtual unit method, the periodic boundary conditions are taken into account, which can improve the accuracy of the study of the equivalent mechanical properties of the propellant.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for studying equivalent mechanical properties of a propellant, comprising:

[0008] The polygonal mesh model is divided based on the real mesoscopic structure of the propellant, and zero-thickness cohesive force units are inserted between the particle units and the matrix units of the propellant to form a mesoscopic mesh model;

[0009] Setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the mesoscopic grid model;

[0010] Based on the original boundary nodes and newly added boundary nodes of the propellant and the boundary nodes of the cohesive force unit, the node displacement constraint relationship under the periodic boundary condition is constructed, and based on the node displacement constraint relationship under the periodic boundary condition, the corresponding constraint coefficient matrix is ​​obtained;

[0011] Based on the constraint coefficient matrix, construct an overall stiffness matrix and a residual force matrix;

[0012] Based on the overall stiffness matrix and the residual force matrix, the equivalent mechanical performance calculation of the propellant is carried out using the virtual element method to obtain the calculation results of the equivalent mechanical performance of the propellant.

[0013] In combination with the first aspect, further, the original boundary nodes of the propellant are nodes of each propellant unit located on the edge of the mesoscopic grid model, and the boundary nodes of the cohesion unit are nodes of each cohesion unit located on the edge of the mesoscopic grid model;

[0014] Wherein, the propellant unit includes a particle unit and a matrix unit.

[0015] In combination with the first aspect, further, setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the mesoscopic grid model includes:

[0016] On the side opposite to the side where the original boundary node of the propellant is located, newly added boundary nodes corresponding one to one with the original boundary nodes of the propellant are arranged;

[0017] Update the serial numbers of all nodes in the propellant unit where each newly added boundary node is located;

[0018] Wherein, each pair of original boundary nodes and newly added boundary nodes are symmetrical about the central axis of the mesoscopic grid model;

[0019] All nodes of the propellant unit include original boundary nodes and newly added boundary nodes located on the edge of the mesoscopic grid model, and original internal nodes located inside the mesoscopic grid model.

[0020] In combination with the first aspect, further, updating the serial numbers of all nodes of the propellant unit where each newly added boundary node is located includes:

[0021] For all nodes of the propellant unit where each newly added boundary node is located, the serial numbers are updated in a counterclockwise order, starting with the original boundary node with the smallest ordinate.

[0022] In combination with the first aspect, further, based on the original boundary nodes and the newly added boundary nodes of the propellant and the boundary nodes of the cohesive force unit, the node displacement constraint relationship under the periodic boundary condition is constructed, and based on the node displacement constraint relationship under the periodic boundary condition, the corresponding constraint coefficient matrix is ​​obtained, including:

[0023] Sorting the nodes on each edge of the mesoscopic grid model to obtain the order of the nodes on each edge of the mesoscopic grid model;

[0024] Based on the node sequence on each edge of the mesoscopic grid model, a node displacement constraint relationship under periodic boundary conditions is constructed, and based on the node displacement constraint relationship under periodic boundary conditions, a corresponding constraint coefficient matrix is ​​obtained;

[0025] The nodes on the longitudinal edges of the meso-grid model include the original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the lower left corner and the lower right corner of the meso-grid model, and the boundary nodes of the cohesive force unit;

[0026] The nodes on the lateral sides of the meso-grid model include original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the four corners of the meso-grid model, and boundary nodes of the cohesive force unit.

[0027] In combination with the first aspect, further, sorting the nodes on each edge of the meso-grid model to obtain the order of the nodes on each edge of the meso-grid model includes:

[0028] Determining the order of boundary nodes of the cohesive force unit on each edge of the mesoscopic mesh model;

[0029] Based on the order of boundary nodes of the cohesion unit on each edge of the meso grid model and the coordinates of the original boundary nodes and the newly added boundary nodes of the propellant on each edge of the meso grid model, the nodes on each edge of the meso grid model are sorted to obtain the node order on each edge of the meso grid model.

