Stress constraint system reliability topological optimization method and system oriented to plate shell structure

Abstract

The invention provides a stress constraint system reliability topological optimization method and system oriented to a plate shell structure. The method comprises the following steps: calculating the structural stress response of each unit of a plate shell finite element model; a unit filtering strategy is adopted to obtain an active unit set, and MPP most probable failure points and failure probabilities of the active unit set are calculated; calculating upper and lower bounds of failure probability of the stress constraint system of the plate-shell structure; constructing a reliability topological optimization model of the initial stress constraint system; updating design variables of the initial stress constraint system reliability topological optimization model to obtain a plate shell structure stress constraint system reliability topological optimization model; and based on the reliability topological optimization model of the stress constraint system of the plate-shell structure, completing reliability topological optimization of the stress constraint system of the plate-shell structure. The optimization model constructed by the invention provides a better material topology layout, and the safety performance of the structure is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of structural topology optimization continuum design, and in particular relates to a reliability topology optimization method and system for a stress constraint system of a plate-shell structure. Background Art

[0002] Plate-shell structures play a vital role in aerospace engineering, mainly reflected in their key functions such as load-bearing, weight reduction and pressure resistance. First, plate-shell structures are widely used to carry the main loads of aircraft, such as rocket plates, fuel tanks and engine plates, and can effectively cope with complex mechanical effects and avoid local failure by evenly dispersing stress. Secondly, weight control is a core requirement in aerospace design. Plate-shell structures, with their superior mechanical properties, minimize the use of materials while ensuring strength and stiffness, achieve lightweight design, and thus improve fuel efficiency and mission load capacity. In addition, the geometric characteristics of plate-shell structures give them extremely strong pressure resistance, especially suitable for high-pressure environments such as rocket launches, thrusters and engine compartments. It can withstand complex loads and dynamic environments during the flight of spacecraft, maintain structural stability, and adapt to drastic temperature changes and impact loads. These characteristics make plate-shell structures an irreplaceable structural form in spacecraft, significantly improving the overall performance and reliability of spacecraft, while reducing launch costs. However, in practical applications, plate-shell structures usually need to minimize structural weight while ensuring strength and stiffness, thereby improving the fuel efficiency and mission performance of aircraft. Therefore, the optimal design of plate and shell structures has become an important research topic in aerospace engineering.

[0003] Through advanced numerical simulation and optimization algorithms, engineers can optimize the geometric parameters, material distribution and reinforcement design of plate and shell structures to meet specific mechanical requirements. This not only improves the reliability of structural design, but also accelerates the product development process, helping the aerospace industry to move towards a more efficient and lightweight goal. Topology optimization is a powerful structural optimization concept method that aims to seek the best material layout to improve performance and reduce structural weight. In recent decades, topology optimization has made great progress and has been widely used in many engineering fields, and a variety of methods have been developed to meet the challenges of topology optimization. It is worth noting that a series of topology optimization methods have been developed, such as solid isotropic material with penalty function (SIMP), level set method, moving deformable part method, moving deformable hole method and topology derivative-based method, among which SIMP has been widely used in solving various optimization problems due to its simple conceptual framework and easy implementation. Stress, as a basic indicator for evaluating and quantifying structural strength, plays a vital role in the optimization process. Therefore, topology optimization methods with stress constraints have attracted much attention due to their potential in improving structural performance. In addition, it should be noted that physical and engineering problems in the real world themselves involve many uncertain factors. Therefore, it is necessary to introduce a reliability-based concept to consider the impact of uncertainty and to implement an efficient and high-precision stress constraint reliability topology optimization method to address the difficulties caused by the huge number of stress constraints in plate and shell structures.

