A method, apparatus and electronic device for characterizing the boundary stiffness of a lattice structure
By segmenting and identifying the type of the lattice structure and performing differentiated mechanical calculations based on the boundary conditions of the rods, the problem of decreased accuracy of equivalent stiffness in the heterogeneous multi-scale finite element method is solved, achieving higher computational accuracy and adaptability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NINGBO INST OF MATERIALS TECH & ENG CHINESE ACAD OF SCI
- Filing Date
- 2025-12-08
- Publication Date
- 2026-05-12
AI Technical Summary
Existing heterogeneous multiscale finite element methods, without considering the differences in residual lattice cells, lead to a decrease in the accuracy of equivalent stiffness, making them difficult to adapt to various application scenarios.
By segmenting the lattice structure, the type of lattice cell is determined, and differentiated flexible mechanical calculations are performed based on the type and the boundary conditions of the members, including the correlation equations under full load, no load, and half load constraint states, to accurately determine the equivalent stiffness.
It improves the accuracy of the boundary stiffness of the lattice structure, reduces error accumulation, and can adapt to a variety of application scenarios.
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Figure CN121257136B_ABST
Abstract
Description
Technical Field
[0001] This disclosure relates to the fields of materials mechanics and structural design, and in particular to a method, apparatus and electronic device for characterizing the boundary stiffness of a lattice structure. Background Technology
[0002] Currently, most existing methods for calculating the equivalent stiffness of complex-shaped aperiodic lattice structures employ heterogeneous multi-scale finite element methods (macroscopic decomposition followed by microscopic calculation). However, after macroscopic decomposition, the geometric structures of different residual lattice cells are not identical, making it difficult to apply a unified mechanical calculation method for the microscopic calculation. Using a unified mechanical calculation method may lead to low calculation accuracy and increased risk of error accumulation. In summary, even when using the heterogeneous multi-scale finite element method, the accuracy of the determined equivalent stiffness decreases when the differences in residual lattice cells are not considered, making it difficult to adapt to various application scenarios. Summary of the Invention
[0003] This disclosure provides a method, apparatus, and electronic device for characterizing the boundary stiffness of lattice structures, which to some extent solves the problem that existing methods using heterogeneous multi-scale finite element methods, when not considering the influence of differences in residual lattice cells, result in decreased accuracy in determining the equivalent stiffness and make it difficult to adapt to various application scenarios.
[0004] According to one aspect of this disclosure, a method for characterizing the boundary stiffness of a lattice structure is provided. The method includes: segmenting the lattice structure to obtain segmented lattice cells; determining the type of the lattice cells; the type being used to indicate the integrity of the lattice cells; determining the equivalent stiffness of the lattice cells based on the type and the member boundary conditions of the lattice cells; and the member boundary conditions being used to indicate the stress constraint state of the members.
[0005] Furthermore, according to one aspect of the method of this disclosure, the types include: sub-intact and intact; the sub-intact type is obtained by dividing the residual lattice cells based on symmetry processing.
[0006] Furthermore, according to one aspect of the method of this disclosure, the member boundary conditions include: a fully constrained state, a state without constrained state, and a state with partial constrained state.
[0007] Furthermore, according to one aspect of the method of this disclosure, the equivalent stiffness of a lattice cell is determined based on its type and the boundary conditions of the lattice cell, including: determining the member length, member radius, member spatial tilt angle, and member material elastic modulus of the lattice cell based on its type; when the member boundary conditions are under full constraint, establishing a first correlation equation between load and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under no constraint, establishing a second correlation equation between displacement and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under partial constraint, establishing a third correlation equation between load, displacement, and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness.
[0008] Furthermore, according to one aspect of the method of this disclosure, when the boundary conditions of the member are under full force constraint, a first correlation equation between load and deformation is established for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness. This includes: decomposing the member spatial tilt angle to obtain a first load in a one-dimensional direction; the one-dimensional direction is the Z-axis direction; determining the first deformation of the member based on the member length, member radius, and member material elastic modulus; the first deformation is the axial equivalent deformation of the member along the Z-axis direction; and using the stress-strain mechanism, establishing the first correlation equation based on the first load and the first deformation to solve for the equivalent stiffness.
[0009] Furthermore, according to one aspect of the method of this disclosure, when the boundary conditions of the member are unconstrained, a second correlation equation between displacement and deformation is established based on the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness. This includes: performing three-dimensional displacement decomposition based on the member spatial tilt angle to obtain a first decomposition result; the three-dimensional directions are the X-axis, Y-axis, and Z-axis; determining the second deformation of the member based on the member length, member radius, and member material elastic modulus; the second deformation is the total deformation of the member after superimposing the axial equivalent deformation and bending deformation along the three-dimensional directions; and using the stress-strain mechanism, based on the first decomposition result and the second deformation, establishing a second correlation equation and solving it to obtain the equivalent stiffness.
[0010] Furthermore, according to one aspect of the method of this disclosure, when the boundary condition of the member is a semi-constrained state, a third correlation equation for the load, displacement, and deformation of the member length, member radius, member spatial tilt angle, and member material elastic modulus is established to obtain the equivalent stiffness. This includes: decomposing the member based on the member spatial tilt angle to obtain a second decomposition result of the second load in the one-dimensional direction and the second decomposition result of the displacement in the three-dimensional direction; determining the third deformation of the member based on the member length, member radius, and member material elastic modulus; the third deformation is the total deformation of the member after superimposing the axial equivalent deformation and bending deformation along the three-dimensional direction; and using the stress-strain mechanism, based on the second load, the second decomposition result, and the third deformation, establishing a third correlation equation and solving it to obtain the equivalent stiffness.
[0011] Furthermore, according to one aspect of the method disclosed herein, the segmentation method includes at least one of the following: periodic reference segmentation method, geometric symmetry plane segmentation method, and functional partition boundary segmentation method.
