A topological optimization method for stiffened plate structures based on close-packed criterion

Abstract

The present invention provides a topological optimization method for a stiffened plate structure based on a close arrangement criterion, comprising the following contents: step 100, finite element analysis is performed on the stiffened plate to be optimized, the total strain energy of the stiffened plate to be optimized is obtained and used as an equivalent performance index; step 200, the stiffened plate to be optimized and the flat steel are equivalently converted by using a size optimization method, the total strain energy of the stiffened plate to be optimized is used as a performance constraint index, and the thickness of the flat steel is used as an arbitrary value for finite element analysis to obtain the equivalent thickness of the flat steel; step 300, on the stiffened plate to be optimized, the flat steel equivalent thickness is arranged according to the close arrangement criterion, and the topological analysis is performed until convergence to obtain the optimal layout of the flat steel, that is, the optimal layout of the stiffened plate to be optimized. The present invention proposes to replace any type of stiffeners with flat steel for topological optimization to achieve a larger number of stiffeners arranged in the horizontal and vertical directions, and to find the optimal layout distribution of the stiffeners, thereby solving the problem of insufficient optimization of the stiffener layout in the optimization of stiffened plates.

Description

Technical Field

[0001] The invention relates to the field of structural topology optimization, and in particular to a topology optimization method for a stiffened plate structure based on a close arrangement criterion. Background Art

[0002] Reinforced plate structures are widely used in ships, offshore platforms, aerospace and other fields due to their light weight, small size and strong bearing capacity. Reinforced plate structures are composed of panels and stiffeners. The stiffeners of the traditional stiffeners are arranged crosswise in the horizontal and vertical directions. They are designed by engineers according to classification society regulations and work experience. The type, size and spacing of the stiffeners need to be constantly changed to meet safety and performance requirements. The design cycle is long and the performance of the designed stiffeners is not optimal.

[0003] In recent years, structural topology optimization technology has developed rapidly. This technology aims to achieve the optimal distribution of materials in the design domain under the conditions of constraint functions and objective functions to achieve the optimal performance of the structure. Therefore, the application of topology optimization technology can quickly obtain the optimal layout distribution of stiffened plates, taking into account the best performance of the structure and the shortest design cycle.

[0004] At present, the topology optimization of stiffened plates is mostly focused on conceptual design research, that is, optimizing the distribution of stiffener materials under certain boundary conditions and load conditions to obtain innovative designs. However, there are relatively few studies that apply topology optimization methods to the optimization of stiffener layout. Summary of the invention

[0005] The present invention provides a topological optimization method for a stiffened plate structure based on a close arrangement criterion, and proposes to replace any type of stiffeners with flat steel for topological optimization to achieve a larger number of transverse and longitudinal arrangement combinations of stiffeners, and to find the optimal layout distribution of stiffeners, so as to solve the problem of insufficient optimization of stiffener layout in stiffened plate optimization.

[0006] A topology optimization method for stiffened plate structures based on a close-packed criterion includes the following contents:

[0007] Step 100, performing finite element analysis on the stiffened plate to be optimized, obtaining the total strain energy of the stiffened plate to be optimized and using it as an equivalent performance index;

[0008] Step 200, using a size optimization method to perform equivalent conversion between the reinforced plate to be optimized and the flat steel, taking the total strain energy of the reinforced plate to be optimized in step 100 as a performance constraint index, and taking the thickness of the flat steel as an arbitrary value to perform finite element analysis to obtain the equivalent thickness of the flat steel;

[0009] Step 300: On the stiffened plate to be optimized, the flat steels are arranged according to the close arrangement criterion with the equivalent thickness of the flat steels in step 200, and the optimal layout of the flat steels is obtained by topological analysis until convergence, i.e., the optimal layout of the stiffened plate to be optimized.

[0010] Furthermore, the content of the equivalent conversion in step 200 is:

[0011] The stiffened plate includes a panel domain and a stiffening rib domain. The panel of the stiffened plate to be optimized remains unchanged, and the stiffening ribs of the stiffened plate to be optimized are equivalently converted into flat steel.

