JP2016119087A - Reliability optimization method of plate and shell structure with reinforcement rib in consideration of pluralistic uncertainty - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a reliability optimization method of plate and shell structure with a reinforcement rib in consideration of pluralistic uncertainty.SOLUTION: The reliability optimization method of plate and shell structure with a reinforcement rib in consideration of pluralistic uncertainty includes: performing reliability optimization of plate and shell structure with a reinforcement rib using an equivalent rigidity model; verifying each elite individual of a candidate solution set by means of finite element analysis, in which a single point perturbation weight method is used, a defect element is taken into consideration, nonlinear post-buckling analysis is performed with respect to plate and shell structure with a reinforcement rib having a defect, and an elite individual satisfying a reliability constraint condition is selected; and performing reliability optimization with respect to the plate and shell structure with a reinforcement rib using a finite element model. Efficiency of reliability optimization of plate and shell structure with a reinforcement rib is significantly increased and a calculation cost is reduced.SELECTED DRAWING: Figure 1

Description

  The present invention relates to the technical field of optimum design, and more particularly, to a method for optimizing the reliability of a plate shell structure with reinforcing ribs considering multidimensional uncertainty.

  Since the 21st century, space powers such as the United States, Russia and the European Union have all offered corresponding deep space exploration plans. Japan's “Summary of National Medium and Long-Term Science and Technology Development Plan (2006-2020)” also clarifies the necessity of future missions such as the construction of a space station and landing on the manned lunar surface. Need to develop a transport rocket, which is extremely important for our economy, society and national security. Due to dramatic improvements in the effective loading capacity and launch efficiency of transport rockets, thinner walls and lighter weight have already become a trend in bearing component design, which is the key to rockets. The state of use is also causing. In the future, the diameter-thickness ratio of the thin-wall members in the transport rocket (dividing the rocket body diameter by the equivalent thickness) will increase significantly, objectively increasing the uncertainty of various initial defects, that is, diversifying the types of defects. (Including geometrical defects, manufacturing and assembly tolerances, load and boundary condition defects, residual stresses, etc.), increased randomness (production site, unclear distribution), and between multiple determinism As the coupling effect increases and the propagation law is not clear, the degree of dispersion of the load bearing performance of the structure becomes serious. Because there are too many dimensions of random variables, analysis and optimization for the load bearing performance of axially compressed thin-walled structures under multi-dimensional uncertainty has already become a challenging challenge facing.

  At present, the numerical prediction of the load bearing capacity of a cylindrical shell structure with reinforcing ribs is mostly based on an equivalent stiffness model or a highly accurate finite element model. Early studies often employ equivalent stiffness models with relatively high computational efficiency due to computational limitations. That is, a cylindrical shell with a waffle-type reinforcing rib having periodicity is made equivalent to an anisotropic or isotropic shell, and then its buckling load is obtained using plate shell theory. Although the equivalent stiffness model has extremely high calculation efficiency, the influence of various nonlinear elements cannot be taken into consideration, and a structural design that is conservatively or dangerously biased is likely to be obtained. For cylindrical shells with reinforced ribs under axial compression, the structure loaded in stages may exhibit linear buckling-nonlinear post-buckling-crush fracture behavior. Material nonlinearity, geometrical nonlinearity, and nonlinear factors caused by various defects can be taken into account, and details of the model such as boundary conditions, loading method, structural opening, and rib shape can be accurately reproduced. However, high-accuracy finite element models often have extremely low computational efficiency, which increases the computational cost of reliability-optimized design of reinforced ribbed shell structures, and facilitates optimization failures. Is caused.

  The conventional reliability optimization method for the existing shell structure with reinforcing ribs relies heavily on transition finite element analysis, and it is necessary to use high-precision finite element analysis several times during the optimization process. Even if the global substitution model optimization technique is adopted, the optimization efficiency is greatly reduced. Although many fields have already been developed in this field, a method for optimizing the reliability of a highly efficient plate shell structure with reinforcing ribs has not yet been shown.

  The present invention mainly solves the technical problem of relatively high calculation cost and relatively low optimization efficiency in the reliability-optimized design of the plate structure with reinforcing ribs of the existing technology, and considers multidimensional uncertainty. This paper presents a method for optimizing the reliability of a plate shell structure with reinforcing ribs, and achieves the purpose of improving the calculation efficiency of the optimum reliability design of the plate shell structure with reinforcing ribs and reducing the calculation cost.