[0012] According to another aspect of this disclosure, an apparatus for characterizing the boundary stiffness of a lattice structure is provided. The apparatus includes: a segmentation unit for segmenting the lattice structure to obtain segmented lattice cells; a first determining unit for determining the type of the lattice cells; the type is used to indicate the integrity of the lattice cells; and a second determining unit for determining the equivalent stiffness of the lattice cells based on the type and the member boundary conditions of the lattice cells; the member boundary conditions are used to indicate the stress constraint state of the members.
[0013] According to another aspect of this disclosure, an electronic device is provided, comprising: a memory for storing computer-readable instructions; and a processor for executing the computer-readable instructions, causing the electronic device to perform the method as described in any embodiment of one aspect.
[0014] This disclosure provides a method, apparatus, and electronic device for characterizing the boundary stiffness of a lattice structure. The disclosure involves segmenting the lattice structure to obtain segmented lattice cells; determining the type of each lattice cell; the type indicating the integrity of the lattice cell; and determining the equivalent stiffness of the lattice cell based on the type and the member boundary conditions; the member boundary conditions indicating the stress constraint state of the members. Thus, compared to the fixed calculation method of existing heterogeneous multi-scale finite element methods, this disclosure can employ differentiated and flexible mechanical calculations for lattice cells with different integrity types, combined with their specific member boundary conditions, avoiding errors caused by uniform calculations. In summary, the technical solution provided by this disclosure can improve the accuracy of characterizing the boundary stiffness of lattice structures, reduce error accumulation, and adapt to various application scenarios.
[0015] It should be understood that both the foregoing general description and the following detailed description are exemplary and intended to provide further illustration of the claimed technology. Attached Figure Description
[0016] The above and other objects, features, and advantages of this disclosure will become more apparent from the more detailed description of the embodiments thereof in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this disclosure and form part of the specification. They are used together with the embodiments of this disclosure to explain the disclosure and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.
[0017] Figure 1 A flowchart illustrating a method for characterizing the boundary stiffness of a lattice structure provided in an embodiment of this disclosure;
[0018] Figure 2 A schematic diagram of different lattice cells provided in the embodiments of this disclosure;
[0019] Figure 3 A schematic diagram of a complete or sub-complete lattice cell provided in the embodiments of this disclosure;
[0020] Figure 4 A schematic diagram illustrating the stress and deformation analysis of a lattice under full force constraint state provided in an embodiment of this disclosure;
[0021] Figure 5 A schematic diagram illustrating the stress and deformation analysis of a lattice under unconstrained conditions provided in an embodiment of this disclosure;
[0022] Figure 6 A schematic diagram illustrating the stress and deformation analysis of a lattice under a semi-force-constrained state provided in an embodiment of this disclosure;
[0023] Figure 7 A schematic diagram illustrating the relationship between boundary coefficient and slenderness ratio provided in an embodiment of this disclosure;
[0024] Figure 8 is a schematic diagram of the structural cutting method provided in the embodiments of this disclosure;
[0025] Figure 9 is a schematic diagram showing the results of applying the method of this disclosure to BCC according to an embodiment of this disclosure;
[0026] Figure 10 is a schematic diagram of the results of applying the method of this disclosure to a face-centered cubic (FCC) according to an embodiment of this disclosure.
[0027] Figure 11 is a schematic diagram of the results of applying the method of this disclosure to the face-centered cubic (FCC-C) composite provided in the embodiments of this disclosure.
[0028] Figure 12 is a schematic diagram of the result of applying the method of this disclosure to the rhombic dodecahedron (RD) lattice provided in the embodiments of this disclosure;
[0029] Figure 13 is a schematic diagram of the results of applying the method of this disclosure to the octet lattice structure (OCT) provided in the embodiments of this disclosure;
[0030] Figure 14 A structural block diagram of a device for characterizing the boundary stiffness of a lattice structure provided in this embodiment of the present disclosure;
[0031] Figure 15 This is a hardware block diagram of an electronic device provided in an embodiment of the present disclosure. Detailed Implementation
[0032] To make the objectives, technical solutions, and advantages of this disclosure more apparent, exemplary embodiments according to this disclosure will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this disclosure, and not all embodiments of this disclosure. It should be understood that this disclosure is not limited to the exemplary embodiments described herein.
[0033] Currently, most existing methods for calculating the equivalent stiffness of complex-shaped aperiodic lattice structures employ heterogeneous multi-scale finite element methods (macroscopic decomposition followed by microscopic calculation). However, after macroscopic decomposition, the geometric structures of different residual lattice cells are not identical, making it difficult to apply a unified mechanical calculation method for the microscopic calculation. Using a unified mechanical calculation method may lead to low calculation accuracy and increased risk of error accumulation. In summary, even when using the heterogeneous multi-scale finite element method, the accuracy of the determined equivalent stiffness decreases when the differences in residual lattice cells are not considered, making it difficult to adapt to various application scenarios.
[0034] Therefore, in response to the problems mentioned above, this disclosure provides a method for characterizing the boundary stiffness of lattice structures. Compared with the fixed calculation method of existing heterogeneous multi-scale finite element methods, this disclosure can adopt differentiated and flexible mechanical calculations for lattice cells of different integrity types, combined with their specific rod boundary conditions, thus avoiding the errors caused by uniform calculations.
[0035] This disclosure provides a method for characterizing the boundary stiffness of a lattice structure. Please refer to [reference needed]. Figure 1 , Figure 1 This is a flowchart illustrating a method for characterizing the boundary stiffness of a lattice structure, provided as an embodiment of this disclosure. Figure 1 As shown, the method includes:
[0036] In step S101, the lattice structure is segmented to obtain the segmented lattice cells;
[0037] In step S102, the type of lattice cell is determined; the type is used to indicate the integrity of the lattice cell.