[0012] The height of the flat steel is consistent with the height of the stiffener of the stiffened plate to be optimized, the layout arrangement is consistent with the stiffened plate to be optimized, and the thickness of the flat steel is an arbitrary value.

[0013] Furthermore, in step 200, the thickness of the flat steel is taken as an arbitrary value and combined with the finite element analysis in step 100, the total strain energy of the stiffened plate when the thickness of the flat steel is an arbitrary value is obtained, and compared with the equivalent performance index of step 100 to obtain the equivalent thickness of the flat steel.

[0014] Furthermore, the content of the size optimization is:

[0015] 201) The reinforced plate to be optimized and the flat steel are equivalently converted, the height of the flat steel is consistent with the height of the reinforcement ribs of the reinforced plate to be optimized, and the thickness of the flat steel takes an arbitrary value;

[0016] 202) Based on the equivalent conversion in step 201, create materials and properties and assign them to corresponding parts;

[0017] 203) Establish FE model and set boundary and load conditions;

[0018] 204) Define size optimization, including creating design variables; defining objective function and constraint function; initializing design variables;

[0019] 205) Perform finite element analysis to obtain the strain energy of the stiffened plate;

[0020] 206) determining whether the constraint function satisfies the performance constraint, if so, obtaining the equivalent thickness of the flat steel, if not, executing step 207;

[0021] 207) Use the direct method to perform sensitivity analysis on the objective function and obtain sensitivity information;

[0022] 208) using the sensitivity information to expand the constraint function to obtain a display approximate model;

[0023] 209) The SQP method is used to solve and optimize the display approximate model;

[0024] 210) Update the design variables, that is, update the flat steel thickness, and execute step 205.

[0025] Furthermore, in step 300, the deformation of the stiffened plate to be optimized is obtained by seamlessly arranging the equivalent thickness of the flat steel obtained in step 200, and the volume of the deformation of the stiffened plate to be optimized is obtained by topological analysis. If the tolerance of the volume of the deformation of the stiffened plate to be optimized last time is within the set range, the optimal layout of the flat steel corresponding to the volume of the deformation of the stiffened plate to be optimized is the optimal layout of the stiffened plate to be optimized.

[0026] Furthermore, the specific content of step 300 is:

[0027] 301) seamlessly arranging the flat steel equivalent thickness obtained in step 200 on the panel domain of the stiffened plate to be optimized;

[0028] 302) Create materials and properties and assign them to corresponding parts;

[0029] 303) Establish FE model; set boundary and load conditions;

[0030] 304) Define topology optimization, including creating design variables and response functions; defining objective functions and constraint functions; initializing design variables;

[0031] 305) performing topological analysis;

[0032] 306) judging whether the topological result converges, if converged, the optimal layout of the flat steel is achieved, that is, the optimal layout of the stiffeners of the stiffened plate to be optimized, if not converged, executing step 307;

[0033] 307) Use the adjoint variable method to perform sensitivity analysis on the objective function and obtain sensitivity information;

[0034] 308) using the sensitivity information to expand the constraint function to obtain a display approximate model;

[0035] 309) The DUAL method is used to solve the display approximate model;

[0036] 310) According to the optimization result of step 309, update the design variables and continue to execute step 305.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention provides a topological optimization method for a stiffened plate structure based on a close arrangement criterion, proposes to use a size optimization method to achieve equivalent performance conversion between different types of stiffeners and flat steels, proposes to replace any type of stiffeners with flat steels for topological optimization to achieve a larger number of transverse and longitudinal arrangement combinations of stiffeners, and finds the optimal transverse and longitudinal layout of equivalent flat steels based on topological optimization technology, which is the optimal layout distribution of the original stiffeners. The present invention also proposes a density constraint strategy to convert the continuous topological optimization problem into a discrete topological optimization problem to achieve the "presence" and "absence" of flat steel stiffeners, thereby forming the transverse and longitudinal layout distribution of flat steel stiffeners; the stiffened plate topological layout is the actual usable structure for engineering; it is implemented with the commercial software Hyperworks, which is both robust and efficient, easy to implement, and highly adaptable. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0040] Figure 1 A schematic flow chart of a topology optimization method for a stiffened plate structure based on a close arrangement criterion provided by the present invention;