[0004] The existing stress constraint system reliability topology optimization design methods have the following main problems:

[0005] First, the plate-shell structure contains a large number of stress constraints, and each constraint has an impact on the structural safety. Therefore, all constraints need to be considered and their MPP most likely failure points calculated, which will inevitably result in extremely high computational costs. Second, the traditional reliability optimization method can only consider a single constraint, which will result in low precision when dealing with system reliability optimization problems involving a large number of constraints. Summary of the invention

[0006] In view of the deficiencies in the prior art, the present invention provides a reliability topology optimization method and system for a stress constraint system of a plate-shell structure, which achieves a more optimal material topology layout and effectively improves the safety performance of the structure.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A reliability topology optimization method for a stress-constrained system of a plate-shell structure includes the following steps:

[0009] Establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model;

[0010] Based on the structural stress response of each unit, the unit filtering strategy is adopted to obtain the active unit set, and the MPP most likely failure point and failure probability of the active unit set are calculated;

[0011] Based on the MPP most likely failure point and failure probability of the active unit set, the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure are calculated;

[0012] Based on the upper and lower bounds of failure probability of the plate and shell structure stress constraint system, the random variables and the design variables, a reliability topology optimization model of the initial stress constraint system is constructed;

[0013] The design variables of the reliability topology optimization model of the initial stress constraint system are updated to obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure;

[0014] Based on the reliability topology optimization model of the stress constraint system of plate and shell structures, the reliability topology optimization of the stress constraint system for plate and shell structures is completed.

[0015] Preferably, the method for calculating the structural stress response of each unit of the plate and shell finite element model is:

[0016] Based on the finite element model of plate and shell structure, calculate the Cauchy stress matrix of plate and shell structure;

[0017] The Cauchy stress matrix of the plate-shell structure is relaxed based on the qp relaxation method to obtain the Cauchy stress;

[0018] Based on the Cauchy stress, the structural stress response of each unit of the plate and shell finite element model is obtained.

[0019] Preferably, the method for obtaining the active unit set is:

[0020] Calculate the structural cohesive stress based on the structural stress response of each unit and the preset allowable stress;

[0021] Based on the structural cohesion stress, obtaining a cohesion stress constraint;

[0022] Based on the reliability index method, the MPP most likely failure point corresponding to the cohesive stress constraint and the unit structure stress response at the MPP most likely failure point are calculated;

[0023] The unit filtering strategy is adopted to select the units whose unit structural stress response at the most likely failure point of MPP meets the preset stress threshold among all units to obtain the active unit set.

[0024] Preferably, the method for calculating the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system is:

[0025] Based on the most likely failure points of the MPP corresponding to the cohesive stress constraints in the active unit set, the correlation coefficients between the cohesive stress constraints are obtained;

[0026] Based on the correlation coefficient and the reliability index of the cohesion stress constraint, obtaining the joint failure probability between the cohesion stress constraints;

[0027] Based on the failure probability corresponding to the cohesive stress constraint and the joint failure probability, the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system are obtained.

[0028] Preferably, the method for obtaining the reliability topology optimization model of the plate-shell structure stress constraint system is:

[0029] Based on the structural stress response of each unit and the structural cohesive stress, calculating the sensitivity of the cohesive stress constraint to the random variable and the design variable;

[0030] Based on the sensitivity, the design variables are updated using the moving asymptote method, and when the design variables converge, a reliability topology optimization model of a stress constraint system of a plate and shell structure is obtained.

[0031] The present invention also provides a stress constraint system reliability topology optimization system for plate and shell structures, and the method described herein is applied, including:

[0032] The structural stress calculation module is used to establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model;

[0033] The unit filtering module is used to obtain the active unit set based on the structural stress response of each unit by adopting the unit filtering strategy, and calculate the MPP most likely failure point and failure probability of the active unit set;

[0034] The failure probability upper and lower bound calculation module is used to calculate the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure based on the MPP most likely failure point and failure probability of the active unit set;

[0035] An initial optimization model building module is used to build a reliability topology optimization model of the initial stress constraint system based on the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system, the random variables and the design variables;

[0036] The design variable updating module is used to update the design variables of the reliability topology optimization model of the initial stress constraint system and obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure;

[0037] The optimization module is used to complete the reliability topology optimization of the stress constraint system for plate and shell structures based on the reliability topology optimization model of the stress constraint system of plate and shell structures.

[0038] Preferably, the structural stress calculation module includes:

[0039] The Cauchy stress matrix calculation unit is used to calculate the Cauchy stress matrix of the plate and shell structure based on the finite element model of the plate and shell structure;

[0040] A relaxation unit is used to relax the Cauchy stress matrix of the plate-shell structure based on a qp relaxation method to obtain the Cauchy stress;

[0041] The structural stress response calculation unit is used to obtain the structural stress response of each unit of the plate and shell finite element model based on the Cauchy stress.

