A robust optimization design method for thermal-mechanically coupled continuous fiber composites

Abstract

The present invention discloses a robust optimization design method for a thermomechanically coupled continuous fiber composite material, comprising the following steps: step 1: setting initial conditions, including level set function distribution, temperature change value, uncertainty load magnitude, and direction change; step 2: calculating the deterministic objective function and sensitivity of the structure at the initial moment; step 3: entering the k-th outer loop, and updating the structural topology and fiber routing according to the sensitivity information; step 4: entering the (k, l)-th inner loop, obtaining the uncertainty load corresponding to the current iteration step, calculating and recording the objective function and sensitivity; and step 5: judging the relationship between l and l. T The size of l, if l≤l T , then update the magnitude and direction of the load and repeat step 4; if l>l T , then proceed to step 6; step 7: determine whether the convergence conditions are met; step 8: end the iteration and obtain the final optimized design. This solution can fully consider the impact of ambient temperature changes and external load uncertainty on structural optimization design.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical engineering technology. Specifically, it relates to a robustness optimization design method for thermomechanically coupled continuous fiber composite materials, and more particularly, to a concurrent robustness optimization design method for the structural topology and fiber routing of continuous fiber-reinforced composite materials under 3D-printable thermomechanically coupled working conditions. This method can be applied to the lightweight design of transport equipment structures. Background Art

[0002] Continuous fiber-reinforced composites (CFRCs), characterized by high specific modulus, high specific strength, and robust design capabilities, are gradually replacing traditional alloys in the lightweight design and manufacturing of advanced launch vehicle structures, including launch vehicles, aircraft, high-speed rail, and new energy vehicles. The rapid development of 3D printing technology for continuous fiber-reinforced composites in recent years combines the material performance advantages of composites with the design freedom of 3D-printed structures, enabling the automated rapid prototyping of lightweight, high-strength, complex structural parts. This technology is considered a disruptive technology for the manufacturing of advanced launch vehicle components. Structural topology optimization and fiber routing optimization of composite materials are two methods for further improving material utilization efficiency. Topology optimization is a non-intuitive conceptual design method, distinct from traditional size and shape optimization. It redistributes materials within a design domain based on a given objective function and constraints, resulting in innovative structural designs. Fiber routing optimization utilizes the mechanical anisotropy of composite materials by controlling design variables, such as fiber distribution direction, on a point-by-point and domain-by-domain basis, further enhancing the structural load-bearing capacity. The development of composite 3D printing technology has made it possible to perform concurrent optimization design of topology and fiber routing for continuous fiber reinforced composites. This design can simultaneously leverage the advantages of topology optimization and fiber mechanical anisotropy, achieving a stronger optimization effect than a single optimization method and maximizing the lightweighting of transport equipment structures.

[0003] In order to maximize the use of the material bearing capacity improvement brought about by structural topology and fiber wiring, the invention patent with publication number CN114031794A discloses a variable stiffness hybrid continuous fiber reinforced composite material and preparation method based on 3D printing. By changing the fiber type, matrix material type, fiber content and fiber direction, the design of variable stiffness hybrid continuous fiber reinforced composite materials is realized; the invention patent with publication number CN117497108A discloses a multi-scale optimization method for continuous fiber composite materials based on the improvement of the principal stress direction, which realizes the cyclic correction of fiber direction variables based on the fiber angle interpolation method based on the principal stress direction, and obtains the fiber orientation and topological configuration of the fiber reinforced composite material; the invention patent with publication number CN118471395A discloses a macro-micro collaborative topology optimization design method for continuous fiber additive manufacturing, which adopts the parametric topology optimization design concept and obtains the continuous fiber cross-scale structure with optimal stiffness performance by regulating the unit cell geometric parameters and fiber parameters. In summary, the currently reported optimization design methods for continuous fiber reinforced composite materials for 3D printing have achieved concurrent optimization design of structural topology and fiber path to a certain extent, but have not yet fully considered the impact of environmental factors on structural optimization design, and the ambient temperature and external load are assumed to be constant. In fact, there are significant changes in the service environment of many carriers, such as high-speed trains, airplanes passing through air layers, spacecraft in orbit and other carriers, or there are different degrees of thermomechanical coupling effects caused by changes in ambient temperature, or they are subject to uncertain loads with random perturbation characteristics. Therefore, it is necessary to carry out collaborative optimization design of the structural topology and fiber routing of continuous fiber composite materials based on such complex environmental variables, which is also the problem to be solved by the patent of this invention. Summary of the Invention

[0004] The purpose of this invention is to fully consider the impact of thermal coupling conditions and external load uncertainty on structural optimization design, while ensuring that the composite material structure can be 3D printed, to enhance the load-bearing capacity of continuous fiber reinforced composite materials under complex working conditions, and to achieve structural lightweighting of advanced transportation equipment.

