Isogeometric robust topological optimization method of composite material structure considering thermal-mechanical coupling

Abstract

The invention discloses an isogeometric robust topological optimization method of a composite material structure considering thermal coupling, and the method comprises the steps: describing the internal temperature of the structure as an uncertain variable meeting the non-precise probability distribution through building an isogeometric robust topological optimization model of the composite material structure considering thermal coupling; a corresponding worst target robust performance value is solved through a gradient search algorithm and Gauss-Hermite integral, a constraint performance reliability analysis method considering worst limit state fluctuation is provided, the sensitivity of a worst target performance function, the sensitivity of a worst limit state function and the sensitivity of a volume constraint function are solved, and an optimal topological structure is obtained through a moving asymptote method. The built composite material structure robust topological optimization model truly reflects the internal temperature fluctuation of the structure under the actual working condition, the optimization result can be efficiently obtained, and the method has good engineering application value.

Description

Technical Field

[0001] The invention belongs to the field of structural optimization, and in particular relates to an isogeometric robust topology optimization method for a composite material structure considering thermal-mechanical coupling. Background Art

[0002] In the fields of rail transit, aerospace, etc., when shield machine cutter heads and aircraft landing gear are working, due to the intense friction between the parts, the internal temperature of their structures is often higher than the reference ambient temperature. Their key structures need to withstand both external loads and structural strains caused by thermal expansion of materials. Therefore, the topological optimization research of such structures needs to consider the thermal expansion phenomenon of materials.

[0003] Existing research on uncertainty topology optimization of thermal-mechanical coupling mainly focuses on uncertainty factors such as material properties and external loads, and rarely considers temperature fluctuations inside the structure. However, under actual working conditions, the internal temperature of complex components usually fluctuates due to uncertainty factors such as working conditions and lubrication level, and the temperature change inside the structure will have a significant impact on the optimization results of structures with high thermal expansion coefficients. Therefore, a topology optimization method for composite structures that takes into account temperature fluctuations inside the structure is urgently needed to meet actual engineering needs. Summary of the invention

[0004] In order to solve the shortcomings of the prior art and achieve the purpose of structural design with good rigidity and strength in high temperature scenarios, the present invention adopts the following technical solutions:

[0005] The isogeometric robust topology optimization method for composite structures considering thermal-mechanical coupling includes the following steps:

[0006] Step 1: Construct an isogeometric analysis model of the composite structure to obtain the density of control points;

[0007] Step 2: Based on the uncertainty description of the internal temperature of the composite structure, the overall thermal load considering the internal temperature fluctuation is constructed according to the uncertainty description and the density of the control points to generate the overall flexibility of the composite structure; using the density of the control points as the design variable, combined with the uncertainty description, overall flexibility, stress constraints and optimization space utilization constraints, a geometrically robust topology optimization model of the composite structure considering thermal-mechanical coupling is constructed, and under the constraints, the mean and standard deviation of the thermal flexibility under the influence of the internal temperature uncertainty of the composite structure is minimized;

[0008] Step 3: Calculate the overall stiffness matrix of the composite structure considering the dual modulus characteristics;

[0009] Step 4: Calculate the thermal strain of the composite structure at the unit Gaussian point, and combine the elastic tensor matrix considering the dual modulus characteristics to solve the overall thermal load of the composite structure considering the internal temperature fluctuation. The overall displacement under the influence of the internal temperature uncertainty of the structure is solved by the overall thermal load of the structure and the overall stiffness matrix of the structure to determine the overall flexibility; solve the global failure coefficient of the composite structure considering the internal temperature fluctuation for stress constraint;

[0010] Step 5: Construct and solve the objective function based on the mean and standard deviation of the thermal flexibility of the composite structure to obtain the worst objective performance function;

[0011] Step 6: Calculate the worst limit state corresponding to the stress constraint;

[0012] Step 7: Update the control point density according to the worst objective performance function, the worst limit state and the density sensitivity of the optimized space utilization constraint with respect to the control point to obtain the optimal design variables.