[0038] In step S103, the equivalent stiffness of the lattice cell is determined based on the type and the rod boundary conditions of the lattice cell; the rod boundary conditions are used to indicate the stress constraint state of the rod.
[0039] In this disclosure, a lattice cell can be understood as a basic repeating unit or local substructure that constitutes a lattice structure. It is the basic unit for microscopic mechanical analysis after macroscopic decomposition of the lattice structure.
[0040] In this disclosure, the type of lattice cell can be understood as a category based on whether the cell geometry is complete. For example, it can be divided into complete cells (geometric structure consistent with standard cells) and residual cells (geometric incomplete due to lattice structure boundaries or complex shapes).
[0041] In this disclosure, the boundary conditions of the bars can be understood as the constraint state of each component bar in the lattice cell during force analysis, which can directly affect the mechanical response characteristics of the bars.
[0042] Specifically, methods for determining more accurate equivalent stiffness can include the following steps: First, macroscopically decompose the lattice structure using adaptive mesh segmentation algorithms to ensure that the segmented lattice cells reflect local structural features. Second, extract features such as the number of vertices and member connections of each cell using geometric feature recognition models to determine its specific type, such as complete or residual. Third, for different cell types, construct differentiated finite element calculation methods based on the constraint states of the member endpoints. Complete cells use standard constitutive relations and boundary conditions, while residual cells are supplemented with local geometric correction coefficients and constraint strengthening factors. Fourth, perform micromechanical calculations on each cell to obtain the single-cell equivalent stiffness matrix, then integrate all cell stiffness information using a macroscopic assembly algorithm to finally output the equivalent stiffness of the entire lattice structure.
[0043] The following will specifically describe the types of lattice cells and the rod boundary conditions of this disclosure, including:
[0044] The types include: sub-intact and intact; the sub-intact type is obtained by dividing the residual lattice cells based on symmetry processing.
[0045] Specifically, the sub-complete type can be understood as a non-independent cell generated after the overall segmentation of a lattice structure. It retains the core topological features through the principle of symmetry completion, with only local structural incompleteness at the segmentation interface. Its geometric shape and mechanical response need to be derived in conjunction with the overall symmetry conditions. The complete type can be understood as an independent lattice unit with a completely closed topological structure. It can maintain structural integrity without relying on external symmetry conditions, and can fully reflect the basic mechanical properties and geometric features of the lattice structure. It is the basic independent unit that constitutes the lattice structure.
[0046] For example, Figure 2 This is a schematic diagram of different lattice cells provided in the embodiments of this disclosure. Figure 3 Figure 2 shows schematic diagrams of complete or sub-complete lattice cells provided in embodiments of this disclosure. As can be seen from Figure 2: A and B are both sub-complete cells, which are non-independent cells generated after the overall segmentation of the lattice structure. They have truncated regions and residual regions, and their structural integrity is destroyed, with only local structural incompleteness at the segmentation interface. C is a complete cell, possessing a completely closed topological structure, and is a basic independent unit constituting the lattice structure. As can be seen from Figure 3: there are sub-complete cell types and complete cell types. The sub-complete cell is obtained by symmetric processing of the residual cell.
[0047] The boundary conditions for members include: fully constrained state, unconstrained state, and partially constrained state.
[0048] Specifically, a fully constrained state can be understood as a member being constrained at both ends and critical nodes, allowing load transfer only through internal deformation. An unconstrained state can be understood as a member being unconstrained at both ends and nodes, allowing complete freedom of displacement and rotation, with load transfer only through connections to adjacent cells—a free state. A partially constrained state can be understood as a member being constrained only in certain directions (e.g., axial or radial), while remaining free in the remaining directions, allowing displacement or rotation in a specific dimension.
[0049] The following section will elaborate on how to characterize the boundary stiffness of a lattice structure using type and member boundary conditions, including:
[0050] Based on the type, determine the rod length, rod radius, rod spatial tilt angle, and rod material elastic modulus of the lattice cell;
[0051] When the boundary conditions of the rod are under full force constraint, the first correlation equation between load and deformation is established for the rod length, rod radius, rod spatial tilt angle and rod material elastic modulus, and the equivalent stiffness is obtained.
[0052] When the boundary conditions of the rod are unconstrained, a second correlation equation for displacement and deformation is established for the rod length, rod radius, rod spatial tilt angle and rod material elastic modulus, and the equivalent stiffness is obtained.
[0053] When the boundary conditions of the member are in a semi-constrained state, the third correlation equation of load, displacement and deformation is established for the member length, member radius, member spatial tilt angle and member material elastic modulus to obtain the equivalent stiffness.
[0054] In this disclosure, the length of a rod can be understood as the axial dimension of the rod constituting the lattice cell in space, that is, the straight-line distance between the nodes at both ends of the rod.
[0055] In this disclosure, the radius of a rod can be understood as the radius of the cross-sectional circle of the rod constituting the lattice cell, and is used to characterize the cross-sectional dimensions of the rod.
[0056] In this disclosure, the spatial tilt angle of a member can be understood as the angle between the member in space and a reference coordinate system (such as the coordinate axes of a Cartesian coordinate system), used to describe the spatial orientation of the member.
[0057] In this disclosure, the elastic modulus of the rod material can be understood as the elastic modulus of the material used in the rod, which is a physical quantity that reflects the material's ability to resist elastic deformation and is determined by the material's own properties.
[0058] In this disclosure, the first correlation equation can be understood as the equation relating the member's length, radius, spatial tilt angle, and material elastic modulus to load and deformation when the member is under full constraint, used to describe the force-deformation relationship under this constraint state, and thus derive the equivalent stiffness. The second correlation equation can be understood as the equation relating the member's length, radius, spatial tilt angle, and material elastic modulus to displacement and deformation when the member is under no constraint, used to describe the displacement-deformation relationship under this state, and thus derive the equivalent stiffness. The third correlation equation can be understood as the equation relating the member's length, radius, spatial tilt angle, and material elastic modulus to load, displacement, and deformation when the member is under partial constraint, used to describe the force-displacement-deformation relationship under this intermediate constraint state, and thus derive the equivalent stiffness.