[0005] The technical solution of the present invention is to provide a robust optimization design method for thermally coupled continuous fiber composite materials, which specifically includes:

[0006] Step 1: Set the initial conditions, including the level set function distribution, temperature change value, uncertainty load size and direction change;

[0007] Step 2: Calculate the deterministic objective function and sensitivity of the structure at the initial moment;

[0008] The objective function of the deterministic optimization problem under a given load is taken as the thermal-mechanical coupling structural flexibility, which includes the flexibility term caused by thermal-mechanical coupling and the flexibility term caused by mechanical load. The constraint condition is set as volume constraint. The sensitivity is calculated by taking the partial derivative of the objective function with respect to the level set function.

[0009] Step 3: Enter the kth outer loop and update the structural topology and fiber routing based on the sensitivity information;

[0010] The global velocity is obtained based on the sensitivity information, and then the updated level set function is obtained according to the level set function iteration formula, based on which the topological boundary and internal fiber path of the structure are determined;

[0011] Step 4: Enter the inner loop of step (k, l), obtain the uncertainty load corresponding to the current iteration step, calculate and record the objective function and sensitivity, and increase l by 1;

[0012] Step 5: Determine l and l T The size of l, if l≤l T , then update the magnitude and direction of the load and repeat step 4; if l>l T , then proceed to step 6;

[0013] Step 6: Calculate the robustness objective function and sensitivity, and let k increase by 1 and l = 1;

[0014] Step 7: Determine whether the convergence condition is met; the convergence condition is set as: the relative change of the target value in the last 10 cycles is less than 10 -4 And the difference between the volume fraction and the set value is less than 10 -4 , or the number of cycles k reaches the set value, then convergence. If the convergence condition is not met, return to step 3; if the convergence condition is met, go to step 8;

[0015] Step 8: End the iteration and obtain the final optimized design.

[0016] Furthermore, in step 1, the topology and fiber routing of the structure are represented using a level set function. Given the initial distribution of the level set function, the temperature within the structure is set to vary uniformly, the magnitude of the uncertain load is set to follow a random distribution, and the direction is set to follow an interval distribution.

[0017] Furthermore, in step 4, the total number of uncertainty loads is obtained based on the expansion order p of the robustness objective function, the length n of the random uncertainty variable vector, and the length m of the interval uncertainty variable vector; all uncertainty loads are traversed to obtain the load size and direction of the current iteration step, which are applied to the structure as boundary conditions, and the objective function and sensitivity of the structure under the load are calculated and recorded. After each calculation is completed, l is increased by 1.

[0018] Furthermore, in step 6, under the action of random-interval mixed uncertainty external load, the robustness objective function of the structure, namely the flexibility J R It will be determined by the interval mean μ and interval variance σ of the structural flexibility under all uncertain external loads;

[0019] Using the hybrid orthogonal polynomial expansion method, the robust flexibility is expanded by a p-order random-interval hybrid expansion to obtain J R On the expansion forms of Hermitian chaotic polynomials and Chebyshev polynomial bases;

[0020] According to the properties of the two orthogonal polynomials, the maximum value of the interval mean μ and the interval variance σ is obtained, thereby obtaining J R About the explicit expression of expansion coefficients; J R By taking the partial derivative of the level set function φ, we can obtain the robust sensitivity.

[0021] Furthermore, this method is used for the optimal design of 3D printed thermomechanically coupled continuous fiber reinforced composite structures.

[0022] Beneficial effects of the present invention:

[0023] (1) The present invention provides a concurrent optimization design of the topology and fiber routing robustness of a thermomechanically coupled continuous fiber composite material for 3D printing, which can fully consider the impact of ambient temperature changes and external load uncertainty on structural optimization design.

[0024] (2) This method introduces thermomechanical coupling flexibility, which includes mechanical flexibility and thermal flexibility, as the objective function to quantitatively describe the influence of ambient temperature changes on the overall flexibility of the structure. Through a hybrid uncertainty measurement model, the magnitude and direction of the external load are defined as random variables and interval variables, respectively, and the hybrid orthogonal polynomial expansion method is used to obtain robust flexibility as the objective function, which is more efficient in traversing uncertain load situations.

