A dual-material negative thermal expansion structure and a design method thereof based on multi-island genetic optimization
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-05-19
- Publication Date
- 2026-07-24
Smart Images
Figure CN122452246A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent structure design, and in particular to a dual-material negative thermal expansion structure and its design method based on multi-island genetic optimization. Background Technology
[0002] High precision and thermal stability are crucial directions for the development of next-generation precision equipment. However, extreme thermal environments (such as localized high temperatures and drastic temperature differences) often introduce uncontrollable thermal deformation. Key components of the equipment experience significant thermal stress and uncontrollable thermal deformation due to mismatches in material thermal expansion coefficients or uneven temperature field distribution, severely restricting their precision retention and functional reliability. Such thermal deformation not only leads to a decrease in the absolute accuracy and repeatability of the equipment but also causes component failures, changes in dynamic characteristics, and even premature fatigue damage. Therefore, in this process, efficient and reliable thermal deformation suppression technology directly determines the upper limit of equipment performance under extreme environments.
[0003] In the aerospace field, during satellite flight, the temperature on the sun-facing side exceeds 100°C, while the temperature on the shaded side is -100°C. When in low Earth orbit, the temperature change rate is even faster. Prolonged exposure to this condition can cause irreversible deformation or even damage to the structure. A negative thermal expansion structure can maintain a relatively stable relative distance between the antenna and the satellite with minimal temperature fluctuations, and this connection structure allows for thermal expansion of the antenna, thus reducing thermal stress.
[0004] Traditional thermal deformation compensation techniques still have the following problems:
[0005] On the one hand, traditional passive thermal protection or temperature equalization technologies slow down temperature rise and temperature difference by applying insulation layers and optimizing thermal management. However, under continuous high heat load or drastic temperature change conditions, the insulation effect is limited and may introduce new thermal inertia. On the other hand, relying solely on high thermal conductivity materials for temperature equalization often makes it difficult to completely eliminate thermal mismatch deformation at the interface between different materials, and to some extent sacrifices the lightweight design of the structure, making it difficult to meet the requirements of high dynamic response.
[0006] On the other hand, existing active deformation compensation technologies mostly rely on real-time feedback based on sensors and active correction by actuators, which are complex, costly, and have problems such as response lag and high energy consumption.
[0007] Therefore, there is an urgent need to develop a novel thermal deformation suppression scheme that can balance real-time response capability, structural integration, and high reliability. An ideal compensation technology should possess a passive, autonomous response mechanism to avoid system complexity and hysteresis issues, while simultaneously achieving precise deformation compensation at the structural level rather than simply slowing down heat conduction. Summary of the Invention
[0008] Objective: This invention proposes a dual-material negative thermal expansion structure and its design method based on multi-island genetic optimization, applicable to the passive compensation of thermal deformation in high-precision equipment under extreme thermal environments. By designing a dual-material negative thermal expansion structure with triangles and trapezoids as basic geometric units and introducing a multi-island genetic algorithm for global optimization of structural parameters, the core solution addresses the deformation problem caused by thermal mismatch between components. It significantly suppresses deformation in a specific direction under thermal load, thus providing a passive, real-time, and reliable solution for achieving long-term stability of equipment or structures in extreme thermal environments.
[0009] To achieve the above objectives, this invention proposes a dual-material negative thermal expansion structure, comprising:
[0010] A two-dimensional negative thermal expansion structure composed of rods made of a first material and rods made of a second material with different coefficients of thermal expansion;
[0011] The two-dimensional negative thermal expansion structure includes a trapezoidal unit and multiple triangular units connected to the trapezoidal unit;
[0012] The triangular unit is an obtuse isosceles triangle unit, and the trapezoidal unit is connected to the triangular unit through a preset spatial configuration so that the first material rod and the second material rod form a macroscopic negative thermal expansion effect along the target direction during temperature change, thereby suppressing thermal deformation in the target direction.
[0013] As a preferred embodiment, the triangular unit includes a waist member formed of a first material and a bottom member formed of a second material;
[0014] The trapezoidal unit includes a waist member formed of a first material and a top and bottom member formed of a second material;
[0015] The first material and the second material have different coefficients of thermal expansion, so as to achieve negative thermal expansion at the structural level by utilizing the difference between the thermal expansion behavior of the materials.
[0016] As a preferred embodiment, the two-dimensional negative thermal expansion structure is formed by combining trapezoidal unit ABDC and triangular units CEF and DFG;
[0017] Among them, the rods made of the same material are connected as an integral structure to improve the machinability and connection stability of the structure.