The present invention provides a method for optimizing the reliability of a plate shell structure with reinforcing ribs in consideration of multidimensional uncertainty. The method uses an equivalent stiffness model to optimize the reliability of the reinforced ribbed shell structure 100;
Each elite individual in the candidate solution set is verified by finite element analysis, and a single point perturbation loading method is used. Selecting elite individuals that satisfy a reliability constraint condition, wherein the defect element includes a geometric defect, a stress defect, and a load defect;
Using a finite element model to perform reliability optimization on the reinforced ribbed shell structure,
Step 100 uses the following sub-steps, that is, a global optimization method, to build an equivalent stiffness model of a reinforced ribbed shell structure based on the homogenization theory, and the outer plate thickness, rib thickness, rib height, The design variable is one or a combination of the number of axial ribs, the number of circumferential ribs and the layer angle, and the reliability of the axial compressive strength of the plate shell structure with reinforcing ribs as a constraint, and the weight of the structure and / or Step 101, where the manufacturing cost of the structure is the optimization goal;
Considering uncertain factors, using the equivalent stiffness model that was constructed, reliability optimization was performed on the plate shell structure with reinforced ribs, and several elite individuals with a certain degree of congestion were obtained. Wherein the uncertainties include step 102 including material performance variations, geometric dimension tolerances and layer angle variations,
Step 300 considers the following sub-steps, ie, uncertain elements, while the defective elements are encapsulated using a single point perturbation loading method, of which the defective elements are geometric defects, stress defects, load defects. Including step 301;
Sampling tests are performed within the standard deviation interval of n times the elite individual, and a substitute model of the shell structure with reinforcing ribs is built within the standard deviation interval of n times. The substitute model is the thickness of the outer plate and the rib thickness. One or a combination of the rib height, the number of axial ribs, the number of circumferential ribs, and the layer angle is a design variable, and the reliability of the axial compressive strength of the plate shell structure with reinforcing ribs is a constraint. Step 302 with an optimization goal of structure weight and / or structure manufacturing cost;
Optimize the reliability of the shell structure with reinforcing ribs by optimizing the weight of the structure and / or the manufacturing cost of the structure using the constructed substitute model, and the reliability constraint condition And an optimum design satisfying step 303 is obtained.

  Preferably, the global optimization method includes particle swarm optimization, genetic algorithm, annealing method, ant colony optimization, tabu search, or immune algorithm.

  Preferably, the n times standard deviation interval is a 6 times standard deviation interval.

  Preferably, the plate shell structure with reinforcing ribs includes a plate with flat reinforcing ribs, a cylindrical shell with reinforcing ribs, or a flat shell with reinforcing ribs.

  Preferably, the sampling test includes a Latin hypercube method or an orthogonal array method.

  The reliability optimization method for a plate shell structure with reinforcing ribs taking into account the multi-dimensional uncertainty provided in the present invention is a disadvantage that the efficiency of the conventional reliability optimization method for a plate shell structure with reinforcing ribs is low. Thus, the analysis advantage of each of the equivalent stiffness model and the finite element model is comprehensively utilized, and different analysis models are introduced at different optimization stages. Since the equivalent stiffness model is computationally efficient, the design space can be reduced with high efficiency by using the equivalent stiffness model in the first stage optimization, and several elite individuals with a certain degree of congestion can be obtained. And a candidate solution set is formed. Furthermore, after verifying by finite element analysis and considering defect elements, it is possible to select elite individuals that still satisfy the load bearing reliability constraint, and the equivalent stiffness model of the plate shell with reinforcing ribs considers the effects of defects Compensate for evil that cannot be done. By using the local substitute model of the finite element model structure in the second stage optimization, an optimal design satisfying the reliability constraint can be guaranteed, and the design space can be reduced with high efficiency. Thereby, the efficiency of the reliability optimization of the plate shell structure with the reinforcing rib is greatly improved, and the calculation cost is reduced. The present invention may be one of the main reliability optimization methods for the plate-shell structure with reinforcing ribs in the aerospace field such as the design of a Japanese transportation rocket.