[0042] Preferably, the unit filter module comprises:

[0043] Structural cohesion stress calculation unit, used to calculate the structural cohesion stress based on the structural stress response of each unit and the preset allowable stress;

[0044] A cohesion stress constraint calculation unit, used for obtaining a cohesion stress constraint based on the structural cohesion stress;

[0045] An MPP most probable failure point calculation unit is used to calculate the MPP most probable failure point corresponding to the cohesive stress constraint and the unit structure stress response at the MPP most probable failure point based on a reliability index method;

[0046] The unit filtering unit is used to adopt a unit filtering strategy to select the unit whose unit structural stress response at the most likely failure point of the MPP among all units meets a preset stress threshold, and obtain an active unit set.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows: the stress constraint system reliability topology optimization model of the plate-shell structure of the present invention is established based on the Ditlevsen boundary method, taking into account the uncertainty of loads and material properties. Compared with the traditional deterministic topology optimization results, the model of the present invention introduces the structural system reliability in the optimization process, and takes the structural reliability as a constraint condition, thereby effectively improving the safety performance of the structure. Since the traditional reliability analysis method has low calculation accuracy when dealing with multiple stress constraints, the Ditlevsen boundary method is used to evaluate the reliability of the structural system, which effectively improves the accuracy of the system reliability analysis results. In addition, a unit filtering strategy is proposed, which greatly reduces the number of constraints required to be calculated by the Ditlevsen boundary method, thereby greatly improving the calculation efficiency. Subsequently, the upper bound of the system failure probability obtained by the Ditlevsen boundary method analysis is used as a probability constraint to establish a new topology optimization model, and the moving asymptote method is used to update the design variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0049] Figure 1 This is a flow chart of a reliability topology optimization method for a stress constraint system of a plate-shell structure according to an embodiment of the present invention;

[0050] Figure 2 A schematic diagram of the design domain and boundary conditions for an implementation case of the present invention;

[0051] Figure 3 It is a schematic diagram of the division of the finite element model of the implementation case of the present invention;

[0052] Figure 4 This is a topological diagram of the deterministic optimization results of an implementation case of the present invention;

[0053] Figure 5 Schematic diagram of topological layout of optimization results of functional metric method and Ditlevsen boundary method under different target reliability indicators in the implementation case of the present invention; wherein (a) is the Ditlevsen boundary method (β t =1) Schematic diagram of the optimization result topology; (b) Functional metric method (β t =1) Schematic diagram of the topological optimization result; (c) Ditlevsen boundary method (β t =2) Schematic diagram of the topological optimization result; (d) is the functional measurement method (β t =2) Schematic diagram of the topological optimization result; (e) Ditlevsen boundary method (βt =3) Schematic diagram of the optimization result topology; (f) is the functional measurement method (β t =3) Schematic diagram of topological optimization results. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] Embodiment 1

[0057] A stress-constrained system reliability topology optimization method for plate-shell structures is proposed, taking cylindrical shell structures as the research object. Figure 2 The design domain and boundary conditions are shown in the figure. The outer radius of the cylindrical shell structure is L, the inner radius is 0.6L, the thickness of the shell is 0.2L, and the outer surface of the cylindrical shell is subjected to the load P. The model size L = 1. The cylindrical shell structure problem is simplified to a plane strain problem, as shown in Figure 3 As shown in the figure, the finite element model is divided into 10,000 units. The amplitude of the load, the elastic modulus, and the Poisson's ratio are considered as random variables X = [P, E, υ], which satisfy the normal distribution, and the mean and coefficient of variation are (μ P =10,μ E =7×10 4 ,μ υ =0.25) and (COV P =0.1,COV E =0.1,COV υ =0.1). Set the allowable stress σ lim =150.

[0058] like Figure 1 As shown, the following steps are included:

[0059] S1: Establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model;

[0060] A further implementation method is to calculate the structural stress response of each unit of the plate and shell finite element model by:

[0061] Based on the finite element model of the plate and shell structure, the Cauchy stress matrix of the plate and shell structure is calculated:

[0062]

[0063] Where D represents the elastic matrix of the plate and shell structure, B represents the strain-displacement matrix of the plate and shell structure, and u i Represents the displacement vector of the ith unit.