[0018] As a preferred embodiment, the two-dimensional negative thermal expansion structure establishes an equivalent thermal expansion model based on ideal hinge conditions;
[0019] The equivalent thermal expansion model is used to establish the functional relationship between the structural geometric parameters and the equivalent thermal expansion coefficient in the target direction, and is used to characterize the negative thermal expansion characteristics of the two-dimensional negative thermal expansion structure.
[0020] As a preferred embodiment, the ideal articulation conditions include:
[0021] Each member can expand freely due to thermal expansion;
[0022] The connection angles between the members can change;
[0023] Based on the ideal hinge condition, linear expansion relationships in multiple directions are established to obtain the equivalent thermal expansion coefficient in the target direction.
[0024] As a preferred embodiment, the two-dimensional negative thermal expansion structure is further fitted with a mechanical model.
[0025] The fixed mechanical model is established based on the beam element finite element analysis method, including:
[0026] Establish the element stiffness matrix and thermal load vector in the local coordinate system;
[0027] The global stiffness matrix and global thermal load vector in the global coordinate system are obtained through coordinate transformation.
[0028] Solve for nodal displacements by combining boundary constraints;
[0029] The negative thermal expansion characteristics of the two-dimensional negative thermal expansion structure are verified based on the node displacement.
[0030] As a preferred embodiment, the fixed mechanical model is modeled using a partial region of a symmetrical structure, and corresponding degree-of-freedom constraints are applied to different nodes;
[0031] By accumulating and projecting the global coordinate system stiffness matrix and the global thermal load vector of each beam element, the overall structural equation is established, and the nodal displacements are solved by the linear equation system after reducing the degrees of freedom.
[0032] As a preferred embodiment, the dual-material negative thermal expansion structure includes a three-dimensional negative thermal expansion structure;
[0033] The three-dimensional negative thermal expansion structure includes:
[0034] A first three-dimensional structure consisting of two two-dimensional negative thermal expansion structures sharing a common vertex and having mutually perpendicular base edges; or...
[0035] A second three-dimensional structure is formed by stretching a two-dimensional negative thermal expansion structure along a predetermined direction.
[0036] As a preferred embodiment, the first material structure and the second material structure are connected by an interference fit to eliminate the connection gap between dissimilar material structures and improve the connection rigidity.
[0037] Furthermore, this invention also proposes a design method for a dual-material negative thermal expansion structure based on multi-island genetic optimization, comprising the following steps:
[0038] S1. Construct a dual-material negative thermal expansion structure composed of triangular and trapezoidal units, and determine the geometric and material parameters of the structure.
[0039] S2. Based on the ideal hinge condition, establish the functional relationship between the structural geometric parameters and the equivalent thermal expansion coefficient in the target direction to obtain the structural equivalent thermal expansion model.
[0040] S3. Encode the geometric parameters and material parameters into gene sequences for a multi-island genetic algorithm, and use the equivalent thermal expansion coefficient as a fitness evaluation index;
[0041] S4. The gene sequence is subjected to parallel evolution and migration optimization using a multi-island genetic algorithm to obtain the optimal parameter combination corresponding to the minimum equivalent thermal expansion coefficient in the target direction.
[0042] S5. Map the optimal parameter combination to the fixed-joint mechanical model for mechanical verification to verify the negative thermal expansion characteristics of the structure under fixed-joint conditions.
[0043] S6. Construct a three-dimensional negative thermal expansion structure based on the verified optimal parameter combination.
[0044] As a preferred embodiment, in step S3, the gene sequence includes key structural geometric parameters and material property parameters;
[0045] The fitness evaluation index is the equivalent thermal expansion coefficient in the target direction;
[0046] The optimization objective of the multi-island genetic algorithm is to minimize the equivalent thermal expansion coefficient within a preset size constraint range.
[0047] As a preferred embodiment, in step S4, the multi-island genetic algorithm achieves global optimization through parallel evolution of multiple islands and periodic individual migration;
[0048] The multiple islands perform selection, crossover, and mutation operations respectively, and the individual exchanges between different islands are realized through migration operations to improve the global optimization capability.
[0049] As a preferred embodiment, in step S5, the displacement results of multiple nodes are obtained based on the fixed connection mechanical model;
[0050] When the displacement of the target node in the target direction is negative, it is determined that the dual-material negative thermal expansion structure has negative thermal expansion characteristics, and the dimensionality reduction design route based on the ideal hinge condition is verified to have engineering applicability.