[0013] Furthermore, the step S2 comprises the following steps:

[0014] Step 2.1: Describe the internal temperature of the composite structure affected by multiple sources of uncertainty as a probability variable that satisfies an inexact normal distribution T I represents the internal temperature variable of the composite material structure, I μ with I σ They represent the mean and standard deviation of the internal temperature variables of the composite material structure with interval characteristics, specifically:

[0015]

[0016] in, and They represent the upper and lower limits of the mean and standard deviation of the temperature variables inside the composite structure respectively;

[0017] Step 2.2: Construct the overall thermal load F considering the internal temperature fluctuation by considering the thermal expansion phenomenon of the composite material under high temperature scenario th (ρ,T I ), ρ represents the control point density vector;

[0018] Step 2.3: Based on the inexact probability variables and the overall thermal load, a geometrically robust topology optimization model of composite structures is constructed considering thermal-mechanical coupling:

[0019]

[0020] Among them, ρ i,j represents the control point P i,j The corresponding density, and They represent the mean and standard deviation of the thermal flexibility of the composite structure considering the influence of internal temperature uncertainty, c(ρ,T I ) represents the thermal flexibility of the composite structure under the influence of internal temperature uncertainty, u e (ρ,T I ) represents the displacement vector of unit e under the influence of temperature uncertainty inside the composite structure, which is abbreviated as represents the stiffness matrix of element e considering the dual modulus characteristics, N e represents the number of units e, g V (ρ) represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V 0 and [V] represent the upper limits of the design domain size and space utilization constraints, respectively. P(·) represents the probability calculation function. and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on the Tsai-Wu failure criterion and the set upper limit of the global failure coefficient, respectively. t represents the pre-set stress constraint reliability requirement, K B (ρ) represents the overall stiffness matrix of the composite structure considering the dual modulus characteristics, U represents the overall displacement amplitude vector of the composite structure, and F m Represents the external loads on the composite structure.

[0021] Furthermore, the step 3 comprises the following steps:

[0022] Step 3.1: Based on the Patel model, obtain the elastic tensor matrix considering the dual modulus characteristics Solving the stiffness matrix of composite structural elements considering dual modulus characteristics

[0023] Step 3.2: Through the element stiffness matrix Calculate the overall stiffness matrix K of the composite structure B (ρ).

[0024] Furthermore, the isogeometric analysis model in step 1 is a non-uniform rational B-spline grid model, and the grid model is Gaussian subdivided as a whole, and the Gaussian points of the ii-th row and jj-th column in the e-th unit are obtained from the control points corresponding to the unit e. Density

[0025] Furthermore, step 4 comprises the following steps:

[0026] Step 4.1: Calculate the unit Gaussian points The thermal strain of the composite structure is:

[0027]

[0028] in, represents the structural thermal strain vector at the unit Gauss point, Φ c represents the thermal expansion coefficient vector of the composite material, T R Indicates the reference ambient temperature; T I Represents the internal temperature variable of the composite material structure;

[0029] Combined with the Gaussian subdivision method, the heat load corresponding to the e-th unit is solved. The specific calculation is as follows:

[0030]

[0031] in, represents the heat load vector at element e, N G represents the number of discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents the weights corresponding to the discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents a unit Gaussian point The strain displacement matrix at J e represents the Jacobian matrix of unit e, det(·) represents the operation of solving the determinant, represents the elastic tensor matrix considering the bimodular characteristics;

[0032] Step 4.2: By combining the thermal load vectors at the calculation unit e, the overall thermal load F of the composite structure is obtained. th (ρ,T I );

[0033] Step 4.3: Solve the Gaussian points of the composite structure unit considering internal temperature fluctuations The stress vector is:

[0034]

[0035] in, represents the Gaussian stress vector of the unit considering internal temperature fluctuations, which is abbreviated as

[0036] Step 4.4: Calculate the global failure coefficient of the composite structure based on the Tsai-Wu failure criterion and the P-mean aggregation function Specifically:

[0037]

[0038] Among them, N e represents the number of equal geometric units, Represents the Tsai-Wu failure criterion and the element Gaussian point stress vector The failure coefficient at the Gaussian point of the unit is obtained, p t Represents the P-mean aggregation function coefficient of the stress constraint function.

[0039] Furthermore, the step 5 comprises the following steps:

[0040] Step 5.1: Introduce weight coefficient w T , define the weighted objective function

[0041]

[0042] in, and They represent the mean and standard deviation of the thermal flexibility of the composite structure considering the influence of internal temperature uncertainty, c(ρ,T I ) represents the thermal flexibility of the composite structure under the influence of internal temperature uncertainty, ρ represents the density of the control points, T I Represents the internal temperature variable of the composite material structure;

[0043] Step 5.2: Calculate the thermal flexibility of the composite structure c(ρ,T I )Origin moment E[c m (ρ,T I )] and calculate the uncertainty of the internal temperature T of the structure by using the approximate value I The mean and standard deviation of the thermal flexibility of the structure under influence;

[0044] Step 5.3: Transform the objective function Rewritten as:

[0045]

