A shape and size combination interpretation and optimization method for stiffened plate topology layout

Abstract

The present invention discloses a shape and size combination interpretation and optimization method for the topological layout of a stiffened plate, which belongs to the technical field of stiffened plate optimization design. By constructing multi-directional potential stiffeners and applying the Morris screening method, the optimal arrangement direction of the stiffeners is screened out within a large-scale unit aggregation area of ​​the stiffened plate topological structure; in combination with external optimization software, the shape and size combination optimization is performed on the stiffener arrangement position, length and cross-sectional size of the interpreted structure, so that the detailed design of the stiffened plate after topological optimization can more effectively interpret its topological concept layout, and further optimize the shape and size of its interpreted structure, significantly reducing the structural volume, and greatly reducing the operation difficulty of technical personnel. It is easy to implement, has strong adaptability and fast calculation, and is both robust and efficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimized design of stiffened panels, and in particular relates to a shape and size combination interpretation and optimization method that can more effectively explain the conceptual layout of a stiffened panel and improve subsequent optimization effects in a detailed design after topological optimization. Background Art

[0002] To reduce structural manufacturing materials and improve economic efficiency, structural optimization methods such as size optimization, shape optimization, and topology optimization have been proposed. Compared to the first two, topology optimization is often used in the conceptual design stage of a structure because it is not restricted by the initial structural layout and can generate efficient new material layouts. Size optimization and shape optimization methods, on the other hand, are more commonly used in the detailed design of a structure.

[0003] With the continuous deepening of research, the most mature variable density (SIMP) topology optimization method, combined with commercial optimization software, has gradually gained widespread application in structural design. However, the material distribution of topological structures is irregular and uneven, and the results obtained by the variable density method contain a large number of medium- and low-density units, which makes it difficult to process and produce structures such as stiffened panels. Therefore, scholars and designers often place stiffening ribs at the midline of the high-density material contour in the topological structure and perform dimensional optimization design to interpret and optimize the topological layout of the stiffened panel to meet performance and production requirements.

[0004] However, the traditional topological layout interpretation and optimization method, which is based solely on constructing reinforcement ribs along the midline of the contour of medium- and high-density materials and performing size optimization, has the following problems:

[0005] (1) It is difficult to determine the direction of reinforcement arrangement in a large area where units are concentrated;

[0006] (2) The center line of the contour of medium and high density materials is not the optimal location for rib arrangement;

[0007] (3) The length of the reinforcement ribs is not optimal. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a shape and size combination interpretation and optimization method for the topological layout of the stiffened plate, which can better interpret the topological result reinforcement layout and optimize the reinforcement arrangement position and length in the layout interpretation and optimization design after the topological optimization of the stiffened plate.

[0009] To achieve the above-mentioned purpose, the present invention adopts a technical solution: a shape and size combination interpretation and optimization method for the topological layout of a stiffened plate, comprising the following steps:

[0010] Step 100, taking the topology-optimized stiffened plate as the object, removing low-density units and retaining the topological structure of medium- and high-density units;

[0011] Step 200: Multi-directional potential reinforcements are set in the topological structural unit cluster area (the cluster area is a large-scale cluster area, that is, the units are clustered in a large area and cannot form a relatively dispersed strip distribution). Actual reinforcements are constructed in the remaining locations based on the center line of the material contour.

[0012] Step 300 , performing local sensitivity analysis on potential reinforcements in different directions in each unit cluster area;

[0013] Step 400 , based on the sensitivity analysis results, a potential reinforcement direction with the highest sensitivity value in each unit cluster area is selected, and actual reinforcement is constructed according to the direction;

[0014] Step 500: Divide the actual reinforcement into deformation domains and apply control handles to the reinforcement so that the reinforcement shape can change with the movement of the control handles, and then set a reasonable deformation range for the reinforcement position and length;

[0015] Step 600, optimizing the arrangement position and length of the reinforcement ribs;

[0016] Step 700 , optimizing the cross-section of the shape-optimized stiffener to obtain a stiffened plate optimized design structure that reasonably explains the topological layout and further optimizes the position, length, and cross-sectional size of the stiffener.

[0017] Furthermore, in step 100, the three-dimensional stiffened plate is topologically optimized using a variable density (SIMP) method.

[0018] Furthermore, in step 300, the local sensitivity analysis is based on the Morris screening method.