[0025] (3) The present invention uses the level set method to represent the boundaries of the structure and the paths of the internal fibers, and uses sensitivity information to drive the changes in the level set function to achieve concurrent optimization of the topology and fiber routing of the structure.

[0026] (4) The thermomechanical coupling robustness optimization design obtained by the present invention can significantly improve the load-bearing capacity of the structural unit mass material compared with the initial structure, can fully utilize the anisotropy of the composite material to improve the stiffness of the structure compared with only optimizing the structural topology, and can significantly improve the load-bearing capacity for uncertain loads compared with the traditional deterministic optimization design. It has guiding significance for the design of continuous fiber composite materials for advanced carrier equipment in complex service environments.

[0027] (5) The present invention can also well ensure the additive manufacturability of concurrently optimized composite materials. This method uses a level set function to determine the fiber placement path. Compared with the method of optimizing discrete fiber angles in the prior art, the continuity of the level set function ensures that the reinforcing phase of the composite material is a continuous fiber with sufficient length, avoiding the drastic change in fiber direction caused by the use of short fibers; the method of the present invention also ensures that adjacent fibers are arranged at equal intervals, ensuring that the fiber paths do not cross or interfere with each other, so that the optimized structure can be 3D printed. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of the invented optimization design method;

[0029] Figure 2 are the geometric parameters and boundary conditions of the composite material structure;

[0030] Figure 3 is the topology and fiber routing at the initial moment;

[0031] Figure 4 It is a deterministic concurrent optimization design under fixed load;

[0032] Figure 5 It is a robust concurrent optimization design under uncertain loads;

[0033] Figure 6 It is a robust concurrent optimization design under uncertain load conditions and a temperature rise of 2°C.

[0034] Figure 7 It is a robust concurrent optimization design under uncertain load conditions and a temperature rise of 4°C. DETAILED DESCRIPTION

[0035] The following is combined with Figure 1-7 The technical solution of the present invention is described in detail.

[0036] This embodiment provides a robust optimization design method for thermomechanically coupled continuous fiber composite materials. This method rationally plans the structure's topology and fiber printing path based on the ambient temperature variations of the two-dimensional composite structure, the internal stress state caused by uncertain loads, and the constraints set by the optimization problem. This method leverages the composite material's performance advantages and improves the structure's load-bearing capacity.

[0037] like Figure 1 As shown in FIG, a robust optimization design method for a thermomechanically coupled continuous fiber composite material includes the following steps:

[0038] Step 1: Set the initial conditions, including the level set function distribution, temperature change value, uncertainty load size and direction change, etc.

[0039] like Figure 2 As shown, this embodiment gives the geometric parameters and boundary conditions of a composite material structure. Specifically, the design domain of the structure is a square plate with a side length of 2L, L=0.3m, and a thickness of 1mm. The lower part of the plate is fixed, and a concentrated load is applied to the middle of the upper part. The magnitude of the load is F, and the angle with the vertical direction is represented by θ. When the structure is subjected to a deterministic load, F=100N and θ=90°; when the structure is subjected to an uncertain load, a mixed uncertainty measurement model is used to quantify the load, and its magnitude F is set as a random variable obeying a Gaussian distribution, with a mean of 100N and a variance of 10N, recorded as F~N(100N,10N); the load direction θ is an interval variable, ranging from 70° to 110°, recorded as θ~[70°,110°].

[0040] like Figure 3 As shown, the topological configuration and fiber routing at the initial moment. The black area represents the matrix phase of the composite material, and the white lines represent the continuous fiber reinforcement phase.

[0041] In this embodiment, the fiber material is carbon fiber with a volume fraction of 34%, and the matrix material is nylon. The ambient temperature is set to room temperature (25° C.) by default. The corresponding material parameters are shown in Table 1.

[0042] Table 1 Parameters of nylon-based carbon fiber reinforced composites

[0043]

[0044] Among them, E, G, ν, α, and ρ represent the Young's modulus, shear modulus, Poisson's ratio, thermal expansion coefficient, and density of the composite material, respectively. The subscripts 1, 2, and 12 represent the fiber direction, any direction perpendicular to the fiber, and the plane perpendicular to the fiber, respectively.