[0064] In order to prevent the occurrence of stress singularity, the Cauchy stress matrix of the plate and shell structure is relaxed based on the qp relaxation method to obtain the Cauchy stress:

[0065]

[0066] Among them, p s represents the stress penalty function, represents the density design variable of the ith unit.

[0067] Based on the Cauchy stress, the structural von-mises stress response of each unit of the plate and shell finite element model is obtained:

[0068]

[0069] Where V is a constant matrix, expressed as follows:

[0070]

[0071] S2: Based on the structural stress response of each unit, the unit filtering strategy is used to obtain the active unit set, and the MPP most likely failure point and failure probability of the active unit set are calculated;

[0072] A further implementation method is that the method for obtaining the active unit set is:

[0073] Based on the structural stress response of each unit and the preset allowable stress, the structural cohesion stress is calculated; in this embodiment, the structural cohesion stress is calculated using the p-norm cohesion method as follows:

[0074]

[0075] p represents the aggregation function parameter, represents the unit von-Mises stress; NE represents the total number of structural units;

[0076] Based on the structural cohesive stress, the cohesive stress constraint is obtained:

[0077] g pn =σ PN -1≤0,

[0078] Based on the reliability index method, the MPP most likely failure point corresponding to the cohesive stress constraint and the stress response of the unit structure at the MPP most likely failure point are calculated; the calculation process of the MPP most likely failure point is as follows:

[0079] minβ=||U||

[0080] stg pn (U) = 0,

[0081] Among them, β represents the structural reliability index, which is related to the failure probability P f The relationship can be expressed as P f =Φ(-β), where Φ(·) is the cumulative probability function and U is a random variable in the standard normal space. By solving this optimization problem, the most likely failure point corresponding to the cohesive stress can be obtained. And calculate the MPP pn The structural stress response at .

[0082] The unit filtering strategy is adopted to select the units whose unit structure stress response at the most likely failure point of MPP among all units meets the preset stress threshold, and obtain the active unit set A. In this embodiment, the units whose unit structure stress response at the most likely failure point of MPP among all units is in the top 1% are selected as the active unit set A according to the unit filtering strategy, as shown below:

[0083] A={i|σ i ≥σ 1％ ,i=1,2,...,NE}

[0084] Among them, σ 1％ Indicates the threshold corresponding to the top 1% stress of all elements.

[0085] Calculate the MPP most likely failure point and failure probability P of the active unit f :

[0086] Then, the reliability index method is used to analyze the reliability of each active unit, and the corresponding MPP most likely failure point and failure probability P are calculated. f , the calculation process is as follows:

[0087] minβ=||U||

[0088] stg i (U)=0,i∈A

[0089] Among them, β represents the structural reliability index, which is related to the failure probability P f The relationship can be expressed as P f=Φ(-β), where Φ(·) is the cumulative probability function and U is a random variable in the standard normal space. By solving this optimization problem, the most likely failure point corresponding to the cohesive stress in the active unit can be obtained.

[0090] S3: Based on the MPP most likely failure point and failure probability of the active unit set, calculate the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure;

[0091] A further implementation method is to calculate the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system as follows:

[0092] Based on the MPP most likely failure points corresponding to the cohesive stress constraints in the active unit set, the correlation coefficient between the cohesive stress constraints is obtained; based on the correlation coefficient and the reliability index of the cohesive stress constraints, the joint failure probability between the cohesive stress constraints is obtained; based on the failure probability corresponding to the cohesive stress constraints and the joint failure probability, the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure are obtained.

[0093] In this embodiment, the upper bound of the failure probability of the stress constraint system of the plate and shell structure is calculated by the Ditlevsen boundary method. With the lower bound as follows:

[0094]

[0095] Among them, P fi represents the failure probability of the ith performance function (performance function constrained by cohesive stress), P fij represents the joint failure probability of the i-th and j-th functional functions, which can be calculated by the following formula:

[0096]

[0097] in,

[0098]

[0099] Among them, β i and β j Respectively represent the reliability index of the i-th and j-th performance functions, Corr ij The correlation coefficient between the i-th and j-th performance functions can be calculated as follows:

[0100]

[0101] in, and They represent the most likely failure points MPP of the i-th and j-th performance functions respectively.