It is an implementation | achievement flowchart of the reliability optimization method of the plate-shell structure with a reinforcement rib which considered the multidimensional uncertainty provided in the Example of this invention. It is a schematic diagram of the board shell structure with a reinforcement rib of each type. It is a schematic diagram of the board shell structure with a reinforcement rib of each type. It is a schematic diagram of the board shell structure with a reinforcement rib of each type. It is a schematic diagram of the board shell structure with a reinforcement rib of each type. It is a schematic diagram of the single point perturbation load in the reliability optimization method of the plate shell structure with a reinforced rib in consideration of the multiple uncertainty provided in the embodiment of the present invention. It is a schematic diagram of a cylindrical shell structure with a reinforcing rib. 2 is a first-stage optimization iteration curve for a cylindrical shell with reinforcing ribs provided in an embodiment of the present invention. FIG. 5 is a second-stage optimization iteration curve for a cylindrical shell with reinforcing ribs provided in an embodiment of the present invention. It is a repeat curve of reliability optimization for a cylindrical shell with reinforcing ribs of existing technology.

  In order to clarify the technical problem to be solved by the present invention, the technical solution to be adopted, and the technical effect to be achieved, the present invention will be described in more detail below in combination with the drawings and examples. It will be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, for the convenience of description, it is necessary to explain that only the parts related to the present invention are shown in the figure, but not all the contents.

FIG. 1 is a flowchart for realizing a reliability optimization method for a plate shell structure with reinforcing ribs considering multidimensional uncertainty provided in an embodiment of the present invention. As shown in FIG. 1, the reliability optimization method for a plate shell structure with reinforcing ribs considering multidimensional uncertainty provided in the embodiment of the present invention is as follows.
It includes the step 100 of optimizing the reliability of the reinforced ribbed shell structure using an equivalent stiffness model, which uses the following sub-steps, ie global optimization methods, with reinforced ribs based on homogenization theory An equivalent stiffness model of the plate shell structure is constructed, and one or a combination of the outer plate thickness, rib thickness, rib height, number of axial ribs, number of circumferential ribs and layer angle is set as a design variable, The step 101 includes the reliability of the axial compressive strength of the plate shell structure with the reinforcing rib as a constraint, and the optimization target is the weight of the structure and / or the manufacturing cost of the structure.

Specifically, as an example of optimization of the method provided in the embodiment of the present invention, it can be expressed as follows.
Design variable: d = [t _s , _tr , h, N _a , N _c ]
Target function: W
Constraint: p _f (P <P ^t ) ≦ p ^t _f
Wherein, t _s is the outer plate thickness, t _r is the rib thickness, h is the rib height, N _a is the number of axial ribs, N _c is the number of circumferential ribs, W is the weight of the structure, P the buckling load or crushing loads structure, the P ^t is the design load, p _f of structural failure probability is p ^t _f is a predetermined breaking probability. Specifically, the failure probability can be obtained by reliability analysis, and reliability analysis is incorporated into the inner layer in every iteration of optimization. The predetermined failure probability can be selected based on the safety requirements in the actual use of the structure, for example, the reliability requirement for aerospace structures is high, the failure probability is generally 0.001, reliability = 1.0-destruction probability, or reliability + destruction probability = 1.0 is selected. In the field of optimizing the reliability of the plate shell structure with reinforcing ribs, the thickness of the outer plate, the rib thickness, the rib height, the number of axial ribs, the number of circumferential ribs, and the layer angle are: This is a main factor that affects the axial compressive strength of the shell structure. Usually, the reliability of the plate shell structure with reinforcing ribs is evaluated by evaluating the axial compressive strength of the plate shell with reinforcing ribs. Therefore, the equivalent stiffness model provided in the present invention uses the reliability of the axial compression strength of the plate shell structure with the reinforcing rib as a reliability constraint condition (for example, the probability that the reliability of the axial compression strength is smaller than a certain value is constant) The optimization target is the weight of the structure and / or the manufacturing cost. The axial compressive strength of the plate shell structure with the reinforcing rib can be expressed by two indexes, a buckling load and a crushing load. The buckling load is obtained by linear buckling analysis, the analysis process cannot take into account various nonlinear elements, does not require repetition to find the solution, the analysis efficiency is high, but the axial compressive strength of the structure It is only an estimate. The crushing load is obtained by nonlinear post-buckling analysis, and various nonlinear elements can be accurately taken into account, but the analysis efficiency is relatively low. However, it accurately represents the axial compressive strength of the structure.