[0051] As a preferred embodiment, the three-dimensional negative thermal expansion structure constructed in step S6 is arranged between the structures to be compensated;
[0052] By restricting vertical displacement at the bottom while allowing horizontal displacement, thermally induced deformation of the structure to be compensated in complex thermal environments is suppressed.
[0053] Compared with the prior art, the present invention has at least the following beneficial effects:
[0054] (1) By utilizing two positive thermal expansion materials (with significant differences in CTE), the thermal expansion of the material itself is transformed into macroscopic negative thermal expansion behavior at the structural level through a specific spatial configuration. This overcomes the limitations of high cost, narrow operating temperature range, and easy phase transformation of materials that rely on natural negative thermal expansion materials (such as ZrW2O8), and provides a more robust thermal deformation solution with designable, predictable and robust performance.
[0055] (2) The design method of multi-parameter coupled modeling and multi-island genetic algorithm (MIGA) optimization can systematically solve the multivariable and strongly coupled nonlinear optimization problem in the design of negative thermal expansion structures. This enables the platform to automatically find the optimal solution with the minimum comprehensive thermal deformation under multiple constraints such as strength and lightweight, thereby significantly improving the scientific nature of the design and the performance reliability of the final product.
[0056] (3) Thermal deformation is compensated at its source through a passive, passive, and real-time responsive mechanical structure, rather than relying on a complex active control system for post-processing correction. This method not only improves the reliability of the system but also reduces its dependence on control algorithms and external energy. Attached Figure Description
[0057] Figure 1 Flowchart for the design of a dual-material negative thermal expansion structure.
[0058] Figure 2 This is a schematic diagram of a triangular unit.
[0059] Figure 3 This is a schematic diagram of a trapezoidal unit.
[0060] Figure 4 This is a graph showing the relationship between the equivalent thermal expansion coefficient of the trapezoidal element and various parameters.
[0061] Figure 5 This is a schematic diagram of a negative thermal expansion structure.
[0062] Figure 6 This is a diagram of the multi-island genetic process.
[0063] Figure 7 Optimize the iterative graph for each parameter.
[0064] Figure 8A diagram showing constraints and element / node numbering.
[0065] Figure 9 This is a schematic diagram of a three-dimensional negative thermal expansion structure.
[0066] Figure 10 This is a schematic diagram of a three-dimensional negative thermal expansion structure (Type II).
[0067] Figure 11 This is a simulation diagram of a three-dimensional negative thermal expansion structure.
[0068] Figure 12 This is a simulation diagram of a three-dimensional negative thermal expansion structure.
[0069] The attached figures are labeled as follows: Type I low-carbon steel structure 101, Type I aluminum alloy structure 102, Type II low-carbon steel structure 201, and Type II aluminum alloy structure 202. Detailed Implementation
[0070] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.
[0071] This embodiment proposes a dual-material negative thermal expansion structure. This structure uses triangles and trapezoids as basic geometric units. By specifically configuring and connecting two materials with significantly different coefficients of thermal expansion (high and low), it can generate a macroscopic negative thermal expansion effect along a specific design direction when the temperature changes. This structure can effectively suppress deformation caused by uneven temperature fields or dynamic thermal loads in a specific direction, thereby ensuring high thermal stability of the equipment or structure. The design flowchart is shown below. Figure 1 As shown, to illustrate specific embodiments of the present invention in detail, the present invention will be further described as follows:
[0072] (1) Triangular unit analysis
[0073] like Figure 2 The schematic diagram of the triangular unit is shown. This triangular unit is an isosceles triangle with a leg length of 'a'. The coefficient of thermal expansion of the material used is... The base length is b, and the coefficient of thermal expansion of the material used is... ,and By utilizing the difference in thermal expansion coefficients of the two materials, negative thermal expansion performance in the vertical direction can be achieved. If, under ideal conditions (ideal hinged joint conditions) where all members are in a state of free expansion and the angles between members can change, neglecting the minimum term, the equivalent thermal expansion coefficient function value in the vertical direction of the triangular element can be obtained according to geometric relationships:
[0074]
[0075] From the above function, we can see that the smaller the ratio of the member length 'a' to the member length 'b', the flatter the triangle, and the more pronounced the negative thermal expansion phenomenon of the triangular basic unit structure. When this ratio exceeds a certain value, the triangular unit exhibits positive thermal expansion properties. Therefore, in the following negative thermal expansion structure design, we ensure that the triangular unit is an obtuse triangle.