[0030] In combination with the first aspect, further, determining the order of boundary nodes of the cohesion unit on each edge of the mesoscopic grid model includes:

[0031] For a cohesive unit Two boundary nodes on one edge of the mesoscale mesh model , , loop through each propellant unit until a node containing a boundary is found. And there is a node Located at the border node Propellant unit on the side , and contains boundary nodes And there is a node Located at the border node Propellant unit on the side ;

[0032] Based on propellant unit Node , Propellant unit Node Coordinates of the boundary nodes , order.

[0033] Combined with the first aspect, further, the node displacement constraint relationship under the periodic boundary condition is:

[0034] ;

[0035] in, , The vertical edge on the left side of the micro-grid model The horizontal and vertical coordinates of the nodes, , The vertical edge on the right side of the micro-grid model The horizontal and vertical coordinates of the nodes, , Represents the horizontal edge of the upper part of the micro-grid model. The horizontal and vertical coordinates of the nodes, , Indicates the horizontal edge below the mesoscopic mesh model. The horizontal and vertical coordinates of the nodes, , Represents the node at the lower left corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node at the lower right corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node located at the upper left corner of the mesoscopic mesh model The horizontal and vertical coordinates of Indicates that the node ,node In addition, the total number of nodes on each longitudinal edge of the micro-grid model, Indicates that the node ,node ,node and the node located in the upper right corner of the mesoscopic mesh model The total number of nodes on each horizontal edge of the meso-grid model;

[0036] The node displacement constraint relationship under periodic boundary conditions is rewritten into matrix form:

[0037] ;

[0038] in, represents the constraint coefficient matrix, represents the constraint value vector, , Indicates the horizontal and vertical coordinates of the first node on the edge of the micro-grid model. , Represents the horizontal and vertical coordinates of the second node on the edge of the micro-grid model.

[0039] In combination with the first aspect, further, the relationship between the overall stiffness matrix and the residual force matrix is:

[0040] ;

[0041] in, represents the overall stiffness matrix, represents the residual force matrix.

[0042] Combined with the first aspect, further, the node displacement constraint relationship corresponding to the propellant longitudinal stretching condition is:

[0043] ;

[0044] in, represents the horizontal strain of the propellant, Represents the length of the mesoscopic mesh model.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] The method for studying the equivalent mechanical properties of a propellant provided by the present invention is based on a pre-divided polygonal mesh model, and inserts a zero-thickness cohesive force unit between a particle unit and a matrix unit of the propellant to form a micro-mesh model; by setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the micro-mesh model, a node displacement constraint relationship under a periodic boundary condition is constructed, and a corresponding constraint coefficient matrix is ​​obtained, thereby constructing an overall stiffness matrix and a residual force matrix; based on the overall stiffness matrix and the residual force matrix constructed by the present invention, a virtual unit method is used to carry out calculation of the equivalent mechanical properties of the propellant, and the periodic boundary conditions are taken into consideration, so as to improve the accuracy of the study on the equivalent mechanical properties of the propellant. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of a method for studying the equivalent mechanical properties of a propellant provided in an embodiment of the present invention;

[0048] Figure 2 is a schematic diagram of a newly added boundary node provided in an embodiment of the present invention;

[0049] Figure 3 This is a schematic diagram of updating the sequence number of a newly added boundary node provided by an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram of sorting boundary nodes of a cohesion unit provided by an embodiment of the present invention;

[0051] Figure 5It is a schematic diagram of node screening on the edge of a meso-grid model provided by an embodiment of the present invention, wherein (a) is a schematic diagram of node screening on the longitudinal edge of a meso-grid model, and (b) is a schematic diagram of node screening on the lateral edge of a meso-grid model. DETAILED DESCRIPTION

[0052] The technical solution of the present application is further described in detail below in conjunction with specific implementation methods.

[0053] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and should not be construed as limitations on the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments may be combined with each other.

[0054] Embodiment 1:

[0055] Figure 1 This is a flow chart of a method for studying the equivalent mechanical properties of a propellant provided in this embodiment. This flow chart only shows the logical sequence of the method in this embodiment. Different methods can be used without conflict. Figure 1 The steps shown or described are accomplished in the order shown.