[0102] S4: Based on the upper and lower bounds of failure probability, random variables and design variables of the stress constraint system of plate and shell structures, a reliability topology optimization model of the initial stress constraint system is constructed;

[0103] Calculate the Ditlevsen upper bound After that, the reliability topology optimization model of the stress-constrained system based on the Ditlevsen boundary method can be constructed as follows:

[0104]

[0105] stK(ρ,X)U(ρ,X)=F(X)

[0106]

[0107] 0<ρ min ≤ρ e ≤1(e=1,2,...,NE),

[0108] Where f(ρ) represents the total volume of the structure; v e represents the volume of unit e; K(ρ,X) represents the total stiffness matrix of the structure; U(ρ,X) represents the structural displacement vector; F(X) represents the external load vector.

[0109] S5: Update the design variables of the reliability topology optimization model of the initial stress constraint system to obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure;

[0110] A further implementation method is to obtain a reliability topology optimization model of a plate-shell structure stress constraint system by:

[0111] Based on the structural stress response of each unit and the structural cohesive stress, the sensitivity of the cohesive stress constraint to the random variables and the design variables is calculated; in this embodiment, the sensitivity of the stress constraint to the random variables and the design variables is calculated. pn (ρ,X) for random variable X j The sensitivity of can be obtained by the chain rule as follows:

[0112]

[0113] in,

[0114]

[0115] To calculate The Lagrangian function is constructed using the adjoint vector method as follows:

[0116]

[0117] Among them, Ii To displace the unit vector u i The selection matrix separated from the structural displacement vector U. Since F-KU = 0, the adjoint vector λ X is arbitrary, so the constructed Lagrangian function L X For a random variable X j The sensitivity can be calculated by the following formula:

[0118]

[0119] when Sometimes, there are

[0120]

[0121] Through the above formula, we can get the cohesive stress constraint g pn (ρ,X) for random variable X j The sensitivity is as follows:

[0122]

[0123] Similarly, the stress constraint g of each unit can be obtained i (ρ,X) for random variable X j The sensitivity is as follows:

[0124]

[0125] Cohesion stress constraint g pn (ρ,X) for the design variables The sensitivity of can be obtained by the chain rule as follows:

[0126]

[0127] in,

[0128]

[0129] To calculate The Lagrangian function is constructed using the adjoint vector method as follows:

[0130]

[0131] Since F-KU = 0, the adjoint vector λ X is arbitrary, so the constructed Lagrangian function L ρ For design variables The sensitivity can be calculated by the following formula:

[0132]

[0133] when Sometimes, there are

[0134]

[0135] Through the above formula, we can get the cohesive stress constraint g pn (ρ,X) for the design variables The sensitivity is as follows:

[0136]

[0137] Based on sensitivity, the design variables are updated using the moving asymptote method. When the design variables converge, the reliability topology optimization model of the stress constraint system of the plate and shell structure is obtained. If the preset convergence requirements are not met, k+1 iterations of S1-S5 steps are performed until the preset convergence requirements are met and the optimization model is output.

[0138] S6: Based on the reliability topology optimization model of the stress constraint system of plate and shell structures, complete the reliability topology optimization of the stress constraint system for plate and shell structures.

[0139] Embodiment 2

[0140] The proposed reliability topology optimization model of stress constraint system of plate and shell structure based on Ditlevsen boundary method is compared with the traditional functional measurement method. Figure 4 The resulting topological layout in deterministic optimization is given. Figure 5 The optimization results of the functional metric method and the Ditlevsen boundary method under different target reliability indicators are given in Table 1. t Represents the target reliability index, β mcs Represents the target reliability index verified by the Monte Carlo sampling method. Figure 5 In (a), Ditlevsen boundary method (β t =1) Schematic diagram of the optimization result topology; (b) Functional metric method (β t =1) Schematic diagram of the topological optimization result; (c) Ditlevsen boundary method (β t =2) Schematic diagram of the topological optimization result; (d) is the functional measurement method (β t =2) Schematic diagram of the topological optimization result; (e) Ditlevsen boundary method (β t =3) Schematic diagram of the optimization result topology; (f) is the functional measurement method (β t =3) Schematic diagram of topological optimization results.