[0076] (2) Trapezoidal element analysis
[0077] like Figure 3 The schematic diagram of the trapezoidal element is shown. The length of the leg of the trapezoidal element is 'a', and the coefficient of thermal expansion of the material used is _____. The base length is b, and the coefficient of thermal expansion of the material used is... The top length is c, and the coefficient of thermal expansion of the material used is... ,and If, under ideal conditions where all members are in a state of free expansion and the angles between members can change (ideal hinge condition), ignoring the minimum term, the equivalent thermal expansion coefficient function value in the vertical direction of the trapezoidal element can be obtained according to geometric relationships:
[0078]
[0079] like Figure 4 As shown, the smaller the ratio of member length a to member length b, the more obvious the negative thermal expansion phenomenon of the trapezoidal basic unit structure.
[0080] (3) Two-dimensional negative thermal expansion structure design
[0081] By rationally arranging the geometric configuration, the thermal expansion behavior of two materials with significantly different coefficients of thermal expansion is transformed into a macroscopic negative thermal expansion effect. Furthermore, to improve feasibility and manufacturability, rods made of the same material are connected as a single unit. The final negative thermal expansion structure design is as follows: Figure 5 As shown, it is mainly composed of obtuse isosceles triangular units CEF and DFG and trapezoidal units ABDC.
[0082] The leg length of the triangular element is *a*, and the coefficient of thermal expansion of the material used is... The base length is b, and the coefficient of thermal expansion of the material used is... The trapezoidal element has a leg length of d, and the material used has a coefficient of thermal expansion of . The base length is c, and the coefficient of thermal expansion of the material used is... The top length is e, and the coefficient of thermal expansion of the material used is... .
[0083] (4) Ideal hinged model of two-dimensional negative thermal expansion structure
[0084] The linear expansion coefficient in the EQ direction is:
[0085]
[0086] The linear expansion coefficient in the PR direction is:
[0087]
[0088] The linear expansion coefficient in the QR direction is:
[0089]
[0090] Based on geometric relationships, a functional relationship can be established between multiple parameters and the equivalent thermal expansion coefficient in the vertical direction. The final functional value of the thermal expansion coefficient in the vertical direction is:
[0091]
[0092] (5) Parameter optimization based on multi-island genetic algorithm
[0093] The gene sequence of the multi-island genetic algorithm directly encodes the key geometric dimensions and material properties of the structure. Material a is low-carbon steel, and material b is aluminum alloy. The evaluation index (i.e., fitness function) is defined as the equivalent thermal expansion coefficient of the structure. The optimization objective is to adjust the gene sequence to minimize the fitness function within a specific parameter range (the optimization objective can be changed according to different application scenarios). In this optimization process, the population is divided into 10 islands, with 15 individuals on each island. The number of generations is set to 30, the migration rate is 0.1, the migration interval is 4 generations, the elite size is 1, the crossover rate is 1.0, and the mutation rate is 0.1.
[0094] The length range of each member is determined based on the actual application scenario. In this invention, the ranges of each independent variable are: , , , At the same time, ensure that the relationship between the length values of each member satisfies the actual physical meaning of triangles and trapezoids.
[0095] like Figure 6 As shown, within a certain size constraint range, after multiple independent multi-island genetic algorithm optimizations, the optimal equivalent negative thermal expansion coefficient is -9.91e.-6 / ℃, and generally the greater the difference in the thermal expansion coefficients of the two materials, the better the effect;
[0096] The optimal iterative process for each parameter is as follows: Figure 7 As shown, this meets the objective of a negative coefficient of thermal expansion. The parameter values from the optimization results are used as the design criteria for the two-dimensional negative thermal expansion structure.
[0097] (6) Two-dimensional negative thermal expansion structure fixed mechanical model
[0098] When the above structure is fixed, the derivation of the mechanical response and deformation mechanism of the negative thermal expansion structure is key to evaluating its mechanical properties such as coefficient of thermal expansion (CTE), elastic modulus, and Poisson's ratio. The analysis process strictly follows the five basic assumptions of elasticity: continuity, homogeneity, isotropy, perfect elasticity, and small deformation.
[0099] In the local coordinate system, a 2D beam element has 2 nodes and 6 degrees of freedom, each degree of freedom corresponding to a force or moment. The elastic equation of the 2D beam element after introducing temperature changes can be rewritten as:
[0100]
[0101] In the global coordinate system, the nodal displacement vector and the nodal load vector can be rewritten as:
[0102]
[0103] in, It is a 6×1 nodal load vector. It is a 6×1 nodal displacement vector. It is the 6×6 element stiffness matrix of a 2D beam element. This is the vector form of the axial load. This is a coordinate transformation matrix, with superscripts... Indicates a local coordinate system, superscript Represents the global coordinate system.