[0046] in, represents the hth Gauss-Hermite integration point The corresponding internal temperature value of the structure; represents the hth Gauss-Hermite integration point Corresponding structure internal temperature Thermal flexibility of the structure under

[0047] Step 5.4: Consider the interval characteristics of the internal temperature variable distribution parameters and solve the objective function About the mean internal temperature of the structure I μ With standard deviation I σ The sensitivity of the structure is calculated based on the gradient search algorithm to obtain the internal temperature distribution parameter value of the structure corresponding to the worst objective function value. and Worst temperature condition and the worst objective performance function

[0048] Furthermore, step 5.2 specifically includes the following steps:

[0049] Step 5.2.1: Considering the probability distribution characteristics of the internal temperature variable, the internal temperature variable T I Transformed into a standard normal variable T s , specifically:

[0050]

[0051] Step 5.2.2: Calculate the approximate origin moment when m = 1, 2 based on the Gauss-Hermite integral, specifically:

[0052]

[0053] Among them, c(ρ,T I ) and c s (ρ,T s ) represent the temperature variables T I and the standard normal variable T s represents the thermal flexibility of the structure, ρ represents the density of control points, φ(T s ) represents the standard normal variable T s The probability density distribution function of , H represents the number of selected Gauss-Hermite integration points, w h (h=1,2,…,H) represents the weight corresponding to the hth Gauss-Hermite integration point; T s h is the standard normal variable value corresponding to the hth Gauss-Hermite integration point, c s (ρ,T s h ) indicates that T s h The thermal flexibility of the structure represented by

[0054] Step 5.2.3: Calculate the temperature uncertainty T inside the structure I The mean and standard deviation of the thermal flexibility of the structure under the influence are as follows:

[0055]

[0056] Furthermore, the step 6 comprises the following steps:

[0057] Step 6.1: Stress-based performance function Construct the limit state function, expressed as:

[0058]

[0059] in, and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on the Tsai-Wu failure criterion and the set upper limit of the global failure coefficient, ρ represents the density of the control point, T I Represents the internal temperature variable of the composite material structure;

[0060] Step 6.2: Consider the internal temperature variable T of the structure in the original space I Satisfying the non-exact normal distribution, the variable T in the original space I The variable T is transformed into the standard normal space through standardization s , rewrite the limit state function as a standard normal variable T s and the interval variable I μ with I σ Form of representation

[0061] Step 6.3: Establish a reliability model to solve the worst limit state function on the reliability index surface under the influence of inexact probability variables:

[0062]

[0063] Among them, β t Represents the reliability index corresponding to the constraint performance function, and its corresponding reliability requirement P t Calculated, β t =Φ -1 (P t );Φ -1 (·) represents the inverse function of the standard normal cumulative distribution function, ||·|| represents the modular operation, μ T represents the mean value of the temperature variable inside the structure, σ T represents the standard deviation of the temperature variation inside the structure, and They represent the upper and lower limits of the mean and standard deviation of the temperature variables inside the composite structure respectively;

[0064] Step 6.4: Calculate the stress limit state function About the variable T s , I μ with I σ The sensitivity of the reliability index surface is calculated by the gradient search algorithm to obtain the worst constraint performance point T s MPTP And the worst extreme temperature average With standard deviation And combine to get the worst limit temperature T I MPTP And the worst limit state function

[0065] Furthermore, in step 7, the worst objective performance function, the worst limit state function and the sensitivity of the optimized space utilization constraint to the density of control points of each unit are calculated; based on the calculation results of the control point density sensitivity, the control point density is updated in combination with the moving asymptote method, and the convergence condition is checked, that is, the average relative change degree of the worst objective performance function within several consecutive iterations is not higher than the threshold. If the convergence condition is not met, return to step 3 to iterate.

[0066] The isogeometric robust topology optimization system of the composite material structure considering thermal-mechanical coupling performs topology optimization according to the isogeometric robust topology optimization method of the composite material structure considering thermal-mechanical coupling to obtain the best design variables of the complex material structure.