[0041] Figure 2 A geometric model of a stiffened plate A for verifying the correctness of the topology optimization method considering density constraints proposed in the present invention;

[0042] Figure 3 for Figure 2 Topological density diagram of the stiffened plate A based on the topological optimization method considering density constraints;

[0043] Figure 4 for Figure 2 Corresponding strain energy diagrams for 36 layouts of stiffened panel A;

[0044] Figure 5 It is the geometric model of the long-span stiffened plate B;

[0045] Figure 6 for Figure 5 Strain energy diagram of the finite element analysis of the long-span stiffened plate B;

[0046] Figure 7 for Figure 5 Strain energy diagram of the long-span stiffened panel B based on size optimization;

[0047] Figure 8 for Figure 5Equivalent conversion diagram of the T-beam structure of the long-span stiffened plate B;

[0048] Fig. 9 for Figure 8 The geometric model of the long-span stiffened plate C with closely arranged flat steel bars;

[0049] Fig.10 for Fig. 9 Topology optimization results of the long-span stiffened plate C in FIG. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] A topology optimization method for stiffened plate structures based on a close-packed criterion includes the following contents:

[0052] Step 100: Perform finite element analysis on the stiffened plate to be optimized to obtain the total strain energy of the stiffened plate to be optimized and use it as an equivalent performance index.

[0053] 101) According to the classification society's rules and the designer's experience, determine the type and size of the stiffeners of the stiffened plate to be optimized and arrange them in any layout.

[0054] 102) Meshing the reinforced panels arranged in any layout in step 101 and performing finite element analysis;

[0055] 103) After the finite element analysis of the stiffened plates arranged in any layout in step 102, the total strain energy of the stiffened plates is obtained and used as the equivalent performance index.

[0056] Step 200, using the size optimization method to perform equivalent conversion between the reinforced plate to be optimized and the flat steel, taking the total strain energy of the reinforced plate to be optimized in step 100 as the performance constraint index, taking the thickness of the flat steel as an arbitrary value to perform finite element analysis, and obtaining the equivalent thickness of the flat steel. It should be noted that in the equivalent conversion process, the reinforced plate includes a panel and reinforcement ribs, and the equivalent conversion is that the panel of the reinforced plate to be optimized remains unchanged, and the reinforcement ribs of the reinforced plate to be optimized are equivalently converted to flat steel.

[0057] The size optimization content is as follows:

[0058] 201) The reinforced plate to be optimized is equivalently converted to the flat steel. In order to reduce the space occupancy of the reinforced plate, the height of the flat steel is consistent with the original reinforcement height, the thickness can be any value, and the layout arrangement is consistent with the original reinforcement layout.

[0059] by Figure 8 For example, h is the height of the flat steel and t is the thickness of the flat steel. Figure 8 The left picture shows a T-beam, which consists of a web and a flange, where t1 represents the thickness of the web and t2 represents the thickness of the flange; h2 is the height of the T-beam.

[0060] 202) Based on the above-mentioned flat steel model that has been equivalently converted, create materials and properties and assign them to corresponding parts.

[0061] 203) FE modeling (i.e. finite element modeling), including establishing FE models and setting boundary and load conditions.

[0062] 204) Define dimensional optimization, including creating design variables, i.e., rib thickness; defining objective function and constraint function; and initializing design variables.

[0063] 205) Perform finite element analysis to obtain the strain energy of the stiffened plate.

[0064] In this step, the design variable initialization refers to assigning an initial thickness value to the flat steel, entering the finite element model, and performing finite element analysis to obtain the performance of the stiffened plate, that is, the strain energy of the stiffened plate. The performance of the stiffened plate can be obtained by the method of step 100.

[0065] 206) Determine whether the constraint function meets the performance constraint. If so, obtain the equivalent thickness of the flat steel. If not, execute step 207.

[0066] The strain energy of the stiffened plate obtained in step 205 is compared with the equivalent performance index in step 100 to determine whether the performance constraint is met. If the performance constraint is met, the equivalent thickness of the flat steel of the stiffened plate of the arbitrary layout arrangement is obtained.