  In addition, the present invention constructs an equivalent stiffness model of a plate shell structure with reinforcing ribs based on a homogenization theory. The homogenization theory starts from the unit cells constituting the macro structure. If the unit cells have a spatial periodicity, a homogeneous material equivalent to the macromechanical characteristics of the original structure can be obtained by structural analysis of the unit cells. Based on the homogenization principle, the present invention makes the rib having spatial periodicity equivalent to the orthotropic / isotropic plate shell, and improves the buckling analysis efficiency of the ribbed plate shell. The equivalent stiffness model obtained based on the homogenization principle is always preferred by the engineering industry due to its intuitive and concise solution process, and the initial design and parameters Commonly used in previous studies.

  Among these, particle swarm optimization is a new global optimization method that has been developed in recent years. This also uses a random solution as a starting point, and repeatedly searches for an optimal solution to evaluate the quality of the solution from the fitness. Such an algorithm has been emphasized in the academic world due to advantages such as easy implementation, high accuracy, and rapid convergence, and has shown its superiority in solving actual problems. The present invention employs this method, and can search a global optimum solution with high efficiency.

  Among these, FIG. 2 a-d is a schematic diagram of the plate shell structure with a reinforcement rib of each type. 2a is a schematic diagram of the structure of a plate shell with reinforcing ribs of upright equilateral triangle, FIG. 2b is a schematic diagram of the structure of a plate shell with reinforcing ribs of a vertical equilateral triangle, and FIG. 2c is a structure of a plate shell with upright orthogonal reinforcing ribs. FIG. 2d is a schematic structural view of a plate shell with reinforcing ribs having an arbitrary angle. See Figures 2a-d. The method of optimizing the reliability of the plate shell structure with reinforcing ribs considering multidimensional uncertainty provided by the present invention is a plate with reinforcing ribs such as a plate with flat reinforcing ribs, a cylindrical shell with reinforcing ribs, and a flat shell with reinforcing ribs. Reliability optimization can be performed on the shell.

  Step 102: Considering uncertain factors, using the constructed equivalent stiffness model, the reliability optimization is performed on the plate structure with the reinforcing rib, and several elite individuals having a certain degree of congestion are obtained, A candidate solution set is formed.

  The constraint condition for optimizing the reliability of the plate shell structure with reinforcing ribs in this step is that the buckling load failure probability is specifically greater than a predetermined value. Of these, the uncertainties include material performance variations, geometric dimension tolerances, and layer angle variations. Specifically, material performance variations are obtained by tensile testing and statistics, geometric dimension tolerances are obtained by calipers or optical measurements and statistics, and layer angle variations are obtained by protractor measurements and statistics. Uncertainty can determine the type of random distribution of uncertainties, for example, normal distribution, lognormal distribution, uniform distribution, Weibull distribution, etc. based on statistical data. Different impacts on constraints and optimization goals.

  The elite individual indicates that the constraint condition is satisfied, and the optimization target is an optimal solution or an individual close to the optimal solution. In addition, the candidate solution set is made up of elite individuals with a constant congestion distance. By providing candidate solution sets, the diversity of elite individuals can be maximized and the effects of defects can be considered. After that, it still satisfies the load bearing reliability constraints. Of these, the degree of congestion refers to the relative distance between variables, and is generally indicated by the Euclidean distance. The greater the Euclidean distance, the smaller the variable congestion.

  Step 200: Validate each elite individual in the candidate solution set by finite element analysis, use a single point perturbation loading method, consider the defect element, and post-linearize the reinforced ribbed shell structure including the defect Including performing buckling analysis and selecting elite individuals that satisfy the reliability constraint condition.

  Among these, the defect element includes a geometric defect, a stress defect, and a load defect. Geometric defects, stress defects and load defects are obtained by measuring with a three-dimensional measuring instrument. In addition, the reliability constraint condition in this step is that the fracture probability of the crushing load is larger than a predetermined value.