[0067] The advantages and beneficial effects of the present invention are:

[0068] Compared with the composite structure topology optimization method that does not consider the thermal-mechanical coupling and bimodular characteristics, the present invention fully considers the influence of the thermal expansion and bimodular characteristics of the material, and the obtained optimized structure is more in line with the actual engineering needs and has good stiffness and strength in high temperature scenarios; the present invention describes the internal temperature of the structure affected by multi-source uncertainty factors as a random variable that satisfies the non-precise normal distribution, and proposes a target performance statistical moment solution method based on Gaussian quadrature and gradient search, and uses the Guass-Hermite integral to solve the target performance statistical moment approximation, and then uses the gradient search algorithm to determine the worst target performance function value, which can efficiently and accurately evaluate the target performance statistics under the influence of non-precise probability variables; the present invention proposes a structural constraint performance reliability analysis method considering the worst limit state fluctuation, while considering the probability distribution characteristics of the temperature variables inside the structure and the interval characteristics of its distribution parameters, constructing a reliability analysis model considering the influence of non-precise probability variables, and obtaining the worst limit state function. Compared with the existing reliability evaluation method containing non-precise probability variables, better structural target performance can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of a method according to an embodiment of the present invention.

[0070] Figure 2 It is a schematic diagram of the initial design of the cutter head support plate in an embodiment of the present invention.

[0071] Figure 3 This is the optimal topological diagram of the cutter head support plate in the embodiment of the present invention. DETAILED DESCRIPTION

[0072] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0073] like Figure 1 As shown, the present invention proposes an isogeometric robust topology optimization method for composite structures considering thermal-mechanical coupling. By considering the thermal expansion phenomenon of the composite material structure in high temperature scenarios and the internal temperature fluctuation of the structure, the internal temperature of the structure, which is susceptible to multi-source uncertainty factors such as lubrication degree and operating state, is described as an imprecise probability variable. At the same time, the mean and standard deviation of the structural thermal flexibility are used as the objective function to establish an isogeometric robust topology optimization model for composite structures under stress constraints and material usage constraints, which fully reflects the high stiffness, high strength and lightweight design requirements for composite structures in high temperature scenarios. At the same time, a target performance statistical moment solution method based on Gaussian quadrature and gradient search and a reliability analysis method considering the worst limit state fluctuation are proposed, which are used to efficiently solve the worst target performance function and the worst limit state function under the influence of imprecise probability variables. On this basis, the sensitivity of the worst target performance function, the worst limit state function and the volume constraint function is derived and solved, and the optimal topology design scheme is obtained using the moving asymptote method.

[0074] Step 1: Construct an isogeometric analysis model of non-uniform rational B-splines (NURBS) of composite material structure, perform Gaussian subdivision on the entire NURBS mesh model, and obtain the Gaussian points of the ii-th row and jj-th column in the e-th unit from the corresponding control points of unit e. Density

[0075] In the embodiment of the present invention, a practical application in topology optimization design is carried out for a certain type of shield machine cutter head support plate made of TM800s / M21 carbon fiber reinforced composite material, such as Figure 2 The design domain of the cutter disc support plate is shown in FIG. 1 . The left end and the lower end of the cutter disc support plate are fixed, and the right end is subjected to a horizontal uniformly distributed load F to the left. The total load is 900 N and the equivalent uniformly distributed line load is 1.9912 N / mm.

[0076] On the basis of constructing NURBS curve, two-way node vector u=(u 0 ,u 1 ,...,u 51+2+1 ) and v=(v 0 ,v 1 ,...,v 26+2+1), introduce 51×26 control points P i,j ,i=1,2,...,51;j=1,2,...,26 and 51×26 weights w i,j ,i=1,2,...,51;j=1,2,...,26.

[0077] Step 2: Construct an isogeometric robust topology optimization model of the composite structure considering thermal-mechanical coupling, which includes the following steps:

[0078] Step 2.1: Consider the temperature inside the composite structure affected by multiple sources of uncertainty and describe it as a probability variable that satisfies an inexact normal distribution. Among them, T I represents the internal temperature variable of the composite material structure, I μ with I σ They represent the mean and standard deviation of the internal temperature variables of the composite material structure with interval characteristics, specifically:

[0079]

[0080] in, and They represent the upper and lower limits of the mean and standard deviation of the internal temperature variables of the composite structure respectively.

[0081] In the embodiment of the present invention, as a cutter head support plate of a composite material structure, the mean and standard deviation of the temperature variable inside the cutter head support plate are as follows:

[0082]

[0083] Step 2.2: Consider the thermal expansion of composite materials under high temperature scenarios and construct the overall thermal load F considering the temperature fluctuation inside the structure th (ρ,T I ), ρ represents the control point density vector.

