A method for reliability topology and size optimization of stiffened plate structure

Abstract

The application belongs to the technical field of structure optimization, and particularly relates to a stiffened plate structure reliability topology and size joint optimization method, which comprises the following steps: taking a three-dimensional stiffened plate structure as an object, selecting the mean value of each random parameter as the initial value, and performing deterministic topology optimization; performing structure reliability analysis based on an HMV algorithm, and searching for the current most likely failure point; judging whether the target converges or not, regularizing and simplifying the material layout of the topology optimization output structure; selecting the mean value of each random parameter as the initial value of the normalized steel structure of the layout explanation, and performing deterministic size optimization; performing structure reliability analysis based on the HMV algorithm, and searching for the current most likely failure point; judging whether the target converges or not, and obtaining the stiffened plate optimization structure which simultaneously satisfies the structure performance and reliability index. The application realizes the reliability topology and size joint optimization of the material distribution optimization and the production demand satisfaction while ensuring the reliability.

Description

Technical Field

[0001] This invention belongs to the technical field of structural optimization, specifically relating to a method for joint optimization of the reliability topology and dimensions of stiffened plate structures. Background Technology

[0002] To reduce structural weight and save materials, structural optimization methods such as size optimization, shape optimization, and topology optimization have been proposed. Compared with the former two, topology optimization is not constrained by the initial structural layout, can fundamentally optimize the force transmission path, generate new forms of efficient material layout, maximize material performance, and generate greater economic benefits.

[0003] As research continues to deepen, numerous structural topology optimization methods have been proposed and are rapidly developing. Representative topology optimization methods mainly include the Variable Density (SIMP) method based on material interpolation models, the Evolutionary Structures (ESO) method which gradually eliminates inefficient elements to optimize the structural element layout, the level set method which uses the solution of level set equations to perform motion analysis and tracking of the boundary curves or surfaces of the optimization mathematical model, and the ICM method which employs independent and continuous variables and mapping transformations and their inversions.

[0004] In real-world engineering environments, stiffened plate structures are affected by various random factors. Furthermore, construction errors and inherent material uncertainties further increase the uncertainties affecting the structure. Deterministic traditional topology optimization design methods suffer from the following problems: the optimized design structure fails to meet reliability indices; the resulting layout is complex and irregular, containing numerous intermediate density elements; and the designed structure is difficult to manufacture. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for joint optimization of the reliability topology and dimensions of stiffened plate structures, which achieves optimal material distribution and meets production requirements while ensuring reliability.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for joint optimization of the reliability topology and dimensions of a stiffened plate structure includes:

[0008] Step 100: Take the three-dimensional stiffened plate structure as the object, select the mean of each random parameter as its initial value, and perform deterministic topology optimization;

[0009] Step 200: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point;

[0010] Step 300: Determine if the objective has converged;

[0011] Step 400: Optimize the topology output structure, and standardize and simplify its material layout interpretation;

[0012] Step 500: For the standardized steel structure of the layout interpretation, select the mean of each random parameter as its initial value and perform deterministic dimensional optimization;

[0013] Step 600: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point;

[0014] Step 700: Determine whether the objective has converged until a stiffened plate optimized structure that simultaneously satisfies the structural performance and reliability indices is obtained.

[0015] Preferably, in step 300, determining whether the target has converged includes:

[0016] If convergence is achieved, the structure is output; if convergence is not achieved, the current random parameter values ​​are updated based on the MPP point information, topology optimization is performed again, and step 200 is repeated until convergence is achieved.

[0017] Preferably, step 400 further includes: replacing the topological material layout with a standardized steel structure according to the layout interpretation.

[0018] Preferably, step 700 further includes: if the target does not converge, updating the current value of the random parameter according to the MPP point information, performing size optimization again, and repeating step 600 until convergence.

[0019] The beneficial effects of this invention are that the method is based on the HMV reliability algorithm and combined with external optimization software under the SIMP kernel to carry out reliability topology optimization of stiffened plate structure to optimize the structural form and meet its reliability requirements; based on the topology results, the material layout is interpreted, and the SORA method is also used to perform reliability-based size optimization to regulate and simplify the design layout, which is simple, practical and easy to produce while ensuring performance and reliability. Attached Figure Description

[0020] The features, advantages, and technical effects of exemplary embodiments of the present invention will now be described with reference to the accompanying drawings.