  The single point perturbation loading method is a method presented by scholars of the European Union in 2008 and envelops the effect of the reduction of various random defects (which are also uncertainties) on the axial compressive strength of thin-walled structures. By applying a single point perturbation load to the outer shell part in the middle of the shell, it is possible to cause an unstable waveform of buckling and a load bearing capacity (buckling load and crushing load) that are sufficiently similar to the experimental results. The method is considered a reasonable equivalent defect. FIG. 3 is a schematic diagram of a single-point perturbation load in the reliability optimization method for a plate shell structure with reinforcing ribs considering multidimensional uncertainty provided in the embodiment of the present invention. Please refer to FIG. A single point perturbation loading method is adopted to introduce defect elements. In other words, a standard concentrated force is applied to the outer shell in the middle of the shell, and this is used as a perturbation load. Further, the displacement vector of the nodal coordinates obtained by calculation is mapped to a complete structure, and the reinforcing ribs containing defects A plate shell model with a rib is formed, and nonlinear post-buckling analysis is performed on the plate shell model with a reinforcing rib including defects. After verifying by finite element analysis and considering defect elements, it is possible to select elite individuals that still satisfy the load bearing reliability constraint, and the equivalent stiffness model of the reinforced ribbed shell considers the effects of defects Compensate for the evils that cannot be done.

  The above is the first stage optimization process of the present invention. Since the equivalent stiffness model is computationally efficient, the design space can be reduced with high efficiency by using the equivalent stiffness model in the first stage optimization, and several elite individuals with a certain degree of congestion can be obtained. A candidate solution set is formed. After verifying by finite element analysis and considering defect elements, it is possible to select elite individuals that still satisfy the load bearing reliability constraint, and the equivalent stiffness model of the reinforced ribbed shell considers the effects of defects Compensate for the evils that cannot be done.

Step 300: Reliability optimization is performed on a plate shell structure with a reinforcing rib using a finite element model. Includes the following substeps:
Please refer to FIG. Step 301, taking into account the uncertainties, and at the same time, the defective elements are enveloped using a single point perturbation loading method.

  Among these, the defect element includes a geometric defect, a stress defect, and a load defect. Envelope is to enclose a set of relatively large values using one relatively small value (axial compressive strength), and the design tends to be safer.

  Step 302: A sampling test is performed within the standard deviation interval of n times the elite individual, and a substitute model of a plate shell structure with reinforcing ribs within the standard deviation interval of n times is constructed. The substitute model has a plate shell structure with reinforcing ribs, using one or a combination of outer plate thickness, rib thickness, rib height, number of axial ribs, number of circumferential ribs, and layer angle as a design variable. The reliability of the axial compression strength of the structure is set as a constraint, and the weight of the structure and / or the manufacturing cost of the structure is set as an optimization target.

  Currently, there are many types of sampling test design methods, and the sampling test methods provided in the present invention include a Latin hypercube method or an orthogonal array method. The basic principle is to obtain more design space information by distributing sampling points as evenly as possible in the design space. Among these, in the industrial design industry, a standard deviation interval of 6 times is widely adopted as a control standard for product quality, that is, 3 or 4 products are rejected for every 1 million products. The design space at this time has already been reduced from the first large design space to a standard deviation section that is six times the circumference of the elite individual. A standard deviation interval of 6 times can be expressed as follows.

  Step 303, using the constructed substitute model, and optimizing the reliability of the plate shell structure with reinforcing ribs by optimizing the weight of the structure and / or the manufacturing cost of the structure. The optimal design that satisfies the reliability constraint is obtained.

  Among these, the reliability constraint condition is that the fracture probability of the crushing load is larger than a predetermined value.

  Step 300 is the second-stage optimization, and the second-stage optimization performs local optimization using a local substitute model of the finite element model structure to guarantee an optimal design satisfying the reliability constraint. be able to. Furthermore, the efficiency of optimizing the reliability of the plate shell structure with reinforcing ribs is greatly improved, and the calculation cost is reduced.

  The method provided by the present invention can search for the optimum design of the plate shell with the reinforcing rib satisfying the reliability constraint of the load bearing capacity with high efficiency, and can obtain much higher efficiency than the conventional reliability optimization method.