[0084] Step 2.3: Based on the inexact probability variables and the overall thermal load, a geometrically robust topology optimization model of composite structures is constructed considering thermal-mechanical coupling:

[0085]

[0086] Among them, ρ i,j represents the control point P i,j The corresponding density, and They represent the mean and standard deviation of the thermal flexibility of the composite material structure considering the influence of the internal temperature uncertainty of the composite material structure, c(ρ,T I) represents the thermal flexibility of the composite structure under the influence of the internal temperature uncertainty of the composite structure, u e (ρ,T I ) represents the displacement vector of unit e under the influence of temperature uncertainty inside the composite structure, which is abbreviated as represents the stiffness matrix of element e considering the dual modulus characteristics, N e represents the number of units e, g V (ρ) represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V 0 and [V] represent the upper limits of the design domain size and space utilization constraints, respectively. P(·) represents the probability calculation function. and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on the Tsai-Wu failure criterion and the set upper limit of the global failure coefficient, respectively. t represents the pre-set stress constraint reliability requirement, K B (ρ) represents the overall stiffness matrix of the composite structure considering the dual modulus characteristics, U represents the overall displacement amplitude vector of the composite structure, and F m Represents the external loads on the composite structure.

[0087] Step 3: Construct the overall stiffness matrix of the composite material structure considering the dual modulus characteristics, which specifically includes the following steps:

[0088] Step 3.1: Based on the Patel model, obtain the elastic tensor matrix considering the dual modulus characteristics Solving the stiffness matrix of composite structural elements considering dual modulus characteristics

[0089] Step 3.2: Calculate the overall stiffness matrix K of the composite structure B (ρ).

[0090] Step 4: Solve the thermal load and global failure coefficient of the composite structure considering the temperature fluctuation inside the structure, which specifically includes the following steps:

[0091] Step 4.1: Calculate the unit Gaussian points The thermal strain of the composite structure is:

[0092]

[0093] in, represents the structural thermal strain vector at the unit Gauss point, Φ c represents the thermal expansion coefficient vector of the composite material, T R Indicates the reference ambient temperature;

[0094] In the embodiment of the present invention, the thermal strain vector at the unit Gauss point is:

[0095]

[0096] Combined with the Gaussian subdivision method, the heat load corresponding to the e-th unit is solved. The specific calculation is as follows:

[0097]

[0098] in, represents the heat load vector at element e, N G represents the number of discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents the weights corresponding to the discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents a unit Gaussian point The strain displacement matrix at J e represents the Jacobian matrix of unit e, det(·) represents the operation of solving the determinant;

[0099] Step 4.2: By combining the thermal load vectors at the calculation unit e, the overall thermal load F of the composite structure is obtained. th (ρ,T I );

[0100] Step 4.3: Solve the Gaussian points of the composite structural unit considering the temperature fluctuation inside the structure The stress vector is:

[0101]

[0102] in, represents the Gaussian stress vector of the unit considering the temperature fluctuation inside the structure, which is abbreviated as

[0103] Step 4.4: Calculate the global failure coefficient of the composite structure based on the Tsai-Wu failure criterion and the P-mean aggregation function Specifically:

[0104]

[0105] Among them, N e represents the number of equal geometric units, Represents the Tsai-Wu failure criterion and the element Gaussian point stress vector The failure coefficient at the Gaussian point of the unit is obtained, p t P-mean aggregation function coefficient representing the stress constraint function;

[0106] In the embodiment of the present invention, the failure coefficient at the unit Gauss point is:

[0107]

[0108] Step 5: Calculate the mean and standard deviation of the thermal flexibility of the composite structure based on Gaussian quadrature and gradient search, specifically:

[0109] Step 5.1: Introduce weight coefficient w T , define the weighted objective function

[0110]

[0111] Step 5.2: Calculate the thermal flexibility of the composite structure c(ρ,T I )Origin moment E[c m (ρ,T I )], specifically:

[0112] Step 5.2.1: Consider the probability distribution characteristics of the temperature variable inside the structure, and standardize the temperature variable inside the structure T I Transformed into a standard normal variable T s , specifically:

[0113]

[0114] Step 5.2.2: Calculate the approximate origin moment when m = 1, 2 based on the Gauss-Hermite integral, specifically:

[0115]

[0116] Among them, c(ρ,T I ) and c s (ρ,T s ) represent the temperature variables T I and the standard normal variable T s The thermal flexibility of the structure represented by φ(T s ) represents the standard normal variable T s The probability density distribution function of ; H represents the number of selected Gauss-Hermite integration points; w h (h=1,2,…,H) represents the weight corresponding to the h-th Gauss-Hermite integration point; Tsh is the standard normal variable value corresponding to the h-th Gauss-Hermite integration point, c s (ρ,T s h ) indicates that T s h The thermal flexibility of the structure represented by