[0059] Specifically, the methods for characterizing the boundary stiffness of a lattice structure include: first, determining the member length, member radius, member spatial tilt angle, and member material elastic modulus based on the type of lattice cell; then, selecting the corresponding first, second, or third correlation equation according to the different member boundary conditions, and solving for the equivalent stiffness. Detailed methods can be found below.
[0060] The following section will elaborate on how to characterize the boundary stiffness of a lattice structure under full force constraint, including the following methods:
[0061] Based on the spatial tilt angle of the rod, the first load in a one-dimensional direction is obtained by decomposition; the one-dimensional direction is the Z-axis direction.
[0062] Based on the length, radius, and elastic modulus of the rod material, the first deformation of the rod is determined; the first deformation is the equivalent axial deformation of the rod along the Z-axis.
[0063] Using the stress-strain mechanism, based on the first load and the first deformation, a first correlation equation is established, and the equivalent stiffness is obtained by solving it.
[0064] In this disclosure, the first load can be understood as the load component obtained by decomposing the spatial load on the member based on its spatial tilt angle in the one-dimensional Z-axis direction.
[0065] In this disclosure, the first deformation can be understood as the axial equivalent deformation of the member under full force constraint along the Z-axis, which is determined by the member length, radius and elastic modulus of the material.
[0066] In this disclosure, the stress-strain mechanism can be understood as the physical relationship (such as Hooke's law) between stress and strain in a material under stress, which is the basis for establishing the relationship between load and deformation.
[0067] Specifically, under full force constraint conditions, the method for characterizing the boundary stiffness of a lattice structure includes the following steps: Step 1: Load decomposition: Obtain the spatial tilt angle of the members in the lattice cell, decompose the total spatial load borne by the members along the Z-axis, and calculate the first load; Step 2: Deformation calculation: Based on the geometric parameters (length, radius) and material properties (elastic modulus) of the members, and combined with the member deformation formula in mechanics of materials, calculate the first deformation of the members along the Z-axis; Step 3: Based on the stress-strain mechanism (such as Hooke's law), establish the first correlation equation between the first load and the first deformation, and solve the equation to obtain the equivalent stiffness under full force constraint conditions.
[0068] For example, Figure 4 Figure 4 is a schematic diagram of the stress and deformation analysis of a lattice under full force constraint provided in an embodiment of this disclosure. As can be seen from Figure 4, under full force constraint, the nodes can only translate along the loading direction, do not move in the in-plane direction, and the nodes do not rotate. Figure 4 (a) shows the total spatial load (including force) borne by the rod. The process of obtaining the first load by decomposing the sum of the torque M and the load along the Z-axis based on its spatial tilt angle ω; Figure 4 (b) shows the first deformation of the rod along the Z-axis (e.g.: (Iconic diagram of deformation). The overall analysis intuitively demonstrates the analytical logic from spatial load decomposition to axial deformation response under full force constraint, which corresponds to the aforementioned method and steps for determining equivalent stiffness under full force constraint (load decomposition, deformation calculation).
[0069] For example, this disclosure also provides a specific first correlation equation that can satisfy the following formula:
[0070] in, It represents the equivalent stiffness under full force constraint. The stress is in the Z-axis direction. The strain is in the Z-axis direction. This is the elastic modulus of the rod material. Let be the radius of the rod. The length of the rod. The angle of inclination of the member in space. For the dimensionless geometric parameters of the rod, it can be based on and Sure.
[0071] The following section will elaborate on how to characterize the boundary stiffness of a lattice structure under unconstrained conditions, including the following methods:
[0072] Based on the spatial tilt angle of the rod, a three-dimensional displacement decomposition is performed to obtain the first decomposition result; the three-dimensional directions are the X-axis, Y-axis and Z-axis;
[0073] Based on the length, radius, and elastic modulus of the rod, the second deformation of the rod is determined; the second deformation is the total deformation of the rod after superimposing the axial equivalent deformation and bending deformation along the three-dimensional direction.
[0074] Using the stress-strain mechanism, based on the first decomposition result and the second deformation, a second correlation equation is established, and the equivalent stiffness is obtained by solving it.
[0075] In this disclosure, the first decomposition result can be understood as the set of axial displacement components obtained by decomposing the three-dimensional spatial displacement of the member under no force constraint state into the X-axis, Y-axis and Z-axis directions based on its spatial tilt angle.
[0076] In this disclosure, the second deformation is the total deformation formed by the superposition of the axial equivalent deformation and bending deformation generated by the member in the three-dimensional directions of the X-axis, Y-axis and Z-axis under the condition of no force constraint.
[0077] Specifically, the method for characterizing the boundary stiffness of a lattice structure under unconstrained conditions includes the following steps: Step 1: Displacement decomposition: Obtain the spatial tilt angle of the members in the lattice cell, decompose the three-dimensional spatial displacement of the members under unconstrained conditions, and obtain the displacement components in the X, Y, and Z axes, i.e., the first decomposition result; Step 2: Calculation of total deformation: Combine the geometric parameters (length, radius) and material properties (elastic modulus) of the members, calculate the axial equivalent deformation and bending deformation of the members along the three-dimensional directions, and then superimpose the axial deformation and bending deformation in each direction to obtain the second deformation; Step 3: Equation establishment and solution: Based on the stress-strain mechanism (such as Hooke's law), establish a second correlation equation between the first decomposition result (each axial displacement component) and the second deformation (total deformation), and obtain the equivalent stiffness under unconstrained conditions by solving this equation.