[0067] 207) Use the direct method to perform sensitivity analysis on the objective function and obtain sensitivity information.

[0068] 208) The constraint function is expanded using the sensitivity information to obtain an explicit approximate model.

[0069] 209) The SQP method (Seqential Quadratic Programming in English, sequential quadratic programming in Chinese) is used to solve and optimize the displayed approximate model, that is, to solve the thickness of the flat steel and optimize the thickness value of the flat steel.

[0070] 210) Update the design variables, that is, update the flat steel thickness, and execute step 205.

[0071] In step 200, it is proposed to use a size optimization method to achieve equivalent conversion of performance between different types of stiffeners and flat steels, and to replace any type of stiffeners with flat steels for topological optimization to achieve a larger number of transverse and longitudinal arrangements of stiffeners, so as to find the optimal transverse and longitudinal layout of equivalent flat steels.

[0072] Step 300: On the stiffened plate to be optimized, the flat steels are arranged according to the close arrangement criterion with the equivalent thickness in step 200, and the optimal layout of the flat steels is obtained by topological analysis until convergence, i.e., the optimal layout of the stiffened plate to be optimized.

[0073] In step 300, the deformation of the stiffened plate to be optimized is obtained by seamlessly arranging the equivalent thickness of the flat steel obtained in step 200, and the volume of the deformation of the stiffened plate to be optimized is obtained by topological analysis. If the tolerance of the volume of the deformation of the stiffened plate to be optimized last time is within the set range, the optimal layout of the flat steel corresponding to the volume of the deformation of the stiffened plate to be optimized is the optimal layout of the stiffened plate to be optimized.

[0074] 301) In the panel domain of the stiffened plate to be optimized, the flat steels of equivalent thickness obtained in step 200 are arranged according to a close arrangement criterion, i.e., seamless arrangement;

[0075] 302) Create materials and properties and assign them to corresponding parts;

[0076] 303) FE modeling, including establishing FE models; setting boundary and load conditions;

[0077] 304) Define topology optimization, including creating design variables (considering density constraints) and response functions; defining objective functions and constraint functions; initializing design variables;

[0078] 305) performing topological analysis;

[0079] 306) Determine whether the topological result converges. If so, the optimal layout of the flat steel is achieved, that is, the optimal layout of the original reinforcement. If not, execute step 307;

[0080] The topological result is a volume index, and the convergence criterion is: |V k+1 -V k |≤ε, where V k+1 is the topological volume of the k+1th iteration, V k is the topological volume of the kth iteration, and ε is the convergence tolerance, which is set manually. When the topological result converges, the optimal layout of the flat steel is the optimal layout of the original reinforcement.

[0081] 307) Use the adjoint variable method to perform sensitivity analysis on the objective function and obtain sensitivity information.

[0082] 308) The constraint function is expanded using the sensitivity information to obtain an explicit approximate model.

[0083] 309) The DUAL method (dual method in Chinese) is used to solve and optimize the displayed approximate model, solve the density of the flat steel, and obtain the layout distribution of flat steels with different densities. The low-density flat steel is removed, and the high-density flat steel is retained.

[0084] 310) According to the optimization result of step 309, update the design variables, that is, update the flat steel thickness, and continue to execute step 305.

[0085] The present invention provides a topological optimization method for a stiffened plate structure based on a close arrangement criterion, proposes to use a size optimization method to achieve equivalent performance conversion between different types of stiffeners and flat steels, replaces any type of stiffeners with flat steels for topological optimization to achieve a larger number of transverse and longitudinal arrangement combinations of stiffeners, and searches for the optimal transverse and longitudinal layout of equivalent flat steels based on topological optimization technology, that is, the optimal layout distribution of the original stiffeners.

[0086] The present invention proposes a density constraint strategy to be considered during the optimization process, and converts the continuous topology optimization problem into a discrete topology optimization problem to realize the "presence" and "absence" of flat steel reinforcement ribs, thereby forming the horizontal and vertical layout distribution of the flat steel reinforcement ribs, and the stiffened plate topology layout is the actual usable structure in the engineering.