[0104] Since the above structure is symmetrical, a half-scale model is used. For example... Figure 8As shown, the overall structure consists of six beam elements with six nodes. Nodes 1 and 3 are only allowed degrees of freedom in the y-direction, node 5 is constrained for all degrees of freedom, and node 6 is only allowed for the x-direction. Each element of the global coordinate system stiffness matrix and global thermal load vector of all elements is accumulated and projected onto the corresponding row and column positions of the global stiffness matrix and global thermal load vector according to its corresponding global node degree of freedom number. Finally, based on the actual boundary conditions of the structure (such as fixed constraints), the rows and columns corresponding to the corresponding degrees of freedom are deleted, resulting in a reduced system of equations. Solving this linear system yields the unknown displacements of each node. The equations can be expressed as:
[0105]
[0106] The 9×9 matrix only lists the upper triangular portion because the lower triangular portion is symmetrical to it; where , See the appendix for the specific expression.
[0107] The optimal parameters obtained based on the hinge theory were mapped to the actual fixed mechanical model for verification. It was found that the vertical displacement of node 1 was -0.012100mm and the vertical displacement of node 2 was -0.003312mm, both of which were negative values. The structure exhibited negative thermal expansion characteristics. The dimension reduction design route based on the "fixed-hinge equivalence" assumption of this invention is reasonable.
[0108] (7) Three-dimensional negative thermal expansion structure design
[0109] like Figure 9 As shown, the three-dimensional negative thermal expansion structure is constructed by two two-dimensional negative thermal expansion structures sharing the top and having their bottom edges perpendicular. In the figure, 101 is a low-carbon steel structure and 102 is an aluminum alloy structure. The dissimilar material structures are fitted with an interference fit to eliminate the connection gap between them.
[0110] like Figure 10 As shown, the three-dimensional negative thermal expansion structure type II is formed by stretching a two-dimensional negative thermal expansion structure. In the figure, 201 is a low-carbon steel structure and 202 is an aluminum alloy structure. The dissimilar material structures are interference-fitted to eliminate the connection gap between the dissimilar material structures.
[0111] (8) Simulation verification
[0112] Depend on Figure 11 Simulation results show that a three-dimensional negative thermal expansion structure is arranged between two aluminum alloy parts. The entire structure's contact surfaces are bonded, restricting vertical displacement of the bottom surface while allowing horizontal displacement. Extracting the coordinates of multiple points on the upper surface of the parts reveals that the equivalent thermal expansion coefficient in the vertical direction of this overall structure is approximately 12.3e. -6 / ℃.
[0113] Depend on Figure 12 Simulation results show that the three-dimensional negative thermal expansion structure type II is arranged between two aluminum alloy parts. The contact surfaces of the entire structure are all bonded, restricting the vertical displacement of the bottom surface while allowing horizontal displacement. By extracting the coordinates of multiple points on the upper surface of the parts, the equivalent thermal expansion coefficient of the overall structure in the vertical direction is approximately 10.9e. -6 / ℃.
[0114] The equivalent coefficients of thermal expansion mentioned above are all significantly smaller than those of aluminum alloys, meaning they are significantly smaller than those of parts made entirely of aluminum alloys. This characteristic can be used to reduce the impact of extreme thermal environments with drastic temperature changes or localized high temperatures on equipment or structures, significantly suppressing deformation in specific directions, thereby ensuring and improving the long-term stability and motion accuracy of equipment or structures under complex thermal loads.
[0115] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims
1. A dual-material negative thermal expansion structure, characterized in that, include: A two-dimensional negative thermal expansion structure composed of rods made of a first material and rods made of a second material with different coefficients of thermal expansion; The two-dimensional negative thermal expansion structure includes a trapezoidal unit and multiple triangular units connected to the trapezoidal unit; The triangular unit is an obtuse isosceles triangle unit, and the trapezoidal unit is connected to the triangular unit through a preset spatial configuration so that the first material rod and the second material rod form a macroscopic negative thermal expansion effect along the target direction during temperature change, thereby suppressing thermal deformation in the target direction.
2. The dual-material negative thermal expansion structure according to claim 1, characterized in that, The triangular unit includes a waist member made of a first material and a bottom member made of a second material; The trapezoidal unit includes a waist member formed of a first material and a top and bottom member formed of a second material; The first material and the second material have different coefficients of thermal expansion, so as to achieve negative thermal expansion at the structural level by utilizing the difference between the thermal expansion behavior of the materials.