[0078] For example, Figure 5 This is a schematic diagram illustrating the stress and deformation analysis of a lattice under unconstrained conditions, provided in an embodiment of this disclosure. Figure 5 It can be seen that under no force constraint, the node can translate in three directions, but according to the requirement of deformation coordination between adjacent cells, the node does not rotate. Figure 5 (a) demonstrates that the rod can withstand complex loads (including force). , , and torque M, The process of decomposing displacements in three dimensions (X-axis, Y-axis, Z-axis) based on the spatial tilt angle ω. Figure 5 (b) presents the total deformation of the member after the superposition of the axial equivalent deformation and bending deformation along the three-dimensional direction (e.g.: Depend on , , (A superimposed deformation diagram). The overall diagram intuitively illustrates the analytical logic from three-dimensional displacement decomposition to total deformation response under unconstrained conditions, which corresponds to the aforementioned method steps for determining equivalent stiffness under unconstrained conditions (displacement decomposition, total deformation calculation).
[0079] For example, this disclosure also provides a specific second correlation equation that can satisfy the following formula:
[0080] in, It is the equivalent stiffness under unrestrained (free) conditions.
[0081] The following section will elaborate on how to characterize the boundary stiffness of a lattice structure under semi-constrained conditions, including the following methods:
[0082] Based on the spatial tilt angle of the rod, the second decomposition results of the second load in the one-dimensional direction and the second displacement in the three-dimensional direction are obtained;
[0083] Based on the length, radius, and elastic modulus of the rod, the third deformation of the rod is determined; the third deformation is the total deformation of the rod after superimposing the axial equivalent deformation and bending deformation along the three-dimensional direction.
[0084] Using the stress-strain mechanism, based on the second load, the second decomposition result, and the third deformation, a third correlation equation is established, and the equivalent stiffness is obtained by solving it.
[0085] In this disclosure, the second load can be understood as the directional load component obtained by decomposing the total spatial load borne by the member under semi-forced constraint state into a specified one-dimensional direction (such as the Z-axis) based on its spatial tilt angle.
[0086] In this disclosure, the second decomposition result can be understood as the set of axial displacement components obtained by decomposing the three-dimensional spatial displacement generated by the member under semi-forced constraint state into the X-axis, Y-axis and Z-axis directions based on its spatial tilt angle.
[0087] In this disclosure, the third deformation can be understood as the total deformation formed by the superposition of the axial equivalent deformation and bending deformation generated by the member in the three-dimensional directions of the X-axis, Y-axis and Z-axis under semi-force constraint.
[0088] Specifically, under semi-constrained conditions (i.e., transitional state), the method for characterizing the boundary stiffness of a lattice structure can include the following steps: Step 1: Dual decomposition of load and displacement: Obtain the spatial tilt angle of the members in the lattice cell. On the one hand, decompose the total spatial load borne by the members into a specified one-dimensional direction (such as the Z-axis) to obtain the second load; on the other hand, decompose the three-dimensional spatial displacement generated by the members into three-dimensional directions (X-axis, Y-axis, Z-axis) to obtain the axial displacement components, i.e., the second decomposition result; Step 2: Calculation of total deformation: Combining the geometric parameters (length, radius) and material properties (elastic modulus) of the members, calculate the axial equivalent deformation and bending deformation of the members along the three-dimensional directions respectively. Superimpose the axial deformation and bending deformation in each direction to obtain the third deformation; Step 3: Equation establishment and solution: Based on the stress-strain mechanism (such as Hooke's law), establish a third correlation equation between the second load, the second decomposition result (each axial displacement component), and the third deformation (total deformation). Solve this equation to obtain the equivalent stiffness under semi-constrained conditions.
[0089] For example, Figure 6 This is a schematic diagram illustrating the stress and deformation analysis of a lattice under semi-forced constraint conditions, provided in an embodiment of this disclosure. From... Figure 6 As can be seen, Figure (a) shows the total spatial load (including force) borne by the rod. , and torque M, The second load is obtained by decomposing the three-dimensional spatial displacement along a specified one-dimensional direction (such as the Z-axis) based on its spatial tilt angle ω. Simultaneously, the three-dimensional spatial displacement is decomposed along the X, Y, and Z axes to obtain the second decomposition result. Figure (b) shows the third deformation amount (e.g., from the superposition of axial equivalent deformation and bending deformation generated by the member along the three-dimensional direction). , , (A schematic diagram of the superimposed deformation). The overall diagram intuitively illustrates the analytical logic from the dual decomposition of load and displacement to the total deformation response under semi-force constraint, which corresponds to the aforementioned method and steps for determining the equivalent stiffness under semi-force constraint (dual decomposition of load and displacement, calculation of total deformation).
[0090] For example, this disclosure also provides a specific third correlation equation that can satisfy the following formula:
[0091] in, Let K be the equivalent stiffness under the semi-stressed (transitional) state. K is the boundary coefficient. Under the semi-stressed state constraint, K can satisfy the following formula:
[0092] in, Let X be the displacement components of the member in the XY plane under semi-forced constraint.
[0093] It is important to note that the selection of K can be related to the length and radius of the member. Figure 7 This is a schematic diagram illustrating the relationship between boundary coefficient and slenderness ratio, provided for embodiments of this disclosure. Figure 7 It can be seen that the boundary coefficient K varies with the slenderness ratio. (Based on the length of the rod) and radius Decide, The slenderness ratio of the boundary coefficient K increases monotonically and the growth rate gradually slows down, which shows that there is a clear positive correlation between the boundary coefficient K and the slenderness ratio of the member. This provides a parameter correlation basis for the slenderness ratio dimension for the accurate calculation of the equivalent stiffness under semi-constrained state.
[0094] The following will specifically describe the segmentation method of this disclosure, which may include, but is not limited to, at least one of the following: periodic reference segmentation method, geometric symmetry plane segmentation method, and functional partition boundary segmentation method.