[0045] This method uses the level set function φ to determine whether a point x in the design domain D has material as follows:

[0046] Material domain: φ(x)<0,x∈Ω

[0047] Boundary: φ(x)=0,x∈Γ

[0048] Void: φ(x)>0,x∈D / (Ω∪Γ)

[0049] Where Ω is the material region and Γ is the boundary of the material region. The level set function is updated by the following Hamilton-Jacobi equation:

[0050]

[0051] Among them, θ eis the external normal velocity of the level set function cluster, obtained from the sensitivity information, t is the virtual time variable, represents the gradient. Therefore, the level set function of the k-th step optimization design can be obtained by the level set function of the k-1 step as follows

[0052]

[0053] Here, Δ represents the increment.

[0054] The fiber path is determined by offsetting the zero level set line to obtain the internal level set function cluster and determining it according to the tangent direction of the level set function cluster. The fiber angle β in each finite element is defined by the following formula:

[0055]

[0056] The stiffness matrix can be obtained by the following transformation formula

[0057] C(β)=R(β)C0R T (β)

[0058] Where R(β) is the rotation matrix related to the fiber angle β, defined as follows

[0059]

[0060] C0 is the stiffness matrix when the fiber rotation angle is 0, which has the following form:

[0061]

[0062] Step 2: Calculate the deterministic objective function and sensitivity of the structure at the initial moment.

[0063] The deterministic optimization problem under thermal-mechanical coupling conditions can be summarized as follows

[0064] Minimize J(φ)=a(ΔT,u,φ)+l(u,φ)

[0065] Constraint condition a(u,v,φ)=a(ΔT,v,φ)+l(v,φ)

[0066] V(φ)≤V max

[0067] where a(ΔT,v)=∫ Ω ε(v)C(β)ε ΔT dΩ

[0068]

[0069] a(u,v)=∫ Ω ε(u)C(β)ε(v)dΩ

[0070] In the above formula, J is the thermal coupling flexibility, which includes the flexibility term a(ΔT,u,φ) caused by thermal coupling and the flexibility term l(u,φ) caused by mechanical load, u represents displacement, v represents accompanying variable, V represents material volume, and V max is the maximum allowable volume, f is the body force, t represents the external force applied by the boundary, ΔT is the change in service temperature compared to the reference temperature, ε represents the mechanical strain, and ε ΔT Represents the thermal strain in the physical coordinate system, which can be obtained from the thermal strain in the fiber coordinate system Obtained by the following coordinate transformation

[0071]

[0072] in, With the following expression

[0073]

[0074] The sensitivity J′ can be obtained by the partial derivative of the objective function J with respect to the design variable φ, which is in the form of J′=∫ Γ [2ε(u)C(β)ε ΔT -ε(u)C(β)ε(u)]θ n dΓ

[0075] The external normal velocity θ of the topological boundary can be obtained from this n

[0076] θ n =ε(u)C(β)ε(u)-2ε(u)Cε ΔT

[0077] Further, the boundary velocity θ is calculated by the following formula: n Expanded to global speed θ e

[0078]

[0079] where α = 10 -3 is a small parameter, The material boundary.

[0080] Step 3: Enter the k-th outer loop and update the structural topology and fiber routing based on the sensitivity information.

[0081] Obtain the global velocity θ based on the sensitivity information e , and then according to the formula summarized in step 1 Get the updated level set function φ k, the topological boundary is determined according to the level set function φ=0, while the level set function cluster inside the material represents the fiber path, thereby obtaining the updated structural topology and fiber routing.

[0082] Step 4: Enter the inner loop of step (k, l), obtain the uncertainty load corresponding to the current iteration step, calculate and record the objective function and sensitivity, and increase l by 1.

[0083] According to the expansion order p of the robustness objective function, the length n of the random uncertainty variable (load intensity) vector, and the length m of the interval uncertainty variable (load direction) vector, the total number of uncertainty loads l is obtained as follows: T

[0084]

[0085] Where C represents the number of combinations. Traverse all uncertain loads and obtain the load magnitude and direction for the current iteration. Apply these as boundary conditions to the structure. Then, using the method summarized in step 2, calculate and record the objective function and sensitivity of the structure under this load.

[0086] Each time a calculation is completed, let l increase by 1.

[0087] Step 5: Determine l and l T If l≤l T , then update the magnitude and direction of the load and repeat step 4; if l>l T , then proceed to step 6.

[0088] Step 6: Calculate the robustness objective function and sensitivity, and let k increase by 1 and l = 1.