[0087] Example 1

[0088] The following is a further description of a topology optimization method for a stiffened plate structure based on a close arrangement criterion provided by the present invention by way of example:

[0089] (1) Verification of the correctness of the topology optimization method considering density constraints.

[0090] like Figure 2 As shown, the stiffened plate A has 8 transverse beams arranged transversely and 8 longitudinal bones arranged longitudinally.

[0091] Its material parameters are:

[0092] E=2.06×10 5 Mpa, ν=0.3, ρ=7.85×10 -9 t / mm 3 ;

[0093] The boundary conditions are:

[0094] x=0:u x =u y =u z =θ x =θ z =0,θ y ≠0

[0095] x=L:u x =u y=u z =θ x =θ z =0,u x ≠0,θ y ≠0

[0096] y=0 / y=B:u y =u z =θ y =θ z =0,u x ≠0,θ x ≠0

[0097] The topological requirements are: (a) symmetrical design; (b) number of beams: 4; (c) number of longitudinal bones: 4. Constrained by the topological requirements, there are a total of 36 layout schemes for the stiffened plates.

[0098] The panel is subjected to a pressure of 0.3 MPa, the mesh size is 25 mm × 25 mm (the mesh convergence has been verified), and the stiffness of the stiffened panel is maximized.

[0099] like Figure 3 As shown in the figure, the topology optimization result is A2A4A5A7-B2B4B5B7. Due to the symmetry design, it is expressed as A2A4-B2B4. To verify the correctness of this method, the strain energy calculations under the same load and boundary conditions were performed for all 36 layout schemes. Figure 4 As shown, the comparison shows that the structural strain energy under the A2A4-B2B4 layout scheme is the smallest, which is consistent with the topology optimization results. This proves the correctness of the topology optimization method considering density constraints, and the traditional optimal layout of the stiffened plate can be achieved.

[0100] (2) Finite element analysis---to obtain the performance index, namely the total strain energy of the stiffened plate.

[0101] The structure studied by finite element analysis and topology optimization is a long-span stiffened plate B, such as Figure 5 As shown. Among them, the specifications of panel B are: 2400*4200*7, the specifications of beam B are T 72*157*5*7, the specifications of longitudinal bone B are: 55*4, the material parameters are the same as above, and the boundary conditions are four-sided simple support. The panel is subjected to a pressure of 0.1Mpa, and the grid size is 25mm×25mm.

[0102] Finite element analysis was performed on the long-span stiffened plate B, and its strain energy distribution diagram was obtained ( Figure 6 ), the total strain energy of the structure is 51982, which is the equivalent performance index.

[0103] (3) Size optimization---obtaining equivalent thickness of flat steel:

[0104] The cross beam B of the large-span stiffened plate B is replaced by the equal-height flat steel A (the thickness of the flat steel can be any value). Taking the above performance indicators as constraints, the volume minimization design of the flat steel is carried out based on the size optimization strategy.

[0105] The size optimization results are as follows Figure 8 As shown, the equivalent crossbeam C specification of crossbeam B is: 157*12.06.

[0106] (4) Topological optimization - achieving the optimal layout of flat steel, that is, the optimal layout of the original reinforcement ribs:

[0107] The equivalent beam C is used and closely arranged on the face plate of the long-span stiffened plate B to form a long-span stiffened plate C, such as Fig. 9 As shown. Density constraints are imposed on the beams C of the long-span stiffened plate C and topological optimization calculations are performed to obtain the optimal beam C layout, as shown in Fig.10 As shown, this layout is the optimal layout of the original beam.

[0108] The above embodiments are only exemplary embodiments of the present application and are not intended to limit the present application. The protection scope of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and protection scope of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the protection scope of the present application.