[0095] Specifically, the periodic benchmark segmentation method uses the inherent periodicity of the lattice structure as a benchmark and determines the segmentation boundary according to the repeating pattern of the cells. The geometric symmetry plane segmentation method is based on the geometric symmetry characteristics of the lattice structure (such as central symmetry or axial symmetry), selecting a symmetry plane as the segmentation interface so that the segmented sub-regions satisfy the symmetry condition. The functional zoning boundary segmentation method is based on the actual load-bearing requirements or functional zoning of the lattice structure (such as stress concentration areas or lightweight areas), using functional boundaries as the segmentation basis to achieve independent segmentation of different functional areas.
[0096] For example, this disclosure provides specific embodiments of applying the method of this disclosure to characterize the boundary stiffness of lattice structures, including:
[0097] A 5x5x5 square body-centered cubic (BCC) lattice structure was selected and cut. Specifically, a 5x4x5 region was selected, and the cells within that region were preserved. The rest of the structure was removed. Simulation conditions were set with the lower nodes fixed and the upper part coupled, with a fixed displacement applied at the coupling reference point. The distance the preserved region moved was... The load was applied to a linear elastic segment with a range of 0-5 mm, and the normalized equivalent modulus was calculated. The normalization standard was the distance traveled. The curves showing the relationship between the equivalent modulus, the distance of movement, and the normalized modulus of the structure obtained at that time reflect the change law of the equivalent stiffness of different lattice structures after the movement of the cut-retained region, which is consistent with the theoretical derivation results of this disclosure.
[0098] Figure 8 is a schematic diagram of the structural cutting method provided in an embodiment of this disclosure. As can be seen from Figure 8, during structural cutting, a reserved area of 545° is determined by a reserved area selection box, and this area can be moved a specified distance along a designated direction. This visually demonstrates how the cut and preserved area can be moved.
[0099] Figure 9 is a schematic diagram showing the results of applying the method of this disclosure to the BCC lattice structure according to the embodiments of this disclosure. As can be seen from Figure 9, the normalized equivalent modulus of the BCC lattice structure varies with the moving distance. The change shows a trend of first decreasing and then increasing, reaching its lowest value when the movement distance is about 2.5mm. The overall change pattern is consistent with the logic of equivalent stiffness change under semi-forced constraint and full-forced constraint states derived by theory.
[0100] Figure 10 is a schematic diagram showing the results of applying the method of this disclosure to a face-centered cubic (FCC) lattice structure according to an embodiment of this disclosure. As can be seen from Figure 10, the normalized equivalent modulus of the FCC lattice structure varies with the moving distance. The change of first decreases and then increases, and its change range and extreme point position are roughly the same as those of BCC. The overall change pattern is consistent with the logic of equivalent stiffness change under the theoretical derivation of half-force constraint, full-force constraint and other states.
[0101] Figure 11 is a schematic diagram showing the results of applying the method of this disclosure to the face-centered cubic (FCC-C) lattice structure provided in the embodiments of this disclosure. As can be seen from Figure 11, the normalized equivalent modulus of the FCC-C lattice structure varies with the moving distance. The variation pattern has its own characteristics, and the overall fluctuation is relatively gentle, reflecting the stability of the equivalent stiffness of the composite face-centered cubic structure when the cut-preserved area moves. The overall variation pattern is consistent with the logic of equivalent stiffness variation under semi-forced constraint and full-forced constraint states derived by theory.
[0102] Figure 12 is a schematic diagram showing the results of applying the method of this disclosure to the rhombic dodecahedron (RD) lattice provided in the embodiments of this disclosure. As can be seen from Figure 12, the normalized equivalent modulus of the RD lattice structure exhibits a specific rising and falling trend with the change of the moving distance, reflecting the unique topological mechanical response of the rhombic dodecahedron lattice. The overall change law is consistent with the logic of equivalent stiffness change under semi-constrained and fully constrained states derived by theory.
[0103] Figure 13 is a schematic diagram showing the results of applying the method of this disclosure to an octet lattice structure (OCT) provided in an embodiment of this disclosure. As can be seen from Figure 13, the normalized equivalent modulus of the OCT lattice structure varies with the moving distance. The changes exhibit obvious patterns or relatively stable characteristics, reflecting the stability of the equivalent stiffness of the octagonal truss lattice when it moves in the cut-retained area. The overall change pattern is consistent with the logic of equivalent stiffness changes under semi-forced and fully-forced conditions derived from theory.
[0104] This disclosure also provides a device for characterizing the boundary stiffness of a lattice structure. Figure 14 A structural block diagram of a device for characterizing the boundary stiffness of a lattice structure provided in this disclosure embodiment is shown below. Figure 14 As shown, the device 1400 for characterizing the boundary stiffness of a lattice structure includes:
[0105] The segmentation unit 1401 is used to segment the lattice structure and obtain the segmented lattice cells;
[0106] The first determining unit 1402 is used to determine the type of the lattice cell; the type is used to indicate the integrity of the lattice cell.
[0107] The second determining unit 1403 determines the equivalent stiffness of the lattice cell based on the type and the rod boundary conditions of the lattice cell; the rod boundary conditions are used to indicate the stress constraint state of the rod.
[0108] In one exemplary embodiment, the first determining unit 1402 is specifically used to: include the type as: sub-intact and intact; the sub-intact type is obtained by dividing the residual lattice cells based on symmetry processing.
[0109] In one exemplary embodiment, the second determining unit 1403 is specifically used to: include the following boundary conditions for the rod: fully constrained state, unconstrained state, and half-constrained state.
[0110] In one exemplary embodiment, the second determining unit 1403 is specifically used to: determine the member length, member radius, member spatial tilt angle, and member material elastic modulus of the lattice cell based on the type; when the member boundary condition is under full force constraint, establish a first correlation equation between load and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain equivalent stiffness; when the member boundary condition is under no force constraint, establish a second correlation equation between displacement and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain equivalent stiffness; when the member boundary condition is under half force constraint, establish a third correlation equation between load, displacement, and deformation for member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain equivalent stiffness.