[0056] See also Figure 1 The method for studying the equivalent mechanical properties of propellants provided in this embodiment specifically includes the following steps:

[0057] Step 1: Divide the polygonal mesh model based on the real mesoscopic structure of the propellant, and insert zero-thickness cohesive force units between the particle units and the matrix units of the propellant to form a mesoscopic mesh model;

[0058] In this embodiment, based on the real microscopic structure of the propellant, the propellant is divided into a polygonal mesh model, such as Figure 4 As shown, based on the divided polygonal mesh model, zero-thickness cohesion units are inserted between the particle units and the matrix units of the propellant to form a micro-mesh model.

[0059] Step 2: Set new boundary nodes on the opposite sides of the mesoscopic grid model that correspond one-to-one to the original boundary nodes of the propellant;

[0060] In this embodiment, Figure 4 As shown, the original boundary nodes of the propellant are the nodes of each propellant unit located on the edge of the micro-grid model, and the boundary nodes of the cohesion unit are the nodes of each cohesion unit located on the edge of the micro-grid model; wherein the propellant unit includes a particle unit and a matrix unit.

[0061] Setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the mesoscopic grid model specifically includes the following steps:

[0062] Step 1: On the opposite side of the edge where the original boundary node of the propellant is located, set a new boundary node that corresponds one-to-one with the original boundary node of the propellant;

[0063] In this embodiment, Figure 2 As shown, if one original boundary node of the propellant is located on the longitudinal edge of the left side of the meso-grid model, then on the longitudinal edge of the right side of the meso-grid model, at the same ordinate as the original boundary node, a newly added boundary node corresponding to the original boundary node is set. Correspondingly, if one original boundary node of the propellant is located on the longitudinal edge of the right side of the meso-grid model, then on the longitudinal edge of the left side of the meso-grid model, at the same ordinate as the original boundary node, a newly added boundary node corresponding to the original boundary node is set. If one original boundary node of the propellant is located on the transverse edge above the meso-grid model, then on the transverse edge below the meso-grid model, at the same abscissa as the original boundary node, a newly added boundary node corresponding to the original boundary node is set. Correspondingly, if one original boundary node of the propellant is located on the transverse edge below the meso-grid model, then on the transverse edge above the meso-grid model, at the same abscissa as the original boundary node, a newly added boundary node corresponding to the original boundary node is set.

[0064] Therefore, each pair of original boundary nodes and newly added boundary nodes are symmetrical about the central axis of the meso-grid model. That is, for the original boundary nodes located on the longitudinal edge of the meso-grid model, the ordinates of the newly added boundary nodes corresponding to them should be the same as the ordinates of the original boundary nodes; for the original boundary nodes located on the transverse edge of the meso-grid model, the abscissas of the newly added boundary nodes corresponding to them should be the same as the abscissas of the original boundary nodes.

[0065] Step 2: Update the serial numbers of all nodes in the propellant unit where each newly added boundary node is located.

[0066] In this embodiment, Figure 3 As shown, all nodes of the propellant unit include the original boundary nodes and newly added boundary nodes located on the edge of the meso-grid model, as well as the original internal nodes located inside the meso-grid model.

[0067] The serial number updating of all nodes of the propellant unit where each newly added boundary node is located specifically includes: starting with the original boundary node with the smallest ordinate, the serial number of all nodes of the propellant unit where each newly added boundary node is located is updated in a counterclockwise order.

[0068] like Figure 3As shown, for the newly added boundary nodes , the propellant unit in which it is located All nodes including the original boundary nodes located at the edge of the mesoscopic mesh model , and new boundary nodes , and the original internal nodes located inside the mesoscale mesh model , , , , with the original boundary node with the smallest ordinate Starting with , the serial number is updated in counterclockwise order, then the propellant unit The serial numbers of all nodes are given by Updated to .

[0069] Step 3: Based on the original boundary nodes and newly added boundary nodes of the propellant and the boundary nodes of the cohesive force unit, the node displacement constraint relationship under the periodic boundary condition is constructed, and based on the node displacement constraint relationship under the periodic boundary condition, the corresponding constraint coefficient matrix is ​​obtained;

[0070] In this embodiment, based on the original boundary nodes and newly added boundary nodes of the propellant and the boundary nodes of the cohesive force unit, a node displacement constraint relationship under periodic boundary conditions is constructed, and based on the node displacement constraint relationship under periodic boundary conditions, a corresponding constraint coefficient matrix is ​​obtained, which specifically includes the following steps:

[0071] Step 1: Sort the nodes on each edge of the meso-grid model to obtain the node order on each edge of the meso-grid model;

[0072] In this embodiment, the nodes on the longitudinal edges of the meso-grid model include the original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the lower left corner and the lower right corner of the meso-grid model, and the boundary nodes of the cohesion unit.