Claims

1. A topology optimization method for stiffened plate structures based on the close packing criterion, characterized in that, it includes the following contents: Step 100: Conduct a finite element analysis on the stiffened plate to be optimized, obtain the total strain energy of the stiffened plate to be optimized, and use this as the equivalent performance index; Step 200: Use the size optimization method to equivalently convert the stiffened plate to be optimized with flat steel. Taking the total strain energy of the stiffened plate to be optimized in Step 100 as the performance constraint index, conduct a finite element analysis with the thickness of the flat steel as an arbitrary value, and obtain the equivalent thickness of the flat steel; Step 300: On the stiffened plate to be optimized, arrange according to the close packing criterion with the equivalent thickness of the flat steel obtained in Step 200, and perform topology analysis until convergence to obtain the optimal layout of the flat steel, that is, the optimal layout of the stiffened plate to be optimized; The content of the equivalent conversion in Step 200 is: The stiffened plate includes a panel domain and a stiffener domain. The panel of the stiffened plate to be optimized remains unchanged, and the stiffeners of the stiffened plate to be optimized are equivalently converted into flat steel; Among them, the height of the flat steel is consistent with the height of the stiffeners of the stiffened plate to be optimized, the layout arrangement is consistent with that of the stiffened plate to be optimized, and the thickness of the flat steel is an arbitrary value; The content of the size optimization is: 201) Equivalently convert the stiffened plate to be optimized with flat steel. The height of the flat steel is consistent with the height of the stiffeners of the stiffened plate to be optimized, and the thickness of the flat steel takes an arbitrary value; 202) On the basis of the equivalent conversion in Step 201, create materials, properties and assign them to the corresponding components; 203) Establish an FE model and set boundary and load conditions; 204) Define size optimization, including creating design variables; defining objective functions and constraint functions; initializing design variables; 205) Perform a finite element analysis to obtain the strain energy of the stiffened plate; 206) Judge whether the constraint function meets the performance constraint. If it meets, obtain the equivalent thickness of the flat steel. If it does not meet, execute Step 207; 207) Use the direct method to conduct a sensitivity analysis on the objective function to obtain sensitivity information; 208) Expand the constraint function using the sensitivity information to obtain an explicit approximate model; 209) Use the SQP method to solve and optimize the explicit approximate model; 210) Update the design variables, that is, update the thickness of the flat steel, and execute Step 205.

2. A topology optimization method for stiffened plate structures based on the close packing criterion according to Claim 1, characterized in that, in Step 200, combined with the finite element analysis in Step 100 with the thickness of the flat steel as an arbitrary value, obtain the total strain energy of the stiffened plate when the thickness of the flat steel is an arbitrary value, and compare and judge with the equivalent performance index in Step 100 to obtain the equivalent thickness of the flat steel.

3. A topology optimization method for stiffened plate structures based on the close packing criterion according to Claim 1, characterized in that, in Step 300, arrange seamlessly with the equivalent thickness of the flat steel obtained in Step 200 to obtain the deformation of the stiffened plate to be optimized. Through topology analysis, obtain the volume of the deformation of the stiffened plate to be optimized this time. When the tolerance with the volume of the deformation of the stiffened plate to be optimized last time is within the set range, the optimal layout of the flat steel corresponding to the volume of the deformation of the stiffened plate to be optimized this time is the optimal layout of the stiffened plate to be optimized.

4. According to claim 3, a topology optimization method for a stiffened plate structure based on a close arrangement criterion, It is characterized in that The specific content of step 300 is: 301) On the panel domain of the stiffened plate to be optimized, the flat steel equivalent thickness obtained in step 200 is seamlessly arranged; 302) Create materials and properties and assign them to corresponding parts; 303) Establish FE model; set boundary and load conditions; 304) Define topology optimization, including creating design variables and response functions; defining objective functions and constraint functions; initializing design variables; 305) Perform topological analysis; 306) Determine whether the topology result converges. If it converges, the optimal layout of the flat steel is achieved, that is, the optimal layout of the stiffeners of the stiffened plate to be optimized. If it does not converge, execute step 307; 307) Use the adjoint variable method to perform sensitivity analysis on the objective function and obtain sensitivity information; 308) Using sensitivity information to expand the constraint function, an explicit approximate model is obtained; 309) The DUAL method is used to solve the display approximate model; 310) According to the optimization result of step 309, the design variables are updated and step 305 is continued.

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