[0021] Figure 1 This is a schematic diagram of the optimized method steps of one embodiment of the present invention;

[0022] Figure 2 This is a flowchart of structural reliability analysis based on the HMV algorithm;

[0023] Figure 3 This is a schematic diagram of an optimized method flow for one embodiment of the present invention;

[0024] Figure 4This is an initial optimized geometric domain diagram of the stiffened plate structure in one embodiment of the present invention;

[0025] Figure 5 This is an initial mesh generation model diagram of a stiffened plate structure in one embodiment of the present invention;

[0026] Figure 6 yes Figure 5 Schematic diagram of load and boundary conditions for a stiffened plate structure under load condition 1;

[0027] Figure 7 yes Figure 5 Schematic diagram of load and boundary conditions for a stiffened plate structure under load condition 2;

[0028] Figure 8 yes Figure 5 Schematic diagram of load and boundary conditions for a stiffened plate structure under load condition 3;

[0029] Figure 9 yes Figure 5 Figure showing the deterministic topology optimization results of a stiffened plate structure;

[0030] Figure 10 yes Figure 5 Reliability topology optimization results of the stiffened plate structure;

[0031] Figure 11 yes Figure 10 The standard steel rectangular beam section diagram used in the structural topology layout interpretation;

[0032] Figure 12 yes Figure 10 Structural layout explanation diagram;

[0033] Figure 13 yes Figure 12 The layout explains the reliability and dimensional optimization results of the structure. Detailed Implementation

[0034] If certain terms are used in the specification and claims to refer to specific components, those skilled in the art will understand that hardware manufacturers may use different names to refer to the same component. This specification and claims do not distinguish components based on differences in name, but rather on differences in function. The term "comprising" as used throughout the specification and claims is an open-ended term and should be interpreted as "comprising but not limited to." "Approximately" means that within an acceptable margin of error, those skilled in the art can solve the technical problem and substantially achieve the technical effect within a certain margin of error.

[0035] Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be interpreted as indicating or implying relative importance.

[0036] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0037] The following is in conjunction with the appendix Figures 1-13 The present invention will be described in further detail, but this is not intended to limit the invention.

[0038] A joint optimization method for the reliability topology and dimensions of stiffened plate structures includes:

[0039] Step 100: Take the three-dimensional stiffened plate structure as the object, select the mean of each random parameter as its initial value, and perform deterministic topology optimization;

[0040] Step 200: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point;

[0041] Step 300: Determine if the objective has converged;

[0042] Step 400: Optimize the topology output structure, and standardize and simplify its material layout interpretation;

[0043] Step 500: For the standardized steel structure of the layout interpretation, select the mean of each random parameter as its initial value and perform deterministic dimensional optimization;

[0044] Step 600: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point;

[0045] Step 700: Determine whether the target has converged, and obtain the stiffened plate optimized structure that simultaneously satisfies the structural performance and reliability indicators.

[0046] In the joint optimization method for the reliability topology and dimensions of the stiffened plate structure according to the present invention, step 300, determining whether the objective has converged, includes:

[0047] If convergence is achieved, the structure is output; if convergence is not achieved, the current random parameter values ​​are updated based on the MPP point information, topology optimization is performed again, and step 200 is repeated until convergence is achieved.

[0048] In the joint optimization method of topology and dimensions for the reliability of stiffened plate structure according to the present invention, step 400 further includes: replacing the topology material layout with a standardized steel structure according to the layout interpretation.

[0049] In the joint optimization method of topology and size for the reliability of stiffened plate structure according to the present invention, step 700 further includes: if the target does not converge, then update the current value of the random parameter according to the MPP point information, perform size optimization again, and repeat step 600 until convergence.

[0050] like Figure 1 As shown, in one embodiment of the present invention, the following steps are included:

[0051] Step 100: Taking the three-dimensional stiffened plate structure as the object, the mean value of each random parameter is selected as its initial value. Using OptiStruct optimization software, the SIMP (material interpolation model) variable density topology optimization method is used to perform deterministic topology optimization on the stiffened plate structure.

[0052] The mathematical model for topology optimization can be expressed in the following form:

[0053] Find: ρ = {ρ1, ρ2, ..., ρ n} T ∈Ω

[0054] Minimize: f(ρ)

[0055]

[0056] Where ρ={ρ1,ρ2,...,ρ n} T Let f(ρ) be the relative density of the material element; f(ρ) be the optimization objective of the topology optimization; h(ρ) be the optimization constraint; F be the external load term; K be the global stiffness matrix; U be the displacement term of the structure; ρ min This is the lower limit of the relative density of the material unit.