[0111] In one exemplary embodiment, the second determining unit 1403 is specifically used to: decompose the first load in a one-dimensional direction based on the spatial tilt angle of the rod; the one-dimensional direction is the Z-axis direction; determine the first deformation of the rod based on the rod length, rod radius and the material elastic modulus of the rod; the first deformation is the axial equivalent deformation of the rod along the Z-axis direction; and establish a first correlation equation based on the first load and the first deformation using the stress-strain mechanism, and solve for the equivalent stiffness.
[0112] In one exemplary embodiment, the second determining unit 1403 is specifically used to: perform three-dimensional displacement decomposition based on the spatial tilt angle of the rod to obtain a first decomposition result; the three-dimensional directions are the X-axis, Y-axis, and Z-axis; determine the second deformation of the rod based on the rod length, rod radius, and the material elastic modulus of the rod; the second deformation is the total deformation of the rod after superimposing the axial equivalent deformation and bending deformation along the three-dimensional directions; and establish a second correlation equation based on the first decomposition result and the second deformation using the stress-strain mechanism, and solve for the equivalent stiffness.
[0113] In one exemplary embodiment, the second determining unit 1403 is specifically used to: decompose the second load in the one-dimensional direction and the second decomposition result of the displacement in the three-dimensional direction based on the spatial tilt angle of the rod; determine the third deformation of the rod based on the rod length, the rod radius and the elastic modulus of the material of the rod; the third deformation is the total deformation after the axial equivalent deformation and bending deformation of the rod along the three-dimensional direction are superimposed; and establish a third correlation equation based on the second load, the second decomposition result and the third deformation using the stress-strain mechanism, and solve it to obtain the equivalent stiffness.
[0114] In one exemplary embodiment, the segmentation unit 1401 is specifically used for: the segmentation method includes at least one of the following: periodic reference segmentation method, geometric symmetry plane segmentation method, and functional partition boundary segmentation method.
[0115] Figure 15 This is a hardware block diagram of an electronic device provided according to an embodiment of the present disclosure. The electronic device 1500 according to an embodiment of the present disclosure includes at least a processor and a memory for storing computer-readable instructions. When the computer-readable instructions are loaded and executed by the processor, the processor performs the method for characterizing the boundary stiffness of a lattice structure as described in any of the preceding embodiments of the present disclosure.
[0116] Figure 15 The illustrated electronic device 1500 specifically includes a central processing unit (CPU) 1501, a graphics processing unit (GPU) 1502, and a memory 1503. These units are interconnected via a bus 1504. The CPU 1501 and / or GPU 1502 can function as the aforementioned processor, and the memory 1503 can function as the aforementioned memory storing computer-readable instructions. Furthermore, the electronic device 1500 may also include a communication unit 1505, a storage unit 1506, an output unit 1507, an input unit 1508, and an external device 1509, all of which are also connected to the bus 1504.
[0117] In summary, this disclosure provides a method, apparatus, and electronic device for characterizing the boundary stiffness of a lattice structure. This disclosure involves segmenting the lattice structure to obtain segmented lattice cells; determining the type of the lattice cells; the type indicating the integrity of the lattice cells; and determining the equivalent stiffness of the lattice cells based on the type and the member boundary conditions; the member boundary conditions indicating the stress constraint state of the members. Thus, compared to the fixed calculation method of existing heterogeneous multi-scale finite element methods, this disclosure can employ differentiated and flexible mechanical calculations for lattice cells with different integrity types, combined with their specific member boundary conditions, avoiding errors caused by uniform calculations. In conclusion, the technical solution provided by this disclosure can improve the accuracy of characterizing the boundary stiffness of lattice structures, reduce error accumulation, and adapt to various application scenarios.
[0118] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this disclosure.
[0119] The basic principles of this disclosure have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this disclosure are merely examples and not limitations, and should not be considered as essential features of each embodiment of this disclosure. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the scope of this disclosure to the necessity of employing the aforementioned specific details for implementation.
[0120] The block diagrams of devices, apparatuses, devices, and systems disclosed herein are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.
[0121] Additionally, as used herein, the "or" used in a list of items beginning with "at least one" indicates a separate list, such that a list of, for example, "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not imply that the described example is preferred or better than other examples.
[0122] It should also be noted that in the systems and methods of this disclosure, the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered as equivalent solutions to this disclosure.
[0123] Various changes, substitutions, and modifications can be made to the technology described herein without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of this disclosure is not limited to the specific aspects of the processes, machines, manufactures, events, means, methods, and actions described above. Currently existing or later-developed processes, machines, manufactures, events, means, methods, or actions that perform substantially the same function or achieve substantially the same result as the corresponding aspects described herein can be utilized. Therefore, the appended claims include such processes, machines, manufactures, events, means, methods, or actions within their scope.
[0124] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of this disclosure. Therefore, this disclosure is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.
[0125] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this disclosure to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.