[0073] like Figure 5 As shown in (a), when sorting the nodes on the longitudinal edge of the meso-grid model, the nodes located at the lower left and lower right corners of the meso-grid model , Does not participate in sorting.

[0074] The nodes on the lateral edges of the meso-grid model include the original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the four corners of the meso-grid model, and the boundary nodes of the cohesive force unit.

[0075] like Figure 5 As shown in (b), when sorting the nodes on the horizontal edge of the meso-grid model, the nodes located at the four corners of the meso-grid model , , , Does not participate in sorting.

[0076] Sorting the nodes on each edge of the meso-grid model and obtaining the node order on each edge of the meso-grid model specifically includes the following steps:

[0077] Step ①: Determine the order of the boundary nodes of the cohesive force unit on each edge of the mesoscopic mesh model;

[0078] In this embodiment, the order of determining the boundary nodes of the cohesion unit on each edge of the meso-grid model specifically includes the following steps:

[0079] Step 1: For a cohesive unit Two boundary nodes on an edge of a mesoscale mesh model , , loop through each propellant unit until a node containing a boundary is found. And there is a node Located at the border node Propellant unit on the side , and contains boundary nodes And there is a node Located at the border node Propellant unit on the side ;

[0080] Step ii: Propellant unit based Node , Propellant unit Node Coordinates of the boundary nodes , order.

[0081] like Figure 4 As shown, the node , , , Located on the longitudinal edge of the micro-grid model, if in order from bottom to top, based on the node The vertical coordinate is less than the node The vertical coordinate of the node , The order is ; If in order from top to bottom, based on the node The vertical coordinate is less than the node The vertical coordinate of the node , The order is .

[0082] Different from Figure 4 As shown, assuming that the node , , , Located on the horizontal edge of the micro-grid model, if in order from left to right, based on the node The horizontal coordinate is smaller than the node The horizontal coordinate of the node , The order is ; If in order from right to left, based on the node The horizontal coordinate is smaller than the node The horizontal coordinate of the node , The order is .

[0083] Step ②: Based on the order of the boundary nodes of the cohesive force unit on each edge of the meso-grid model and the coordinates of the original boundary nodes and the newly added boundary nodes of the propellant on each edge of the meso-grid model, the nodes on each edge of the meso-grid model are sorted to obtain the node order on each edge of the meso-grid model.

[0084] In this embodiment, the order of nodes on the longitudinal edge of the meso-grid model can be from bottom to top or from top to bottom, and the order of nodes on the transverse edge of the meso-grid model can be from left to right or from right to left. However, the order of nodes on the longitudinal edge on the left side of the meso-grid model should be consistent with the order of nodes on the longitudinal edge on the right side, and the order of nodes on the transverse edge above the meso-grid model should be consistent with the order of nodes on the transverse edge below.

[0085] Step 2: Based on the node order on each edge of the mesoscopic mesh model, construct the node displacement constraint relationship under the periodic boundary condition, and obtain the corresponding constraint coefficient matrix based on the node displacement constraint relationship under the periodic boundary condition.

[0086] In this embodiment, the node displacement constraint relationship under the periodic boundary condition is:

[0087] ;

[0088] in, , The vertical edge on the left side of the micro-grid model The horizontal and vertical coordinates of the nodes, , The vertical edge on the right side of the micro-grid model The horizontal and vertical coordinates of the nodes, , Represents the horizontal edge of the upper part of the micro-grid model. The horizontal and vertical coordinates of the nodes, , Indicates the horizontal edge below the mesoscopic mesh model. The horizontal and vertical coordinates of the nodes, , Represents the node at the lower left corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node at the lower right corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node located at the upper left corner of the mesoscopic mesh model The horizontal and vertical coordinates of Indicates that the node ,node In addition, the total number of nodes on each longitudinal edge of the micro-grid model, Indicates that the node ,node ,node and the node located in the upper right corner of the mesoscopic mesh model In addition, the total number of nodes on each horizontal edge of the meso-mesh model.