[0117] Step 5.2.3: Calculate the temperature uncertainty T inside the structure I The mean and standard deviation of the thermal flexibility of the structure under the influence are as follows:

[0118]

[0119] Step 5.3: Transform the objective function Rewritten as:

[0120]

[0121] Among them, T I h represents the hth Gauss-Hermite integration point T s h The corresponding internal temperature value of the structure; c(ρ,T I h ) represents the hth Gauss-Hermite integration point T s h Corresponding structure internal temperature T I h Thermal flexibility of the structure under

[0122] Step 5.4: Consider the interval characteristics of the temperature variable distribution parameters inside the structure and solve the objective function About the mean internal temperature of the structure I μ With standard deviation I σ The sensitivity of the structure is calculated based on the gradient search algorithm to obtain the internal temperature distribution parameter value of the structure corresponding to the worst objective function value. and Worst temperature condition and the worst objective performance function

[0123] In the embodiment of the present invention, w h (h=1,2,…,5), correspondingly:

[0124]

[0125]

[0126] Step 6: Use the gradient search algorithm to solve the worst limit state function corresponding to the probability constraint function, specifically:

[0127] Step 6.1: Stress-based performance function Construct the limit state function, expressed as:

[0128]

[0129] In the embodiment of the present invention, [ωTW ]=0.6, therefore, correspondingly:

[0130]

[0131] Step 6.2: Consider the internal temperature variable T of the structure in the original space I Satisfying the non-exact normal distribution, the variable T in the original space I The variable T is transformed into the standard normal space through standardization s , rewrite the limit state function as a standard normal variable T s and the interval variable I μ with I σ Form of representation

[0132] Step 6.3: Establish a reliability model to solve the worst limit state function on the reliability index surface under the influence of inexact probability variables:

[0133]

[0134] Among them, β t Represents the reliability index corresponding to the constraint performance function, and its corresponding reliability requirement P t Calculated, β t =Φ -1 (P t );Φ -1 (·) represents the inverse function of the standard normal cumulative distribution function, ||·|| represents the modular operation, μ T represents the mean value of the temperature variable inside the structure, σ T represents the standard deviation of the temperature variable inside the structure;

[0135] Step 6.4: Calculate the stress limit state function About the variable T s , I μ with I σ The sensitivity of the reliability index surface is calculated by the gradient search algorithm to obtain the worst constraint performance point T s MPTP And the worst extreme temperature average With standard deviation And combine to get the worst limit temperature T I MPTP And the worst limit state function

[0136] Step 7: Solve for the worst objective performance function Worst limit state function And the volume constraint function g V (ρ) Regarding the control point density of each unit ρi,j According to the sensitivity information of the worst objective performance function, the worst limit state function and the volume constraint function, the moving asymptote method is used to update the control point density; the convergence condition (the worst objective performance function within three consecutive iterations) is checked. The relative change degree average is not higher than the threshold value 0.03); if the convergence condition is not met, return to step 3 to iterate.

[0137] In the embodiment of the present invention, Figure 3 The figure shows the optimal topology of the cutter head support plate. The convergence condition is met at 25 iterations. The average thermal flexibility of the optimized cutter head support plate is With standard deviation Global failure coefficient The design needs and working requirements of the cutterhead support plate of the shield machine are met, thus verifying the effectiveness of the proposed method.

[0138] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An isogeometric robust topology optimization method for composite structures considering thermal-mechanical coupling, characterized by The steps include: Step 1: Construct an isogeometric analysis model of the composite structure to obtain the density of control points; Step 2: Based on the uncertainty description of the internal temperature of the composite structure, the overall thermal load considering the internal temperature fluctuation is constructed according to the uncertainty description and the density of the control points to generate the overall flexibility of the composite structure; using the density of the control points as the design variable, combined with the uncertainty description, overall flexibility, stress constraints and optimization space utilization constraints, a geometrically robust topology optimization model of the composite structure considering thermal-mechanical coupling is constructed, and under the constraints, the mean and standard deviation of the thermal flexibility under the influence of the internal temperature uncertainty of the composite structure is minimized; Step 3: Calculate the overall stiffness matrix of the composite structure considering the dual modulus characteristics; Step 4: Calculate the thermal strain of the composite structure at the unit Gaussian point, and combine the elastic tensor matrix considering the dual modulus characteristics to solve the overall thermal load of the composite structure considering the internal temperature fluctuation. The overall displacement under the influence of the internal temperature uncertainty of the structure is solved by the overall thermal load of the structure and the overall stiffness matrix of the structure to determine the overall flexibility; solve the global failure coefficient of the composite structure considering the internal temperature fluctuation for stress constraint; Step 5: Construct and solve the objective function based on the mean and standard deviation of the thermal flexibility of the composite structure to obtain the worst objective performance function; Step 6: Calculate the worst limit state corresponding to the stress constraint; Step 7: Update the control point density according to the worst objective performance function, the worst limit state and the density sensitivity of the optimized space utilization constraint with respect to the control point to obtain the optimal design variables.

2. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: The step S2 comprises the following steps: Step 2.1: Describe the internal temperature of the composite structure affected by multiple sources of uncertainty as a probability variable that satisfies an inexact normal distribution T I represents the internal temperature variable of the composite material structure, I μ with I σ They represent the mean and standard deviation of the internal temperature variables of the composite material structure with interval characteristics, specifically: in, and They represent the upper and lower limits of the mean and standard deviation of the temperature variables inside the composite structure respectively; Step 2.2: Construct the overall thermal load F considering the internal temperature fluctuation by considering the thermal expansion phenomenon of the composite material under high temperature scenario th (ρ,T I ), ρ represents the control point density vector; Step 2.3: Based on the inexact probability variables and the overall thermal load, a geometrically robust topology optimization model of composite structures is constructed considering thermal-mechanical coupling: st g V (ρ)=V(ρ) / V0≤[V] K B (p)U=F m +F th (p,T I ) p={p i,j },10 -9 ≤ρ i,j ≤1 (i=1,2,…,m;j=1,2,…,n) Among them, ρ i,j represents the control point P i,j The corresponding density, and They represent the mean and standard deviation of the thermal flexibility of the composite structure considering the influence of internal temperature uncertainty, c(ρ,T I ) represents the thermal flexibility of the composite structure under the influence of internal temperature uncertainty, u e (ρ,T I ) represents the displacement vector of unit e under the influence of temperature uncertainty inside the composite structure, which is abbreviated as represents the stiffness matrix of element e considering the dual modulus characteristics, N e represents the number of units e, g V (ρ) represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V0 and [V] represent the upper limit of the design domain size and space utilization constraint, respectively, P(·) represents the probability calculation function, and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on the failure criterion and the set upper limit of the global failure coefficient, respectively. t represents the pre-set stress constraint reliability requirement, K B (ρ) represents the overall stiffness matrix of the composite structure considering the dual modulus characteristics, U represents the overall displacement amplitude vector of the composite structure, and F m Represents the external loads on the composite structure.

3. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: The step 3 comprises the following steps: Step 3.1: Obtain the elastic tensor matrix considering the dual modulus characteristics, and solve the stiffness matrix of the composite material structural unit considering the dual modulus characteristics; Step 3.2: Calculate the overall stiffness matrix of the composite structure through the unit stiffness matrix.

4. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: The isogeometric analysis model in step 1 is a non-uniform rational B-spline grid model. The grid model is Gaussian subdivided as a whole, and the Gaussian points of the units in the iith row and jjth column in the eth unit are obtained from the control points corresponding to the unit e. Density 5. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 4, characterized in that: The step 4 comprises the following steps: Step 4.1: Calculate the unit Gaussian points The thermal strain of the composite structure is: in, represents the structural thermal strain vector at the unit Gauss point, Φ c represents the thermal expansion coefficient vector of the composite material, T R Indicates the reference ambient temperature; T I Represents the internal temperature variable of the composite material structure; Combined with the Gaussian subdivision method, the heat load corresponding to the e-th unit is solved. The specific calculation is as follows: in, represents the heat load vector at element e, N G represents the number of discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents the weights corresponding to the discrete Gaussian integration points in the row and column directions of each unit in the parameter domain, Represents a unit Gauss point The strain displacement matrix at J e represents the Jacobian matrix of unit e, det(·) represents the operation of solving the determinant, represents the elastic tensor matrix considering the bimodular characteristics; Step 4.2: By combining the thermal load vectors at the calculation unit e, the overall thermal load F of the composite structure is obtained. th (ρ,T I ); Step 4.3: Solve the Gaussian point of the composite material structure unit considering internal temperature fluctuations The stress vector is: in, represents the Gaussian stress vector of the unit considering internal temperature fluctuations, which is abbreviated as Step 4.4: Calculate the global failure coefficient of the composite structure based on the failure criterion and the aggregation function Specifically: Among them, N e represents the number of equal geometric units, Represents the Tsai-Wu failure criterion and the element Gaussian point stress vector The failure coefficient at the Gaussian point of the unit is obtained, p t Represents the P-mean aggregation function coefficient of the stress constraint function.

6. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: The step 5 comprises the following steps: Step 5.1: Introduce weight coefficient w T , define the weighted objective function in, and They represent the mean and standard deviation of the thermal flexibility of the composite structure considering the influence of internal temperature uncertainty, c(ρ,T I ) represents the thermal flexibility of the composite structure under the influence of internal temperature uncertainty, ρ represents the density of the control points, T I Represents the internal temperature variable of the composite material structure; Step 5.2: Calculate the thermal flexibility of the composite structure c(ρ,T I )Origin moment E[c m (ρ,T I )] and calculate the uncertainty of the internal temperature T of the structure by using the approximate value I The mean and standard deviation of the thermal flexibility of the structure under influence; Step 5.3: Transform the objective function Rewritten as: in, represents the hth Gauss-Hermite integration point The corresponding internal temperature value of the structure; represents the hth Gauss-Hermite integration point Corresponding structure internal temperature Thermal flexibility of the structure under Step 5.4: Consider the interval characteristics of the internal temperature variable distribution parameters and solve the objective function About the mean internal temperature of the structure I μ With standard deviation I σ The sensitivity of the structure is calculated based on the gradient search algorithm to obtain the internal temperature distribution parameter value of the structure corresponding to the worst objective function value. and Worst temperature condition and the worst objective performance function 7. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 6, characterized in that: Step 5.2 specifically includes the following steps: Step 5.2.1: Considering the probability distribution characteristics of the internal temperature variable, the internal temperature variable T I Transformed into a standard normal variable T s , specifically: Step 5.2.2: Calculate the approximate origin moment when m = 1, 2 based on the Gauss-Hermite integral, specifically: Among them, c(ρ,T I ) and c s (ρ,T s ) represent the temperature variables T I and the standard normal variable T s represents the thermal flexibility of the structure, ρ represents the density of control points, φ(T s ) represents the standard normal variable T s The probability density distribution function of , H represents the number of selected integration points, w h (h=1,2,…,H) represents the weight corresponding to the hth integral point; is the standard normal variable value corresponding to the hth integration point, Indicated by The thermal flexibility of the structure represented by Step 5.2.3: Calculate the temperature uncertainty T inside the structure I The mean and standard deviation of the structural thermal flexibility under the influence are as follows:

8. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: The step 6 comprises the following steps: Step 6.1: Stress-based performance function Construct the limit state function, expressed as: in, and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on the failure criterion and the set upper limit of the global failure coefficient, ρ represents the density of the control point, T I Represents the internal temperature variable of the composite material structure; Step 6.2: Consider the internal temperature variable T of the structure in the original space I Satisfying the non-exact normal distribution, the variable T in the original space I The variable T is transformed into the standard normal space through standardization s , rewrite the limit state function as a standard normal variable T s and the interval variable I μ with I σ Form of representation Step 6.3: Establish a reliability model to solve the worst limit state function on the reliability index surface under the influence of inexact probability variables: s.t. ||T s ||=β t Among them, β t Represents the reliability index corresponding to the constraint performance function, and its corresponding reliability requirement P t Calculated, β t =Φ -1 (P t );Φ -1 (·) represents the inverse function of the standard normal cumulative distribution function, ||·|| represents the operation of solving the modulus, μ T represents the mean value of the temperature variable inside the structure, σ T represents the standard deviation of the temperature variation inside the structure, and They represent the upper and lower limits of the mean and standard deviation of the temperature variables inside the composite structure respectively; Step 6.4: Calculate the stress limit state function (ρ,T s ,I μ ,I σ ) About variable T s , I μ with I σ The sensitivity of the reliability index is calculated by the gradient search algorithm to obtain the worst constraint performance point on the reliability index surface. And the worst extreme temperature average With standard deviation And combine to get the worst limit temperature And the worst limit state function 9. The isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to claim 1, characterized in that: In step 7, the worst objective performance function, the worst limit state function and the sensitivity of the optimized space utilization constraint to the density of control points of each unit are calculated; based on the calculation result of the control point density sensitivity, the control point density is updated in combination with the moving asymptote method, and the convergence condition is checked, that is, the average relative change degree of the worst objective performance function within several consecutive iteration steps is not higher than the threshold. If the convergence condition is not met, return to step 3 to iterate.

10. An isogeometric robust topology optimization system for composite structures considering thermal-mechanical coupling, characterized by According to the isogeometric robust topology optimization method for composite material structures considering thermal-mechanical coupling according to any one of claims 1 to 9, topology optimization is performed to obtain optimal design variables for complex material structures.

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