[0057] Step 200: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point (MPP).

[0058] like Figure 2 As shown, the specific process is as follows:

[0059] 1. First, transform the random variable or random parameter x that does not conform to the standard normal distribution into a standard normal distribution variable (parameter) u. In the first iteration, let k = 1, and use the mean of the random variable or random parameter (i.e., the origin of the coordinate space U of the standard normal random space) as the starting search point:

[0060]

[0061] 2. Calculate the limiting state function G(u) in the transformed standard normal random space U. k ) value and its gradient value

[0062] 3. Calculate the descent gradient n(u) of the limiting state function G. k ):

[0063]

[0064] 4. Before searching for the next possible search point, first determine the concavity / convexity of the limit state function G in order to select an appropriate reliability analysis method. Define the concavity / convexity determination function S. (k+1) :

[0065] S (k+1) =(n k+1 -n k )·(n k -n k-1 )

[0066] When S (k+1) When S ≥ 0, the limit state function G is a convex function; when S (k+1) When < 0, the limit state function G is a concave function. Here, k is the number of iterations when searching for the MPP point.

[0067] 5. Based on the specified reliability index β t The value of is determined by the limit state function being convex, or by using the AMV search method to find the coordinates of the next search point u when k ≤ 2. k+1 :

[0068] u k+1 =β t ·n(u k )

[0069] When the limit state function is concave and k > 2, the CMV search method is used to find the coordinates u of the next search point. k+1 :

[0070]

[0071] 6. Based on the coordinates u of the found search point k+1 Calculate the corresponding limit state function value G(u) k+1 ) and its limit state function value G(u) at the previous search point k The difference |ΔG k |:

[0072]

[0073] When the difference |ΔG k When the result is less than the set convergence tolerance ε, the result is considered convergent, and the iterative search stops. The current search point is the most likely failure point (MPP point). Otherwise, proceed to the next step.

[0074] 7. When the difference |ΔG k When the result is greater than the set convergence tolerance ε, it is considered convergent. Let k = k + 1, and return to step 2 to continue the iterative search.

[0075] Step 300: Determine whether the target has converged. If not, update the current value of the random parameter according to the MPP point information, perform topology optimization again and return to step 200 until convergence.

[0076] Step 400: For the topology-optimized output structure, regularize and simplify its material layout interpretation. Based on the layout interpretation, replace the topology material layout with a standardized steel structure;

[0077] Step 500: For the standardized steel structure of the layout interpretation, select the mean value of each random parameter as its initial value, and use OptiStruct optimization software to perform deterministic dimensional optimization on the stiffened plate interpretation structure.

[0078] The mathematical model for size optimization can be expressed in the following form:

[0079] Find: d = {d1, d2, ..., d} n} T ∈Ω

[0080] Minimize:f(d)

[0081]

[0082] Where d = {d1, d2, ..., d} n} T Let f(d) be the relative density of the material element; f(d) be the optimization objective of the topology optimization; h(d) be the optimization constraints; F be the external load term; K be the global stiffness matrix; U be the displacement term of the structure; d min d max These represent the lower and upper limits of the optimization range for steel cross-sectional dimensions, respectively.

[0083] Step 600, also based on the HMV algorithm, performs structural reliability analysis to search for the most probable point of failure (MPP), such as... Figure 2 As shown;

[0084] Step 700: Determine whether the target has converged. If not, update the current value of the random parameter based on the MPP point information, perform size optimization again, and return to step 600 until convergence is achieved, resulting in a stiffened plate optimized design structure that simultaneously meets structural performance and reliability indicators and is easy to produce in practice.

[0085] This implementation method applies the SORA reliability optimization method, based on the HMV reliability algorithm and combined with external optimization software under the SIMP kernel, to carry out reliability topology optimization of stiffened plate structures, thereby optimizing the structural form and meeting its reliability requirements. Based on the topology results, the material layout is interpreted, and the SORA method is also used to perform reliability-based dimensional optimization to regulate and simplify the design layout. This method is simple, practical, and easy to implement in actual production while ensuring performance and reliability.