[0019] Furthermore, in step 500, the actual reinforcement of the structure is divided into deformation domains and control handles are applied using Hypermesh commercial software.

[0020] Furthermore, in step 600, the OptiStruct optimization software is used to perform shape optimization on the arrangement position and length of the reinforcement ribs.

[0021] Furthermore, in step 700, OptiStruct is called to perform size optimization on the cross section of the reinforcement rib after shape optimization.

[0022] By adopting the above-mentioned technical solution, the present invention constructs multi-directional potential reinforcements and applies the Morris screening method to screen the optimal reinforcement layout direction within a large-scale unit cluster area of ​​the stiffened plate topology structure. In conjunction with external optimization software, the shape and size combination of the reinforcement layout position, length, and cross-sectional dimensions of the interpreted structure is optimized. This allows the detailed design of the stiffened plate after topological optimization to more effectively interpret its topological conceptual layout and further optimize the shape and size of the interpreted structure, significantly reducing the structural volume. Furthermore, this method, combined with external optimization software, greatly reduces the operational difficulty for technicians, making it easy to implement, highly adaptable, and computationally fast, combining robustness with efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will be described in detail below with reference to the accompanying drawings and in combination with examples, and the advantages and implementation modes of the present invention will become more apparent. The contents shown in the accompanying drawings are only used to illustrate the present invention and do not constitute any limitation to the present invention. In the accompanying drawings:

[0024] Figure 1 It is a schematic diagram of the steps of the present invention;

[0025] Figure 2 is a schematic diagram of a flow chart of an embodiment of the present invention;

[0026] Figure 3 is a topological structure diagram of medium and high density units of the topological optimization result of the stiffened plate in an embodiment of the present invention;

[0027] Figure 4 yes Figure 3 A preliminary explanation of the topological structure of the stiffened plate in Figure 2;

[0028] Figure 5 yes Figure 4 Meshing model for preliminary interpretation of structure in topology;

[0029] Figure 6 yes Figure 5 The schematic diagram of the load and boundary conditions of the structure under working condition 1 is preliminarily explained in the figure;

[0030] Figure 7 yes Figure 5 The schematic diagram of the load and boundary conditions of the structure under working condition 2 is preliminarily explained in the figure;

[0031] Figure 8 yes Figure 5 The schematic diagram of the load and boundary conditions of the structure under working condition 3 is preliminarily explained in the figure;

[0032] Figure 9 yes Figure 5 The schematic diagram of load and boundary conditions of the structure under working condition 4 is preliminarily explained in the figure;

[0033] Figure 10 yes Figure 5 Statistical chart of sensitivity indices of 44 potential reinforcements in the preliminary interpretation of the structure;

[0034] Figure 11 Yes Figure 5 The preliminary interpretation structure is analyzed and the topological layout of the stiffened plate is interpreted after screening;

[0035] Figure 12 yes Figure 11 The reinforcement deformation domain and its control handle model of the structure with medium topological interpretation;

[0036] Figure 13 yes Figure 11 Optimization results of the rib shape of the structure with medium topological interpretation;

[0037] Figure 14 yes Figure 13 Dimensional optimization results of the stiffened plate shape optimization structure;

[0038] Figure 15 yes Figure 3 Conventional interpretation and optimization results of topological layout structure of reinforced plates. DETAILED DESCRIPTION

[0039] The specific implementation process of this solution is described in detail below through specific embodiments and drawings.

[0040] like Figure 1 As shown, a shape and size combination interpretation and optimization method for the topological layout of a stiffened plate includes the following steps:

[0041] In step 100, the three-dimensional stiffened plate structure after topology optimization using the variable density (SIMP) method is selected to remove low-density units in the topological structure and retain medium- and high-density units.

[0042] Step 200: In a large-scale clustering area of ​​topological structure units (units are clustered in a large area, such as Figure 4 The *-shaped distribution inside cannot form a similar Figure 4 Multi-directional potential reinforcement is set in the relatively scattered strip distribution, and the remaining positions are based on the actual reinforcement of the material contour centerline.

[0043] Step 300: Perform local sensitivity analysis on potential reinforcements in different directions within each unit cluster area.