[0089] Under the action of random-interval mixed uncertainty external load, the robustness objective function of the structure is the flexibility J R Has the following form:

[0090] J R (X,Y)=max{μ(J(X,Y,φ))+hσ(J(X,Y,φ))}

[0091] Where X represents a random uncertainty variable (load size) vector of length n, which can be expressed in component form as X = (X1, X2, ..., X n ), Y represents the interval uncertainty variable (load direction) vector with a length of m, which can be expressed in component form as Y=(Y1,Y2,…,Y m ), μ is the interval mean, σ is the interval variance, and h=1 is the weight factor.

[0092] Furthermore, a hybrid orthogonal polynomial expansion method is used to efficiently obtain the robustness objective function and its sensitivity. This method first transforms the random uncertainty variable vector X into a standard random variable vector ξ, which can be written in component form as ξ=(ξ1,ξ2,…,ξ n ), convert the interval uncertainty variable vector Y into a standard random variable vector η, which can be written in component form as η=(η1,η2,…,η m ). The robustness objective function J R After the p-order random-interval mixed expansion, it has the following form

[0093]

[0094] Among them, χ1 is the index of random uncertainty variable, χ2 is the index of interval uncertainty variable, is the expansion coefficient, is the product of n random variables consisting of a Hermitian chaotic polynomial basis, is the product of m interval variables composed of Chebyshev polynomial basis. According to the properties of Hermite chaos polynomial and Chebyshev polynomial, J can be obtained from the above formula. R The maximum value of the mean and standard deviation is as follows

[0095]

[0096] in, and These are two forms of realization of the indicator χ2. R It can be further expressed as follows

[0097]

[0098] in, Robustness objective function J R The sensitivity with respect to the design variable φ has the form

[0099] Among them, tanh is the hyperbolic tangent function, sech is the hyperbolic secant function, β = 100 is a coefficient, is the partial derivative of the expansion coefficient with respect to the design variable.

[0100] Each time step 6 is completed, k is increased by 1, and l=1.

[0101] Step 7: Determine whether the convergence condition is met. The convergence condition is set as follows: the relative change of the target value in the last 10 cycles is less than 10 -4 And the difference between the volume fraction and the set value is less than 10 -4, or the number of cycles k reaches the set value, then convergence occurs. If the convergence condition is not met, return to step 3; if the convergence condition is met, proceed to step 8.

[0102] Step 8: End the iteration and obtain the final optimized design.

[0103] Figures 4 to 7 The fiber composite material structure optimization design results obtained according to the above steps are given and will be explained below.

[0104] Figure 4 The continuous fiber composite structure is given by the method under the deterministic load F = 100N, θ = 90° for the concurrent optimization design of the structural topology and fiber routing. The target volume fraction is Figure 1 30% in the design domain, the actual volume fraction is 30%. After finite element calculation, we can get Figure 4 The structural specific stiffness of the structure is 53.0N·mm -1 ·g -1 ,compared to Figure 2 The specific stiffness of the structure under the same deterministic load at the initial moment is 7.9 N·mm -1 ·g -1 It has increased by nearly 7 times, greatly improving the material carrying efficiency.

[0105] Figure 5 The continuous fiber composite structure is given by this method under the action of uncertain load F~N(100N,10N),θ~[70°,110°] for the concurrent optimization design of structural topology and fiber routing. The target volume fraction is Figure 1 30% in the design domain, the actual volume fraction is 30%. After finite element calculation, we can get Figure 5 The structural specific stiffness corresponding to the structure is 22.8N·mm -1 ·g -1 ,compared to Figure 2 The specific stiffness of the structure under the same uncertain load at the initial moment is 4.4 N·mm -1 ·g -1 The material load efficiency is significantly improved by 5 times. Figure 4 Given the optimal design under deterministic conditions, the structural specific stiffness is 11.8N·mm -1 ·g -1 , which is only half of the robust optimization design. Considering the uncertainty of actual loads, this comparison illustrates the importance of robust optimization design.

[0106] Figure 6The continuous fiber composite structure is given by this method under the action of uncertain load F~N(100N,10N),θ~[70°,110°] and temperature rise of 2℃, with the simultaneous optimization design of structural topology and fiber routing robustness. The target volume fraction is Figure 1 30% in the design domain, the actual volume fraction is 30%. Figure 5 , Figure 6 More material is concentrated in the lower half of the structure, and the stiffness of the structure decreases by 21%, illustrating the impact of temperature changes on the structure.