[0089] The node displacement constraint relationship under periodic boundary conditions is rewritten into matrix form:

[0090] ;

[0091] in, represents the constraint coefficient matrix, represents the constraint value vector, , Indicates the horizontal and vertical coordinates of the first node on the edge of the micro-grid model. , Represents the horizontal and vertical coordinates of the second node on the edge of the micro-grid model.

[0092] The node displacement constraint relationship corresponding to the propellant longitudinal stretching condition is:

[0093] ;

[0094] in, represents the strain in the horizontal direction of the propellant, Represents the length of the mesoscopic mesh model.

[0095] Step 4: Based on the constraint coefficient matrix, construct the overall stiffness matrix and residual force matrix;

[0096] In this embodiment, the relationship between the overall stiffness matrix and the residual force matrix is:

[0097] ;

[0098] in, represents the overall stiffness matrix, represents the residual force matrix.

[0099] Step 5: Based on the overall stiffness matrix and the residual force matrix, the virtual element method is used to calculate the equivalent mechanical performance of the propellant to obtain the calculation results of the equivalent mechanical performance of the propellant.

[0100] The method for studying the equivalent mechanical properties of propellants provided in the present embodiment is based on a pre-divided polygonal mesh model, and inserts zero-thickness cohesive force units between the particle units and the matrix units of the propellant to form a micro-mesh model; by setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the micro-mesh model, a node displacement constraint relationship under periodic boundary conditions is constructed, and the corresponding constraint coefficient matrix is ​​obtained, and then an overall stiffness matrix and a residual force matrix are constructed; based on the overall stiffness matrix and the residual force matrix constructed in the present embodiment, the equivalent mechanical properties of the propellant are calculated using the virtual unit method, and the periodic boundary conditions are taken into consideration, which can improve the accuracy of the study on the equivalent mechanical properties of the propellant.

[0101] The above are only preferred implementations of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for studying the equivalent mechanical properties of a propellant, characterized in that: include: The polygonal mesh model is divided based on the real mesoscopic structure of the propellant, and zero-thickness cohesive force units are inserted between the particle units and the matrix units of the propellant to form a mesoscopic mesh model; Setting new boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the mesoscopic grid model; Based on the original boundary nodes and newly added boundary nodes of the propellant and the boundary nodes of the cohesive force unit, the node displacement constraint relationship under the periodic boundary condition is constructed, and based on the node displacement constraint relationship under the periodic boundary condition, the corresponding constraint coefficient matrix is ​​obtained; Based on the constraint coefficient matrix, the overall stiffness matrix and residual force matrix are constructed; Based on the overall stiffness matrix and the residual force matrix, the equivalent mechanical performance calculation of the propellant is carried out using the virtual element method to obtain the calculation results of the equivalent mechanical performance of the propellant; The node displacement constraint relationship under periodic boundary conditions is: ； in, , The vertical edge on the left side of the micro-grid model The horizontal and vertical coordinates of the nodes, , The vertical edge on the right side of the micro-grid model The horizontal and vertical coordinates of the nodes, , Represents the horizontal edge of the upper part of the micro-grid model. The horizontal and vertical coordinates of the nodes, , Indicates the horizontal edge below the mesoscopic mesh model. The horizontal and vertical coordinates of the nodes, , Represents the node at the lower left corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node at the lower right corner of the mesoscopic mesh model The horizontal and vertical coordinates of , Represents the node located at the upper left corner of the mesoscopic mesh model The horizontal and vertical coordinates of Indicates that the node ,node In addition, the total number of nodes on each longitudinal edge of the micro-grid model, Indicates that the node ,node ,node and the node located in the upper right corner of the mesoscopic mesh model The total number of nodes on each horizontal edge of the meso-grid model; The node displacement constraint relationship corresponding to the propellant longitudinal stretching condition is: ； in, represents the strain in the horizontal direction of the propellant, Represents the length of the mesoscopic mesh model.