Below, the plan provided in the present embodiment will be described in the form of an example.
Illustratively, FIG. 4 is a schematic view of a cylindrical shell structure with reinforcing ribs. Please refer to FIG. Radius R = 1500 mm upstanding orthogonal reinforcing ribbed cylindrical shell, a length L = 2000 mm, the outer plate thickness t _s = 4.0 mm, rib thickness t _r = 9.0 mm, the rib height h = 15.00mm, shaft Consider the number of directional ribs N _a = 90 and the number of circumferential ribs N _c = 25. The structural material is an aluminum alloy (elastic modulus E = 70 GPa, Poisson's ratio υ = 0.33, yield stress σ _s = 410 MPa, ultimate stress σ _b = 480 MPa, stretch ratio 0.07, density ρ = 2.7E-6 kg / mm ³ ) Adopt. The structural weight of the initial design is 354.6 kg, the buckling load of the structure based on the prediction of the equivalent stiffness model is 12747 kN, the crushing load of the structure based on the prediction of the finite element model is 16853 kN, and the single point perturbation load is When considering that it is 30 kN, the crushing load of the structure is 1,018 kN. The elastic modulus and Poisson's ratio are considered to be normally distributed random variables, and the variation coefficient is 0.03. Outer plate thickness, rib thickness, and rib height are also considered to be normally distributed random variables with a standard deviation of 0.05.

  In the first stage of optimization, the reliability of the cylindrical shell with reinforcing ribs is optimized based on the equivalent stiffness model. It only considers uncertain factors such as material performance and geometric dimensions, the optimization goal is to minimize the structure weight, and the reliability constraint is that the failure probability is greater than 0.001. Use particle swarm optimization to perform global optimization, and further obtain inner layer reliability information. An optimization iteration curve is shown in FIG. Finally, 20 elite individuals having a certain degree of congestion are obtained, and a candidate solution set is formed.

  Each elite individual in the candidate solution set is verified by nonlinear finite element analysis, and an elite individual satisfying the reliability constraint condition is selected in consideration of a defect state in which the single point perturbation load is 30 kN. The weight of the structure is 285.6 kg, the crushing load is 1,018 kN, and the failure probability can be obtained as 0.016 by Monte Carlo simulation. This design is the initial design for the second stage optimization.

  In the second stage optimization, the reliability optimization of the cylindrical shell with the reinforcing rib is performed based on the finite element model. In addition to considering uncertain factors such as material performance and geometric dimensions, a defect state with a single point perturbation load of 30 kN is considered. First, 32 samples are sampled by adopting the orthogonal arrangement method within the standard deviation section of 6 times which is a design variable in the initial design of the second stage optimization, and a local Kriging substitution model is constructed. Subsequently, particle group optimization is adopted to optimize the reliability of the cylindrical shell with reinforcing ribs based on the substitute model. The optimization iteration curve is shown in FIG. Finally, an optimal design that satisfies the specified reliability constraints is obtained. The structure weight of the optimum design is 291.4 kg, the crushing load when considering that the single point perturbation load is 30 kN is 13108 kN, and the failure probability can be obtained as 0.001 by Monte Carlo simulation. Failure probability is a reliability characterization method. For this embodiment, the reliability constraint is that the failure probability does not exceed 0.001, and the optimum design satisfies the constraint. In contrast, the reliability of cylindrical shells with reinforcing ribs is optimized based on existing technology. That is, the direct substitution model optimization method is adopted, 150 samples are sampled in the entire design area based on the optimum Latin hypercube method, and a Kriging substitution model is constructed. Next, particle group optimization is adopted to optimize the reliability of the cylindrical shell with reinforcing ribs based on the substitute model. An optimization iteration curve is shown in FIG. The structural weight of the optimum design is 305.6 kg, the crushing load when considering that the single point perturbation load is 30 kN is 13555 kN, and the failure probability can be obtained as 0.001 by Monte Carlo simulation. From the viewpoint of the number of times of nonlinear post buckling analysis, the technical solution of the present invention needs to be used 56 times, and the existing technology needs to be used 154 times. From the comparison, it can be seen that the technical solution of the present invention can realize more reduction of the structural weight with relatively low calculation cost, and the optimization efficiency is greatly increased over the existing technology.