[0044] Based on the Morris screening method, a potential directional reinforcement is selected in a cluster area each time, and its cross-sectional height value Δx is changed. i Keeping other parameters unchanged, analyze the effect of the change of the potential stiffener section height in this direction on the objective function y=f(x1,x2...xn )

[0045]

[0046] Where: y is the model objective function value before the parameter change; Δx i is the change in the cross-sectional height of the reinforcement in the i-th potential direction (i=1,2,...,n); y i is the model objective function value after the height of the stiffener section in the i-th potential direction is changed; s i is the sensitivity index corresponding to the reinforcement in the i-th potential direction.

[0047] Step 400: Select the sensitivity value s in each unit cluster area based on the sensitivity analysis results. i The highest potential reinforcement direction is determined and the actual reinforcement is constructed according to its direction.

[0048] In step 500, the Hypermesh commercial software is used to automatically divide the deformation domain of the stiffened plate interpretation structure obtained in step 400 and apply control handles so that the shape of the stiffener can change with the movement of the control handles, and then set a reasonable deformation range for the stiffener arrangement position and length.

[0049] Step 600 , using OptiStruct optimization software to optimize the layout and length of the reinforcement ribs;

[0050] The mathematical model of shape optimization can be expressed as follows:

[0051] Solution: α={α1,α2,...,α m}

[0052] Minimize: f(α)

[0053] Constraints:

[0054] Where: α={α1,α2,...,α m} is the deformation scaling factor of the rib position and length; f(α) is the optimization target of shape optimization; h(α) is the optimization constraint; F is the external load term; K is the overall stiffness matrix; U is the displacement term of the structure; S is the final shape vector of the structure; S 0 is the initial shape vector; ΔS i is the local deformed shape vector (i=1,2,...,m).

[0055] Step 700, calling OptiStruct to optimize the size of the rib cross section after shape optimization;

[0056] The mathematical model of size optimization is expressed as follows:

[0057] Solution: d={d1,d2,...,d z}

[0058] Minimize: f(d)

[0059] Constraints:

[0060] Where: d={d1,d2,...,d z} is the relative density of the material unit; f(d) is the optimization target of size optimization; h(d) is the optimization constraint; F is the external load term; K is the overall stiffness matrix; U is the displacement term of the structure; d min d max are the lower and upper limits of the optimization range of the rib cross-section size, respectively.

[0061] Thus, an optimized design structure of the stiffened plate is obtained, which has a reasonable explanation of the topological layout and further optimizes the position, length and cross-sectional size of the stiffeners.

[0062] This method constructs multi-directional potential reinforcements and applies the Morris screening method to identify the optimal reinforcement layout within a large cluster of units within the stiffened plate topology. In conjunction with external optimization software, the shape and size of the reinforcement layout, length, and cross-sectional dimensions of the interpreted structure are combined to optimize the shape and size. This allows the detailed design of the stiffened plate topology to more effectively interpret its conceptual topological layout and further optimize the shape and size of the interpreted structure, significantly reducing the structural volume. This method, combined with external optimization software, significantly reduces the operational complexity for technicians, making it easy to implement, highly adaptable, and computationally fast, combining robustness with efficiency.

[0063] Example:

[0064] like Figure 2 As shown in Figure 1, a shape and size combination interpretation and optimization method for the topological layout of stiffened panels is implemented as follows:

[0065] (1) If Figure 3 As shown in the figure, for the three-dimensional stiffened plate after topology optimization using the variable density (SIMP) method, the low-density elements in the topology structure are screened out and the medium and high-density elements are retained;

[0066] (2) If Figure 4 As shown, the medium and high density unit topology structure obtained in step (1) is used to perform a preliminary interpretation of the rib baseline position, and multi-directional potential rib baselines are set in 11 areas where the units are widely clustered. The actual rib baselines are constructed based on the material contour midline in the remaining positions.

[0067] (3) Create components named beam and face using Hypermesh, move the actual reinforcement baseline into the component named beam, move the lower surface of the structural rectangle that will serve as the stiffened panel into the component named face, and then create and move 44 potential reinforcement baselines in different directions into corresponding components numbered 1 to 44.