2. The method for studying the equivalent mechanical properties of propellants according to claim 1, characterized in that: The original boundary nodes of the propellant are nodes of each propellant unit located on the edge of the mesoscopic grid model, and the boundary nodes of the cohesion force unit are nodes of each cohesion force unit located on the edge of the mesoscopic grid model; Wherein, the propellant unit includes a particle unit and a matrix unit.

3. The method for studying the equivalent mechanical properties of propellants according to claim 1, characterized in that: The newly added boundary nodes corresponding to the original boundary nodes of the propellant on the opposite sides of the mesoscopic mesh model include: On the side opposite to the side where the original boundary node of the propellant is located, newly added boundary nodes corresponding one to one with the original boundary nodes of the propellant are arranged; Update the serial numbers of all nodes in the propellant unit where each newly added boundary node is located; Wherein, each pair of original boundary nodes and newly added boundary nodes are symmetrical about the central axis of the mesoscopic grid model; All nodes of the propellant unit include original boundary nodes and newly added boundary nodes located on the edge of the mesoscopic grid model, and original internal nodes located inside the mesoscopic grid model.

4. The method for studying the equivalent mechanical properties of propellants according to claim 3, characterized in that: The serial number of all nodes in the propellant unit where each newly added boundary node is located is updated, including: For all nodes of the propellant unit where each newly added boundary node is located, the serial numbers are updated in a counterclockwise order, starting with the original boundary node with the smallest ordinate.

5. The method for studying the equivalent mechanical properties of propellants according to claim 1, characterized in that: Based on the original boundary nodes and newly added boundary nodes of the propellant, as well as the boundary nodes of the cohesive force unit, the node displacement constraint relationship under the periodic boundary condition is constructed, and based on the node displacement constraint relationship under the periodic boundary condition, the corresponding constraint coefficient matrix is ​​obtained, including: Sorting the nodes on each edge of the mesoscopic grid model to obtain the order of the nodes on each edge of the mesoscopic grid model; Based on the node sequence on each edge of the mesoscopic grid model, a node displacement constraint relationship under periodic boundary conditions is constructed, and based on the node displacement constraint relationship under periodic boundary conditions, a corresponding constraint coefficient matrix is ​​obtained; The nodes on the longitudinal edges of the meso-grid model include the original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the lower left corner and the lower right corner of the meso-grid model, and the boundary nodes of the cohesive force unit; The nodes on the lateral sides of the meso-grid model include original boundary nodes and newly added boundary nodes of the propellant except the nodes located at the four corners of the meso-grid model, and boundary nodes of the cohesive force unit.

6. The method for studying the equivalent mechanical properties of propellants according to claim 5, characterized in that: Sorting the nodes on each edge of the mesoscopic grid model to obtain the order of the nodes on each edge of the mesoscopic grid model includes: Determining the order of boundary nodes of the cohesive force unit on each edge of the mesoscopic mesh model; Based on the order of boundary nodes of the cohesion unit on each edge of the meso grid model and the coordinates of the original boundary nodes and the newly added boundary nodes of the propellant on each edge of the meso grid model, the nodes on each edge of the meso grid model are sorted to obtain the node order on each edge of the meso grid model.

7. The method for studying the equivalent mechanical properties of propellants according to claim 6, characterized in that: The order of determining the boundary nodes of the cohesive force unit on each edge of the mesoscopic mesh model includes: For a cohesive unit Two boundary nodes on one edge of the mesoscale mesh model , , loop through each propellant unit until a node containing a boundary is found. And there is a node Located at the border node Propellant unit on the side , and contains boundary nodes And there is a node Located at the border node Propellant unit on the side ; Propellant unit based Node , Propellant unit Node Coordinates of the boundary nodes , order.

8. The method for studying the equivalent mechanical properties of propellants according to claim 1, characterized in that: The node displacement constraint relationship under periodic boundary conditions is rewritten into matrix form: ； in, represents the constraint coefficient matrix, represents the constraint value vector, , Indicates the horizontal and vertical coordinates of the first node on the edge of the micro-grid model. , Represents the horizontal and vertical coordinates of the second node on the edge of the micro-grid model.

9. The method for studying the equivalent mechanical properties of propellants according to claim 8, characterized in that: The relationship between the overall stiffness matrix and the residual force matrix is: ； in, represents the overall stiffness matrix, represents the residual force matrix.

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