[0086] like Figure 3 As shown, the optimization process is as follows:

[0087] 1. A topology optimization geometric domain for the stiffened plate structure was established using HyperMesh software. To fully utilize the structural optimization characteristics of the topology optimization method, a cuboid geometric domain was used to replace the original stiffened plate structure as the initial optimization geometric domain, such as... Figure 4 As shown;

[0088] 2. Create components named design and face. Move the cuboid geometry that serves as the design domain for the stiffener to the component named design. Move the bottom surface of the cuboid that serves as the non-design domain panel of the stiffener to the component named face.

[0089] 3. Define the material's elastic modulus as a random parameter, E ~ N (2.1 × 10⁻⁶). 5 4.41×10 8 Using the mean of these values ​​as the initial value, create a material named "steel" with the property E = 2.1 × 10⁻⁶. 5 MPa, ν=0.3, card image is MAT1;

[0090] 4. Create attributes named design and face and assign them to the corresponding components. The design attribute uses a 3D solid element and the face attribute uses a 2D shell element. Both are made of steel, which was created in step (3).

[0091] 5. Mesh generation: For the stiffening rib design domain, three-dimensional hexahedral elements are used for mesh generation, with a mesh size of 10mm × 10mm × 10mm; for the non-design domain of the stiffened plate panel, two-dimensional quadrilateral shell elements are used for mesh generation, with a mesh size of 10mm × 10mm. Figure 5 As shown;

[0092] 6. The out-of-plane uniform pressure p, the linearly distributed load q, and the concentrated force load F are random parameters, p ~ N (0.015, 1×10⁻⁶). -4 ), q~N(2500,62500), F~N(20000,4×10 6Select the mean values ​​as initial values, create load sets named spc1 and p for case 1, select load set spc1 and apply simply supported constraints around the perimeter, select load set p and apply a downward vertical load of 0.015 MPa at the structural panel, as follows. Figure 6 As shown; create load sets named spc2 and q for load case 2, select the spc2 load set and constrain the displacement in the Z direction at both ends, select the q load set and apply a uniformly distributed line load of magnitude 2500 N / cm in opposite directions at both ends of the structure, as shown. Figure 7 As shown; create load sets named spc3 and F for case 3, select load set spc3 and apply simply supported constraints around the perimeter, select load set F and apply concentrated upward force loads of magnitude 20000N at the midpoint and 1 / 4 midpoint of the structure, as shown. Figure 8 As shown;

[0093] 7. Create three working condition analysis steps named step1, step2, and step3, and select the load sets spc1 and p, spc2 and q, and spc3 and F respectively;

[0094] 8. Create a design variable. Create a design variable named topology and select the attribute named design. Set the type to PSOLID, the minimum member size to 30mm, the maximum member size to 60mm, and apply draft constraints in the Z direction and a maximum stress constraint of 235MPa.

[0095] 9. Create response functions. Create a response named "volume" and select both "volume" and "total"; create a response named "displacement" and select both "static displacement" and "allnodes" and "total disp";

[0096] 10. Create constraint functions. Create a constraint named disp_1 and select the response named displacement, set the upper limit to 15mm, and select the load step named step1 for loadstep; create a constraint named disp_2 and select the response named displacement, set the upper limit to 6mm, and select the load step named step2 for loadstep; create a constraint named disp_3 and select the response named displacement, set the upper limit to 6mm, and select the load step named step3 for loadstep;

[0097] 11. Create the objective function. Minimize the response, which is renamed to volume;

[0098] 12. Use OptiStruct optimization software to perform deterministic topology optimization of the structure. The results are as follows: Figure 9 As shown;

[0099] 13. Based on the HMV algorithm, the reliability index of the structure is set to β = 3, and the function G(X) of the structure is shown below:

[0100]

[0101] Among them, C k It is the structural compliance value calculated in the k-th iteration of the current structural reliability calculation; C DTO It is the compliance value obtained from the current deterministic topology optimization.

[0102] The value of the function represents the state of the structure:

[0103]

[0104] Perform reliability analysis on the topology optimization results and search for the MPP point of the current optimization results;

[0105] 14. Determine whether the volume change of the optimization result is less than the convergence tolerance. If convergence is achieved, stop the calculation to obtain the reliability topology optimization result. If convergence is not achieved, update the random parameter values ​​in the structural deterministic topology optimization model with MPP point information and execute steps (12)-(14).