[0068] (4) Create a material named steel with the following material properties: , , cardimage (card information) is MAT1 (material 1);

[0069] (5) Create 44 rectangular beam sections named 1 to 44 and one rectangular beam section named beam, with the width and height dimensions of the sections being ;

[0070] (6) Create attributes named beam and face and assign them to the corresponding components. The beam attribute uses a one-dimensional beam element and its corresponding rectangular beam section. The face attribute uses a two-dimensional shell element with a shell thickness of ; Then create 44 attributes named 1 to 44. All 44 attributes use one-dimensional beam elements and their corresponding rectangular beam sections. The materials of the above attributes are all steel created in step (4) and assigned to the corresponding components.

[0071] (7) If Figure 5 As shown in the figure, the mesh division uses one-dimensional beam elements for both actual reinforcement and potential reinforcement, and the mesh size is ; The stiffened panel area is divided by two-dimensional quadrilateral shell elements, and the mesh size is ;

[0072] (8) The working condition setting is the same as that during topology optimization, with uniform pressure outside the surface. , uniformly distributed load , single concentrated force load , torsional torque ,

[0073] like Figure 6 As shown, create a file named spc1 (constraint 1), Select the spc1 load set and apply the four-sided simply supported constraints. The load set is applied to the structural panel with a magnitude of Loads directed vertically upward;

[0074] like Figure 7 As shown, create a file named spc2 (constraint 2), Select the spc2 load set and set the Z-direction displacement constraints at both ends. The load set is applied at both ends of the structure with a magnitude of Uniformly distributed loads on lines with opposite directions;

[0075] like Figure 8 As shown, create a file named spc3 (constraint 3), Select the spc3 load set and apply the four-sided simply supported constraints. The load set is applied at the midpoint and 1 / 4 midpoint of the structure. Concentrated load in upward direction;

[0076] like Figure 9 As shown, create a file named spc4 (constraint 4), Select the spc4 load set and set the Y-direction displacement constraints at both ends. The load sets exert opposite torsional moments on the structure. ;

[0077] (9) Create four working condition analysis steps named step1 (analysis step 1), step2 (analysis step 2), step3 (analysis step 3), and step4 (analysis step 4), and select spc1 and 、spc2 and 、spc3 and 、spc4 and load sets;

[0078] (10) Based on the Morris screening method, the initial objective function y = 0 is set, and the objective function y after the height of the potential direction reinforcement section changes i The expression is as follows:

[0079]

[0080] Where: is the compliance value of the initial structure under working condition 1; is the compliance value of the initial structure under working condition 2; is the compliance value of the initial structure under working condition 3; is the compliance value of the initial structure under working condition 4; is the compliance value of the structure under working condition 1 after the height of the stiffener section in the i-th potential direction is changed (i = 1, 2, ..., 44); is the compliance value of the structure under working condition 2 after the height of the stiffener section in the i-th potential direction is changed; is the compliance value of the structure under working condition 3 after the height of the stiffener section in the i-th potential direction is changed; is the compliance value of the structure under working condition 4 after the height of the stiffener section in the i-th potential direction is changed;

[0081] like Figure 10 As shown, the Morris screening method is used to calculate the sensitivity index s of 44 reinforcement bars. i ;

[0082] (11) Based on the sensitivity analysis results, the potential reinforcement direction with the highest sensitivity value in each of the 11 unit cluster areas was selected, and 11 actual reinforcements were constructed according to their directions, as shown in the following figure. Figure 11 The topological layout of the stiffened panels shown explains the structure;

[0083] (12) Figure 12 As shown, the Hypermesh commercial software is used to automatically divide the deformation domain of the stiffened plate interpretation structure obtained in step (11) and apply a control handle so that the shape of the stiffener can change with the movement of the control handle, and then set the reasonable deformation range of the stiffener arrangement position and length;

[0084] (13) Using the working conditions in step (8), create an objective function to minimize the response of the sum of the compliance under each working condition;

[0085] (14) Figure 13 As shown in the figure, the OptiStruct optimization software is used to optimize the layout and length of the reinforcement ribs, and the results shown in the figure are obtained;

[0086] (15) Create size optimization design variables, using the height and width of each rib rectangular cross section in the shape optimization result of step (14) as design variables, and set the size optimization upper limit to 50 mm;

[0087] (16) Using the operating conditions in step (8), create a response function,

[0088] Create a response named volume and select volume and total. Create a response named displacement and select static displacement, all nodes and total disp.