[0107] Figure 7 The continuous fiber composite structure is given by this method under the action of uncertain load F~N(100N,10N),θ~[70°,110°] and temperature rise of 4℃, with the simultaneous optimization design of structural topology and fiber routing robustness. The target volume fraction is Figure 1 The actual volume fraction is 24% in the design domain, indicating that the material cannot be fully utilized. Figure 5 , Figure 7 The shape of the structure is quite different and the structural stiffness decreases by 62%, which illustrates the impact of temperature change on the structure.

[0108] The above describes in detail the concurrent optimization design method for the topology and fiber routing robustness of a thermomechanically coupled continuous fiber-reinforced composite structure for 3D printing provided by the present invention. However, it should be understood that this description merely illustrates the principles and implementation methods using specific examples and is not intended to limit the application of the present invention. The scope of protection of the present invention includes various modifications and equivalent solutions made to the invention patent without departing from the scope and spirit of the present invention.

Claims

1. A robust optimization design method for thermally coupled continuous fiber composite materials, characterized in that ； Step 1: Set the initial conditions, including the level set function distribution, temperature change value, uncertainty load size and direction change; Step 2: Calculate the deterministic objective function and sensitivity of the structure at the initial moment; The objective function of the deterministic optimization problem under a given load is taken as the thermal-mechanical coupling structural flexibility, which includes the flexibility term caused by thermal-mechanical coupling and the flexibility term caused by mechanical load. The constraint condition is set as volume constraint. The sensitivity is calculated by taking the partial derivative of the objective function with respect to the level set function. Step 3: Enter the kth outer loop and update the structural topology and fiber routing based on the sensitivity information; The global velocity is obtained based on the sensitivity information, and then the updated level set function is obtained according to the level set function iteration formula, based on which the topological boundary and internal fiber path of the structure are determined; Step 4: Enter the inner loop of step (k, l), obtain the uncertainty load corresponding to the current iteration step, calculate and record the objective function and sensitivity, and increase l by 1; Step 5: Determine l and l T The size of l, if l≤l T , then update the magnitude and direction of the load and repeat step 4; if l>l T , then proceed to step 6; Step 6: Calculate the robustness objective function and sensitivity, and let k increase by 1 and l = 1; Step 7: Determine whether the convergence condition is met; the convergence condition is set as: the relative change of the target value in the last 10 cycles is less than 10 -4 And the difference between the volume fraction and the set value is less than 10 -4 , or the number of cycles k reaches the set value, it converges; if the convergence condition is not met, return to step 3; if the convergence condition is met, go to step 8; Step 8: End the iteration and obtain the final optimized design.

2. The robustness optimization design method for force-coupled continuous fiber composite materials according to claim 1, characterized in that: In step 1: the level set function is used to represent the topology and fiber routing of the structure. Given the initial distribution of the level set function, the temperature in the structure is set to vary uniformly everywhere, the magnitude of the uncertainty load is set to obey a random distribution, and the direction is set to obey an interval distribution.

3. The robustness optimization design method for force-coupled continuous fiber composite materials according to claim 1, characterized in that: In step 4, the total number of uncertainty loads is obtained according to the expansion order p of the robustness objective function, the length n of the random uncertainty variable vector, and the length m of the interval uncertainty variable vector; Traverse all uncertain loads, obtain the load size and direction of the current iteration step, apply it to the structure as a boundary condition, calculate and record the objective function and sensitivity of the structure under the load, and increase l by 1 each time a calculation is completed.

4. The robustness optimization design method for force-coupled continuous fiber composite materials according to claim 1, characterized in that: In step 6, under the action of random-interval mixed uncertainty external load, the robustness objective function of the structure, namely the flexibility J R It will be determined by the interval mean μ and interval variance σ of the structural flexibility under all uncertain external loads; Using the hybrid orthogonal polynomial expansion method, the robust flexibility is expanded by a p-order random-interval hybrid expansion to obtain J R On the expansion forms of Hermitian chaotic polynomials and Chebyshev polynomial bases; According to the properties of the two orthogonal polynomials, the maximum value of the interval mean μ and the interval variance σ is obtained, thereby obtaining J R About the explicit expression of expansion coefficients; J R By taking the partial derivative of the level set function φ, we can obtain the robust sensitivity.

5. The robustness optimization design method for force-coupled continuous fiber composite materials according to claim 1, characterized in that: This method is used for the optimal design of 3D-printed thermomechanically coupled continuous fiber-reinforced composite structures.

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