Claims
1. A method for characterizing the boundary stiffness of a lattice structure, characterized in that, The method includes: The lattice structure is segmented to obtain the segmented lattice cells; Determine the type of the lattice cell; the type is used to indicate the integrity of the lattice cell; Based on the type and the rod boundary conditions of the lattice cell, the equivalent stiffness of the lattice cell is determined; the rod boundary conditions are used to indicate the force constraint state of the rod. The determination of the equivalent stiffness of the lattice cell based on the type and the member boundary conditions of the lattice cell includes: determining the member length, member radius, member spatial tilt angle, and member material elastic modulus of the lattice cell based on the type; when the member boundary conditions are under full force constraint, establishing a first correlation equation between load and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under no force constraint, establishing a second correlation equation between displacement and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under partial force constraint, establishing a third correlation equation between load, displacement, and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness. When the boundary condition of the rod is under full force constraint, a first correlation equation between load and deformation is established for the rod length, rod radius, rod spatial tilt angle, and rod material elastic modulus to obtain the equivalent stiffness. This includes: decomposing the rod spatial tilt angle to obtain a first load in a one-dimensional direction; the one-dimensional direction is the Z-axis direction; determining the first deformation of the rod based on the rod length, rod radius, and rod material elastic modulus; the first deformation is the axial equivalent deformation of the rod along the Z-axis direction; and using the stress-strain mechanism, establishing the first correlation equation based on the first load and the first deformation to solve for the equivalent stiffness. When the boundary conditions of the rod are unconstrained, a second correlation equation is established for displacement and deformation based on the rod length, rod radius, rod spatial tilt angle, and rod material elastic modulus to obtain the equivalent stiffness. This includes: performing three-dimensional displacement decomposition based on the rod spatial tilt angle to obtain a first decomposition result; the three-dimensional directions are the X-axis, Y-axis, and Z-axis; determining a second deformation of the rod based on the rod length, rod radius, and rod material elastic modulus; the second deformation is the total deformation of the rod after superimposing the axial equivalent deformation and bending deformation along the three-dimensional directions; and using a stress-strain mechanism, based on the first decomposition result and the second deformation, establishing the second correlation equation and solving it to obtain the equivalent stiffness. When the boundary condition of the member is in a semi-force-constrained state, a third correlation equation is established for the load, displacement, and deformation of the member length, the member radius, the member spatial tilt angle, and the member material elastic modulus to obtain the equivalent stiffness. This includes: decomposing the member based on the member spatial tilt angle to obtain a second decomposition result of the second load in the one-dimensional direction and the second decomposition result of the displacement in the three-dimensional direction; determining the third deformation of the member based on the member length, the member radius, and the member material elastic modulus; the third deformation is the total deformation of the member after superimposing the axial equivalent deformation and bending deformation along the three-dimensional direction; and using the stress-strain mechanism, based on the second load, the second decomposition result, and the third deformation, the third correlation equation is established, and the equivalent stiffness is obtained by solving it.
2. The method according to claim 1, characterized in that, The types include: sub-intact and intact; the sub-intact type is obtained by dividing the residual lattice cells based on symmetry processing.
3. The method according to claim 1, characterized in that, The boundary conditions of the members include: fully constrained state, unconstrained state, and partially constrained state.
4. The method according to claim 1, characterized in that, The segmentation method for dividing the lattice structure includes at least one of the following: periodic reference segmentation method, geometric symmetry plane segmentation method, and functional partition boundary segmentation method.
5. A device for characterizing the boundary stiffness of a lattice structure, characterized in that, The device includes: The segmentation unit is used to segment the lattice structure and obtain the segmented lattice cells; A first determining unit is configured to determine the type of the lattice cell; the type is used to indicate the integrity of the lattice cell. The second determining unit determines the equivalent stiffness of the lattice cell based on the type and the rod boundary conditions of the lattice cell; the rod boundary conditions are used to indicate the force constraint state of the rod. The determination of the equivalent stiffness of the lattice cell based on the type and the member boundary conditions of the lattice cell includes: determining the member length, member radius, member spatial tilt angle, and member material elastic modulus of the lattice cell based on the type; when the member boundary conditions are under full force constraint, establishing a first correlation equation between load and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under no force constraint, establishing a second correlation equation between displacement and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness; when the member boundary conditions are under partial force constraint, establishing a third correlation equation between load, displacement, and deformation for the member length, member radius, member spatial tilt angle, and member material elastic modulus to obtain the equivalent stiffness. When the boundary condition of the rod is under full force constraint, a first correlation equation between load and deformation is established for the rod length, rod radius, rod spatial tilt angle, and rod material elastic modulus to obtain the equivalent stiffness. This includes: decomposing the rod spatial tilt angle to obtain a first load in a one-dimensional direction; the one-dimensional direction is the Z-axis direction; determining the first deformation of the rod based on the rod length, rod radius, and rod material elastic modulus; the first deformation is the axial equivalent deformation of the rod along the Z-axis direction; and using the stress-strain mechanism, establishing the first correlation equation based on the first load and the first deformation to solve for the equivalent stiffness. When the boundary conditions of the rod are unconstrained, a second correlation equation is established for displacement and deformation based on the rod length, rod radius, rod spatial tilt angle, and rod material elastic modulus to obtain the equivalent stiffness. This includes: performing three-dimensional displacement decomposition based on the rod spatial tilt angle to obtain a first decomposition result; the three-dimensional directions are the X-axis, Y-axis, and Z-axis; determining a second deformation of the rod based on the rod length, rod radius, and rod material elastic modulus; the second deformation is the total deformation of the rod after superimposing the axial equivalent deformation and bending deformation along the three-dimensional directions; and using a stress-strain mechanism, based on the first decomposition result and the second deformation, establishing the second correlation equation and solving it to obtain the equivalent stiffness. When the boundary condition of the member is in a semi-force-constrained state, a third correlation equation is established for the load, displacement, and deformation of the member length, the member radius, the member spatial tilt angle, and the member material elastic modulus to obtain the equivalent stiffness. This includes: decomposing the member based on the member spatial tilt angle to obtain a second decomposition result of the second load in the one-dimensional direction and the second decomposition result of the displacement in the three-dimensional direction; determining the third deformation of the member based on the member length, the member radius, and the member material elastic modulus; the third deformation is the total deformation of the member after superimposing the axial equivalent deformation and bending deformation along the three-dimensional direction; and using the stress-strain mechanism, based on the second load, the second decomposition result, and the third deformation, the third correlation equation is established, and the equivalent stiffness is obtained by solving it.
6. An electronic device, characterized in that, include: Memory, used to store computer-readable instructions; as well as A processor for executing the computer-readable instructions, causing the electronic device to perform the method as described in any one of claims 1-4.