[0141] It can be seen from Table 1 that the macroscopic volume and stress of the deterministic topology optimization and the optimization results under different target reliability indicators meet the constraints. The structural volume ratio of the deterministic optimization result is 26.38%, and the reliability index βmcs is -0.156. t =1, 2, 3, the structural volume ratios of the optimization results obtained by the functional measurement method are 27.60%, 29.25% and 29.38% respectively, while the structural reliability index β mcs They are 0.902, 1.874 and 2.832 respectively. Obviously, the result of the functional measurement method does not reach the specified reliability index and cannot guarantee the structural safety. t =1, 2, 3, the structural volume ratios of the optimization results obtained by the Ditlevsen boundary method are 27.87%, 28.95% and 29.56% respectively, and the structural reliability index β mcs They are 1.080, 2.062 and 3.033 respectively. Compared with the results of the functional metric method, the results obtained by the Ditlevsen boundary method have greatly improved the structural reliability while increasing the volume rate slightly. The results meet the target reliability index. The results of this method can effectively ensure the expected safety of the cylindrical shell structure.

[0142] Table 1

[0143]

[0144] Embodiment 3

[0145] The present invention also provides a stress constraint system reliability topology optimization system for plate and shell structures, and an application method thereof, comprising:

[0146] The structural stress calculation module is used to establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model;

[0147] The unit filtering module is used to obtain the active unit set based on the structural stress response of each unit by adopting the unit filtering strategy, and calculate the MPP most likely failure point and failure probability of the active unit set;

[0148] The failure probability upper and lower bound calculation module is used to calculate the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure based on the MPP most likely failure point and failure probability of the active unit set;

[0149] The initial optimization model building module is used to build a reliability topology optimization model of the initial stress constraint system based on the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system, random variables, and design variables;

[0150] The design variable updating module is used to update the design variables of the reliability topology optimization model of the initial stress constraint system and obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure;

[0151] The optimization module is used to complete the reliability topology optimization of the stress constraint system for plate and shell structures based on the reliability topology optimization model of the stress constraint system of plate and shell structures.

[0152] A further implementation is that the structural stress calculation module includes:

[0153] The Cauchy stress matrix calculation unit is used to calculate the Cauchy stress matrix of the plate and shell structure based on the finite element model of the plate and shell structure;

[0154] The relaxation unit is used to relax the Cauchy stress matrix of the plate and shell structure based on the qp relaxation method to obtain the Cauchy stress;

[0155] The structural stress response calculation unit is used to obtain the structural stress response of each unit of the plate and shell finite element model based on the Cauchy stress.

[0156] In a further embodiment, the unit filter module comprises:

[0157] Structural cohesion stress calculation unit, used to calculate the structural cohesion stress based on the structural stress response of each unit and the preset allowable stress;

[0158] A cohesion stress constraint calculation unit, used to obtain the cohesion stress constraint based on the structural cohesion stress;

[0159] The MPP most probable failure point calculation unit is used to calculate the MPP most probable failure point corresponding to the cohesive stress constraint and the unit structure stress response at the MPP most probable failure point based on the reliability index method;

[0160] The unit filtering unit is used to adopt a unit filtering strategy to select the unit whose unit structural stress response at the most likely failure point of the MPP among all units meets a preset stress threshold, and obtain an active unit set.

[0161] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A stress constraint system reliability topology optimization method for plate and shell structures, characterized in that: The following steps are involved: Establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model; Based on the structural stress response of each unit, the unit filtering strategy is adopted to obtain the active unit set, and the MPP most likely failure point and failure probability of the active unit set are calculated; Based on the most likely failure point and failure probability of the MPP of the active unit set, the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure are calculated; Based on the upper and lower bounds of failure probability of the plate and shell structure stress constraint system, the random variables and the design variables, a reliability topology optimization model of the initial stress constraint system is constructed; The design variables of the reliability topology optimization model of the initial stress constraint system are updated to obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure; Based on the reliability topology optimization model of the stress constraint system of plate and shell structures, the reliability topology optimization of the stress constraint system for plate and shell structures is completed.

2. The reliability topology optimization method for stress constraint system of plate and shell structure according to claim 1 is characterized in that: The method for calculating the structural stress response of each unit of the plate and shell finite element model is: Based on the finite element model of plate and shell structure, calculate the Cauchy stress matrix of plate and shell structure; The Cauchy stress matrix of the plate-shell structure is relaxed based on the qp relaxation method to obtain the Cauchy stress; Based on the Cauchy stress, the structural stress response of each unit of the plate and shell finite element model is obtained.