3. The dual-material negative thermal expansion structure according to claim 1, characterized in that, The two-dimensional negative thermal expansion structure is based on an equivalent thermal expansion model established under ideal hinge conditions. The equivalent thermal expansion model is used to establish the functional relationship between the structural geometric parameters and the equivalent thermal expansion coefficient in the target direction, and is used to characterize the negative thermal expansion characteristics of the two-dimensional negative thermal expansion structure. The ideal hinge conditions include: each member can expand freely due to thermal expansion; and the connection angle between each member can change. Based on the ideal hinge condition, linear expansion relationships in multiple directions are established to obtain the equivalent thermal expansion coefficient in the target direction.
4. The dual-material negative thermal expansion structure according to claim 1, characterized in that, The two-dimensional negative thermal expansion structure is further established with a fixed mechanical model. The fixed mechanical model is established based on the beam element finite element analysis method, including: Establish the element stiffness matrix and thermal load vector in the local coordinate system; The global stiffness matrix and global thermal load vector in the global coordinate system are obtained through coordinate transformation. Solve for nodal displacements by combining boundary constraints; The negative thermal expansion characteristics of the two-dimensional negative thermal expansion structure are verified based on the node displacement.
5. The dual-material negative thermal expansion structure according to claim 4, characterized in that, The fixed mechanical model is modeled using a partial region of a symmetrical structure, and corresponding degree-of-freedom constraints are applied to different nodes. By accumulating and projecting the global coordinate system stiffness matrix and the global thermal load vector of each beam element, the overall structural equation is established, and the nodal displacements are solved by the linear equation system after reducing the degrees of freedom.
6. The dual-material negative thermal expansion structure according to claim 1, characterized in that, The dual-material negative thermal expansion structure includes a three-dimensional negative thermal expansion structure; The three-dimensional negative thermal expansion structure includes: The first three-dimensional structure is composed of two two-dimensional negative thermal expansion structures sharing a vertex and having mutually perpendicular base edges. or, A second three-dimensional structure is formed by stretching a two-dimensional negative thermal expansion structure along a predetermined direction; The first material structure and the second material structure are connected by an interference fit to eliminate the connection gap between dissimilar material structures and improve the connection rigidity.
7. A design method for a dual-material negative thermal expansion structure based on multi-island genetic optimization, characterized in that, Includes the following steps: S1. Construct a dual-material negative thermal expansion structure composed of triangular and trapezoidal units, and determine the geometric and material parameters of the structure. S2. Based on the ideal hinge condition, establish the functional relationship between the structural geometric parameters and the equivalent thermal expansion coefficient in the target direction to obtain the structural equivalent thermal expansion model. S3. Encode the geometric parameters and material parameters into gene sequences for a multi-island genetic algorithm, and use the equivalent thermal expansion coefficient as a fitness evaluation index; S4. The gene sequence is subjected to parallel evolution and migration optimization using a multi-island genetic algorithm to obtain the optimal parameter combination corresponding to the minimum equivalent thermal expansion coefficient in the target direction. S5. Map the optimal parameter combination to the fixed-joint mechanical model for mechanical verification to verify the negative thermal expansion characteristics of the structure under fixed-joint conditions. S6. Construct a three-dimensional negative thermal expansion structure based on the verified optimal parameter combination.
8. The dual-material negative thermal expansion structure design method according to claim 7, characterized in that, In step S3, the gene sequence includes key structural geometric parameters and material property parameters; The fitness evaluation index is the equivalent thermal expansion coefficient in the target direction; The optimization objective of the multi-island genetic algorithm is to minimize the equivalent thermal expansion coefficient within a preset size constraint range.
9. The dual-material negative thermal expansion structure design method according to claim 7, characterized in that, In step S5, the displacement results of multiple nodes are obtained based on the fixed connection mechanical model; When the displacement of the target node in the target direction is negative, it is determined that the dual-material negative thermal expansion structure has negative thermal expansion characteristics, and the dimensionality reduction design route based on the ideal hinge condition is verified to have engineering applicability.
10. The dual-material negative thermal expansion structure design method according to claim 7, characterized in that, The three-dimensional negative thermal expansion structure constructed in step S6 is arranged between the structures to be compensated; By restricting vertical displacement at the bottom while allowing horizontal displacement, thermally induced deformation of the structure to be compensated in complex thermal environments is suppressed.