[0106] 15. Based on the reliability topology optimization results, such as Figure 10 As shown, its material layout is explained in a standardized and simplified manner. According to the layout explanation, a standardized steel structure (with...) is used. Figure 11 Taking the rectangular steel shown as an example, replacing the topological material layout, we obtain... Figure 12 The structure shown;

[0107] 16. Create size optimization design variables to explain the height and width of each rectangular steel section in the structure as design variables, and set their optimization upper limit based on reliability topology results and actual production conditions;

[0108] 17. Similarly, perform steps (2)-(11) to carry out pre-processing for size optimization;

[0109] 18. Use OptiStruct optimization software to perform deterministic dimensional optimization of the structure;

[0110] 19. Based on the HMV algorithm, perform reliability analysis on the size optimization results and search for the MPP point of the current optimization result;

[0111] 20. Determine whether the volume change of the optimization result is less than the convergence tolerance. If it is not less, update the random parameter values ​​in the structural deterministic size optimization model with MPP point information and execute steps (18)-(20); if it is less, stop the calculation and obtain the reliability size optimization result, such as Figure 13 As shown;

[0112] In this embodiment, when considering uncertainties, the results obtained using traditional deterministic topology optimization methods are as follows: Figure 9 As shown, the reliability probability of the structure is only 50%, making it highly susceptible to structural failure and unable to meet the required reliability. However, after adopting the stiffened plate reliability topology and size joint optimization design method of the present invention, the resulting structure is as follows: Figure 13 The Monte Carlo reliability test results are shown in Table 1 below:

[0113] project Operating Condition 1 Operating Condition 2 Operating Condition 3 Reliability index β 3.0045 4.2649 3.8082 Reliability probability 99.867％ 99.999％ 99.993％

[0114] Therefore, it can be seen that the layout of the design structure accurately meets the reliability requirement of the design reliability index β=3. Even when affected by uncertain factors, it can still meet the optimization constraints under the three working conditions, which greatly enhances the structure's ability to resist uncertain events.

[0115] Meanwhile, compared to the structure obtained by a single reliability topology optimization method, such as Figure 10 As shown, the structure obtained by using the reliability topology and size joint optimization method of the present invention is as follows: Figure 13 As shown, it can retain the excellent layout of topology optimization to a large extent, and also make the structural form regular and simple, which can facilitate actual engineering construction and mass production while ensuring structural performance and reliability.

[0116] Compared to traditional deterministic topology optimization of stiffened plate structures, this invention provides a joint optimization design method for the reliability topology and dimensions of stiffened plate structures. It applies the SORA reliability optimization method, based on the HMV reliability algorithm and combined with external optimization software under the SIMP kernel, to perform reliability topology optimization of the stiffened plate structure, optimizing the structural layout while meeting reliability requirements. Then, based on the topology results, the material layout is interpreted, and the SORA method is used again for reliability-based dimensional optimization, streamlining and simplifying the design layout, ensuring structural performance while facilitating engineering manufacturing. This method achieves lightweight and economical stiffened plates that are engineerable and easy to manufacture, while ensuring structural safety and reliability. It is easy to implement and highly adaptable.

[0117] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments described above, and any obvious improvements, substitutions, or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention. Furthermore, although some specific terms are used in this specification, these terms are only for convenience of explanation and do not constitute any limitation on the present invention.

Claims

1. A method for joint optimization of the reliability topology and dimensions of a stiffened plate structure, characterized in that, include: Step 100: Take the three-dimensional stiffened plate structure as the object, select the mean of each random parameter as its initial value, and perform deterministic topology optimization; Step 200: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point, i.e., the MPP point; Step 300: Determine if the objective has converged; Step 400: Optimize the topology output structure, and standardize and simplify its material layout interpretation; Step 500: For the standardized steel structure of the layout interpretation, select the mean of each random parameter as its initial value and perform deterministic dimensional optimization; Step 600: Perform structural reliability analysis based on the HMV algorithm to search for the most likely failure point; Step 700: Determine whether the objective has converged until a stiffened plate optimized structure that simultaneously satisfies the structural performance and reliability indices is obtained; In step 300, determining whether the target has converged includes: If convergence is achieved, the structure is output; if convergence is not achieved, the current random parameter values ​​are updated based on the MPP point information, topology optimization is performed again, and step 200 is repeated until convergence is achieved. Step 400 further includes: replacing the topological material layout with a standardized steel structure according to the layout interpretation.

2. The method for joint optimization of reliability topology and dimensions of a stiffened plate structure as described in claim 1, characterized in that, Step 700 further includes: if the target does not converge, update the current value of the random parameter according to the MPP point information, perform size optimization again, and repeat step 600 until convergence.

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