  The reliability optimization method of the plate shell structure with reinforcing ribs considering the multi-dimensional uncertainty provided in this embodiment is a disadvantage that the efficiency of the conventional reliability optimization method of the plate shell structure with reinforcing ribs is low. On the other hand, the analysis advantages of the equivalent stiffness model and the finite element model are comprehensively used, and different analysis models are introduced at different optimization stages. Since the equivalent stiffness model is computationally efficient, the design space can be reduced with high efficiency by using the equivalent stiffness model in the first stage optimization, and several elite individuals with a certain degree of congestion can be obtained. And a candidate solution set is formed. Furthermore, after verifying by finite element analysis and considering defect elements, it is possible to select elite individuals that still satisfy the load bearing reliability constraint, and the equivalent stiffness model of the plate shell with reinforcing ribs considers the effects of defects Compensate for evil that cannot be done. By using the local substitute model of the finite element model structure in the second stage optimization, an optimal design satisfying the reliability constraint can be guaranteed, and the design space can be reduced with high efficiency. Thereby, the efficiency of the reliability optimization of the plate shell structure with the reinforcing rib is greatly improved, and the calculation cost is reduced. The present invention may be one of the main reliability optimization methods for the plate-shell structure with reinforcing ribs in the aerospace field, such as the design of a Japanese transportation rocket.

  Finally, it should be explained that the above embodiments are merely used for explaining the technical solution of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to each of the above embodiments, the technical solution described in each of the above embodiments is corrected, or some or all of the technical features thereof are corrected. Those skilled in the art should understand that even if equivalent substitutions are made, the essence of the corresponding technical solutions does not depart from the scope of the technical solutions in the embodiments of the present invention.

Claims (5)

A method for optimizing the reliability of a plate shell structure with reinforcing ribs considering multidimensional uncertainty, wherein the method optimizes the reliability of the plate shell structure with reinforcing ribs using an equivalent stiffness model 100. When,
Each elite individual in the candidate solution set is verified by finite element analysis, and a single point perturbation loading method is used. Selecting elite individuals that satisfy a reliability constraint condition, wherein the defect element includes a geometric defect, a stress defect, and a load defect;
Using a finite element model to perform reliability optimization on the reinforced ribbed shell structure,
Step 100 uses the following sub-steps, that is, a global optimization method, to build an equivalent stiffness model of a reinforced ribbed shell structure based on the homogenization theory, and the outer plate thickness, rib thickness, rib height, One or a combination of the number of axial ribs, the number of circumferential ribs, and the layer angle is a design variable, and the reliability of the axial compression strength of the plate shell structure with reinforcing ribs is a constraint, and the weight of the structure and / or Or step 101, where the manufacturing cost of the structure is the optimization goal,
Considering uncertain factors, using the equivalent stiffness model that was constructed, reliability optimization was performed on the plate shell structure with reinforced ribs, and several elite individuals with a certain degree of congestion were obtained. Wherein the uncertainties include material performance variations, geometric dimension tolerances, and layer angle variations, and
Step 300 considers the following sub-steps, ie, uncertain elements, while the defective elements are encapsulated using a single point perturbation loading method, of which the defective elements are geometric defects, stress defects and load defects. Including step 301;
Sampling tests are performed within the standard deviation interval of n times the elite individual, and a substitute model of the shell structure with reinforcing ribs is built within the standard deviation interval of n times. The substitute model is the thickness of the outer plate and the rib thickness. One or a combination of the rib height, the number of axial ribs, the number of circumferential ribs, and the layer angle is a design variable, and the reliability of the axial compressive strength of the plate shell structure with reinforcing ribs is a constraint. Step 302 with an optimization goal of structure weight and / or structure manufacturing cost;
Optimize the reliability of the shell structure with reinforcing ribs by optimizing the weight of the structure and / or the manufacturing cost of the structure using the constructed substitute model, and the reliability constraint condition And a step 303 for obtaining an optimal design satisfying   The multi-dimensional uncertainty of claim 1, wherein the global optimization method comprises particle swarm optimization, genetic algorithm, annealing method, ant colony optimization, tabu search, or immune algorithm. Reliability optimization method for plate shell structure with reinforcing ribs in consideration.   The method for optimizing the reliability of a plate shell structure with reinforcing ribs according to claim 1, wherein the n-th standard deviation section is a six-fold standard deviation section.   The reinforcing rib considering multidimensional uncertainty according to claim 1, wherein the plate shell structure with reinforcing ribs includes a plate with flat reinforcing ribs, a cylindrical shell with reinforcing ribs, or a flat shell with reinforcing ribs. Method for optimizing the reliability of plate shell structures.   The method of optimizing the reliability of a plate shell structure with reinforcing ribs according to claim 1, wherein the sampling test includes a Latin hypercube method or an orthogonal array method.

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