[0089] (17) Create a constraint function,

[0090] Create a constraint named disp_constants (displacement constraint) and select the response named displacement, set the upper limit to 6mm, and select all load steps in loadstep (load step);

[0091] (18) Create the objective function,

[0092] Minimize the response aliased as volume;

[0093] (19) Figure 14 As shown in the figure, OptiStruct is called to optimize the size of the rib section after shape optimization to obtain the structure shown in the figure.

[0094] like Figure 3 The topological layout of the three-dimensional stiffened plate shown in the figure is arranged in the middle line of the high-density material contour and optimized by using the traditional topological layout interpretation and optimization method. Figure 15 The structure shown has a volume of 3.981×10 7 mm 3 After adopting the shape and size combination interpretation and optimization method proposed in this invention, the result is Figure 14 The volume of the structure is only 3.503×10 7 mm 3 Compared with the traditional method, the volume is reduced by 12.0%, which can greatly reduce the structural volume while ensuring structural performance.

[0095] Compared with the traditional stiffened plate topological layout interpretation and optimization method that is completely based on the midline construction of stiffeners of medium and high density materials and performs size optimization, the shape and size combination interpretation and optimization method for the stiffened plate topological layout provided by the present invention constructs multi-directional potential stiffeners within a large-scale unit aggregation area of ​​the stiffened plate topological structure and applies the Morris screening method to screen out the optimal arrangement direction of the stiffeners.

[0096] In addition, in conjunction with external optimization software, the shape and size of the interpreted structure's reinforcement layout, length, and cross-sectional dimensions were optimized. This allowed the detailed design of the reinforced plate after topological optimization to more effectively interpret its topological conceptual layout. The rib location, length, and size of the interpreted structure were further optimized, significantly reducing the structural volume and fully enhancing the interpretation and optimization of the topological structure. This method, combined with external optimization software, greatly reduced the operational difficulty for technicians, making it easy to implement, highly adaptable, and computationally fast, achieving both robustness and efficiency.

[0097] The embodiments of the present invention are described in detail above, but the contents described are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of this patent.

Claims

1. A shape and size combination interpretation and optimization method for the topological layout of stiffened panels, characterized by: The steps include: Step 100, taking the topology-optimized stiffened plate as the object, removing low-density units and retaining the topological structure of medium- and high-density units; Step 200 , setting multi-directional potential reinforcement ribs in the topological structural unit cluster area, and constructing actual reinforcement ribs in the remaining locations based on the material contour midline; Step 300: Perform local sensitivity analysis on the potential reinforcements in different directions in each unit cluster area. The local sensitivity analysis is based on the Morris screening method. Each time, a potential reinforcement in a cluster area is selected and its cross-sectional height value is changed. , keeping other parameters unchanged, analyze the effect of the change of the potential stiffener section height in this direction on the objective function Impact: Where: is the model objective function value before the parameter changes; For the Change in the potential direction of the rib section height ; For the The model objective function value after the potential direction stiffener section height is changed; For the Sensitivity index corresponding to potential direction reinforcement; Step 400 , based on the sensitivity analysis results, a potential reinforcement direction with the highest sensitivity value in each unit cluster area is selected, and actual reinforcement is constructed according to the direction; Step 500: Divide the actual reinforcement into deformation domains and apply control handles to change the shape of the reinforcement as the control handles are moved, and then set the deformation range of the reinforcement position and length; Step 600, optimizing the arrangement position and length of the reinforcement ribs; Step 700: Optimize the size of the rib cross section after shape optimization.

2. The shape and size combination interpretation and optimization method for the topological layout of stiffened panels according to claim 1, characterized in that: In step 100, a three-dimensional stiffened plate is topologically optimized using a variable density method.

3. The shape and size combination interpretation and optimization method for the topological layout of stiffened panels according to claim 1 is characterized by: In step 500, the actual reinforcement of the structure is divided into deformation domains and control handles are applied using the commercial software Hypermesh.

4. The shape and size combination interpretation and optimization method for the topological layout of stiffened panels according to claim 1, characterized in that: In step 600, the OptiStruct optimization software is used to optimize the arrangement and length of the reinforcement ribs.

5. The shape and size combination interpretation and optimization method for the topological layout of stiffened panels according to claim 1 is characterized by: In step 700, OptiStruct is called to perform size optimization on the rib cross section after shape optimization.

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