3. The reliability topology optimization method for stress constraint system of plate and shell structure according to claim 1 is characterized in that: The method to obtain the active unit set is: Calculate the structural cohesive stress based on the structural stress response of each unit and the preset allowable stress; Based on the structural cohesion stress, obtaining a cohesion stress constraint; Based on the reliability index method, the MPP most likely failure point corresponding to the cohesive stress constraint and the unit structure stress response at the MPP most likely failure point are calculated; The unit filtering strategy is adopted to select the units whose unit structural stress response at the most likely failure point of MPP meets the preset stress threshold among all units to obtain the active unit set.

4. The reliability topology optimization method for stress constraint system of plate and shell structure according to claim 3 is characterized in that: The method for calculating the upper and lower bounds of the failure probability of the stress constraint system of plate and shell structures is: Based on the most likely failure points of the MPP corresponding to the cohesive stress constraints in the active unit set, the correlation coefficients between the cohesive stress constraints are obtained; Based on the correlation coefficient and the reliability index of the cohesion stress constraint, obtaining the joint failure probability between the cohesion stress constraints; Based on the failure probability corresponding to the cohesive stress constraint and the joint failure probability, the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system are obtained.

5. The reliability topology optimization method for stress constraint system of plate and shell structure according to claim 3 is characterized in that: The method to obtain the reliability topology optimization model of the stress constraint system of plate and shell structure is: Based on the structural stress response of each unit and the structural cohesive stress, calculating the sensitivity of the cohesive stress constraint to the random variable and the design variable; Based on the sensitivity, the design variables are updated using the moving asymptote method, and when the design variables converge, a reliability topology optimization model of a stress constraint system of a plate and shell structure is obtained.

6. A stress constraint system reliability topology optimization system for plate and shell structures, using the method described in any one of claims 1 to 5, characterized in that: include: The structural stress calculation module is used to establish a finite element model of the plate and shell structure, initialize the random variables and design variables of the plate and shell structure, and calculate the structural stress response of each unit of the plate and shell finite element model; The unit filtering module is used to obtain the active unit set based on the structural stress response of each unit by adopting the unit filtering strategy, and calculate the MPP most likely failure point and failure probability of the active unit set; The failure probability upper and lower bound calculation module is used to calculate the upper and lower bounds of the failure probability of the stress constraint system of the plate and shell structure based on the MPP most likely failure point and failure probability of the active unit set; An initial optimization model building module is used to build a reliability topology optimization model of the initial stress constraint system based on the upper and lower bounds of the failure probability of the plate and shell structure stress constraint system, the random variables and the design variables; The design variable updating module is used to update the design variables of the reliability topology optimization model of the initial stress constraint system and obtain the reliability topology optimization model of the stress constraint system of the plate and shell structure; The optimization module is used to complete the reliability topology optimization of the stress constraint system for plate and shell structures based on the reliability topology optimization model of the stress constraint system of plate and shell structures.

7. The stress constraint system reliability topology optimization system for plate and shell structures according to claim 6 is characterized in that: The structural stress calculation module includes: The Cauchy stress matrix calculation unit is used to calculate the Cauchy stress matrix of the plate and shell structure based on the finite element model of the plate and shell structure; A relaxation unit is used to relax the Cauchy stress matrix of the plate-shell structure based on a qp relaxation method to obtain the Cauchy stress; The structural stress response calculation unit is used to obtain the structural stress response of each unit of the plate and shell finite element model based on the Cauchy stress.

8. The stress constraint system reliability topology optimization system for plate and shell structures according to claim 6 is characterized in that: The unit filter module comprises: Structural cohesion stress calculation unit, used to calculate the structural cohesion stress based on the structural stress response of each unit and the preset allowable stress; A cohesion stress constraint calculation unit, used for obtaining a cohesion stress constraint based on the structural cohesion stress; An MPP most probable failure point calculation unit is used to calculate the MPP most probable failure point corresponding to the cohesive stress constraint and the unit structure stress response at the MPP most probable failure point based on a reliability index method; The unit filtering unit is used to adopt a unit filtering strategy to select the unit whose unit structural stress response at the most likely failure point of the MPP among all units meets a preset stress threshold, and obtain an active unit set.

Images