Modeling and topology optimization design method and device for reinforced flat plate with embedded acoustic black hole

Abstract

The present application discloses a method and device for modeling and topological optimization design of a reinforced flat plate with an embedded acoustic black hole. The method includes: dividing the design domain into units based on design variables to construct a collaborative optimization model; dividing the reinforced area with solid units and the flat plate area with variable thickness shell units to simulate acoustic black holes; coupling the variable thickness shell units with the solid units and determining the stiffness matrix; introducing maximum size constraints and / or geometric non-interference constraints and / or geometric-topological non-interference constraints and / or draft constraints in the design process; solving the sensitivity of the design variables based on the optimization target combined with the stiffness matrix to obtain the optimization result; if the optimization result does not meet the convergence condition, redefine the design variables based on the sensitivity. It solves the problem that the existing vibration reduction means are difficult to efficiently realize the lightweight vibration reduction design of thin-walled structures. It takes into account the structural stiffness and the vibration and noise reduction characteristics of the medium and high frequencies, realizes the structure-function integrated design, and reduces the dynamic response of the thin-walled structure.

Description

Technical Field

[0001] The present application relates to the technical field of engineering structure design, and in particular to a method and device for modeling and topological optimization design of a reinforced flat plate with an embedded acoustic black hole. Background Art

[0002] The acoustic black hole (ABH) structure is a lightweight, high-strength, broadband elastic wave control method. It achieves changes in structural impedance by changing the thickness of its own structure in the form of a certain power function, thereby changing the wave velocity of the bending wave in the structure, so that the vibration energy can be efficiently concentrated in the local area of ​​the structure, thereby effectively improving the dissipation efficiency of the vibration energy. It has broad application prospects in aerospace, automobile, machinery and other fields.

[0003] The topology optimization method is to optimize the material distribution of the structure under given external loads and boundary conditions to seek the best force transmission path of the structure. Compared with size optimization and shape optimization, structural topology optimization can determine more design variables, has a higher degree of design freedom, can save materials more significantly, and achieve greater economic benefits. At the same time, it can provide engineering designers with a comprehensive conceptual design in the initial stage of structural design, which helps to obtain a better structural layout and has broad application prospects in the field of engineering design.

[0004] Regarding the vibration response control of various scientific and technological products today, especially the medium and high frequency vibration problems of thin-walled structures, how to effectively reduce the impact of vibration and noise on the function of thin-walled structures is still an important research topic. The traditional vibration reduction method that simply relies on adding damping structures will greatly increase the weight of the thin-walled structure itself, which is not conducive to the lightweight design of thin-walled structures. Therefore, it is necessary to further explore efficient vibration and noise reduction structural design methods. Summary of the invention

[0005] The embodiment of the present application solves the problem that existing vibration reduction means are difficult to efficiently achieve lightweight vibration reduction design of thin-walled structures by providing a method and device for modeling and topological optimization design of a reinforced flat plate with an embedded acoustic black hole.

[0006] In the first aspect, an embodiment of the present application provides a modeling and topology optimization design method for a reinforced flat plate with an embedded acoustic black hole, comprising: iteratively executing an optimization step until the optimization result meets the convergence condition and obtains the optimal design variable; the optimization step comprises: dividing the design domain into units based on the defined design variables to construct a collaborative optimization model; wherein the reinforced area in the design domain is divided by solid units; the flat plate area in the design domain is divided by variable thickness shell units to simulate the acoustic black hole; the variable thickness shell units are coupled with the solid units to obtain a coupled unit, and its stiffness matrix is ​​determined; a maximum size constraint and / or a geometric non-interference constraint and / or a geometric-topological non-interference constraint and / or a draft constraint are introduced into the design variables to optimize the collaborative optimization model; the sensitivity of the design variables is solved based on the optimization target in combination with the stiffness matrix, and the optimization result of the optimized collaborative optimization model is obtained; if the optimization result does not meet the convergence condition, the design variables are redefined based on the sensitivity, and the optimization step is performed.

[0007] In combination with the first aspect, in a possible implementation, the design variables include topological variables and geometric variables; the topological variables include the material density of each solid unit in the reinforced area; the geometric variables include the position and radius of the acoustic black hole in the flat plate area.

[0008] In combination with the first aspect, in a possible implementation, the flat plate area in the design domain is divided with variable thickness shell elements to simulate the acoustic black hole, including: projecting the cross-sectional thickness variation of the acoustic black hole into a thickness field on a plane; based on the thickness field, traversing all nodes on the flat plate area to determine the thickness of each node in the flat plate area; determining the variable thickness shell element according to the thickness of each node in the flat plate area, and simulating the acoustic black hole based on the variable thickness shell element.

[0009] In combination with the first aspect, in a possible implementation manner, the calculation formula for traversing all nodes on the flat plate region to determine the thickness of each node in the flat plate region based on the thickness field is as follows:

[0010] ;

[0011] In the formula, represents the thickness of any node in the plate region, Indicates The characteristic projection function of an acoustic black hole on a plane, Represents any node in the flat area The position vector of A power function representing the thickness of an acoustic black hole, Indicates The coordinates of the center of the projection of an acoustic black hole on the plane where the flat plate region is located, represents the thickness of the uniform plate in the flat plate region, Represents the total number of acoustic black holes distributed on the flat plate area.

[0012] In combination with the first aspect, in a possible implementation, the coupling of the variable thickness shell unit and the solid unit to obtain a coupling unit includes: if the reinforced area is divided into a single layer by the solid unit, determining the solid unit node on the contact surface of the solid unit, and matching it with the variable thickness shell unit node on the contact surface of the variable thickness shell unit to determine the coupling node; based on the coupling node, coupling the degrees of freedom of the solid unit node and the variable thickness shell unit node to obtain a coupling unit.

[0013] In combination with the first aspect, in a possible implementation, the coupling of the variable thickness shell unit with the solid unit to obtain a coupling unit includes: if the reinforced area is divided into multiple layers by the solid unit, determining the solid unit nodes on the contact surface of the solid unit in the reinforced area that is in contact with the variable thickness shell unit, and matching the variable thickness shell unit nodes on the contact surface of the variable thickness shell unit to determine the coupling nodes; based on the coupling nodes, coupling the degrees of freedom of the solid unit nodes and the variable thickness shell unit nodes to obtain a coupling unit.

[0014] In combination with the first aspect, in a possible implementation, obtaining the optimization result of the optimized collaborative optimization model includes: based on the constraint conditions, establishing a collaborative optimization mathematical model with minimizing the average external force input power as the optimization goal, as follows:

[0015] , ;

[0016] In the formula, represents the average external input power, a pseudo-density vector representing the material density of the solid element in the reinforced region, A vector set of geometric variables representing the acoustic black hole in the slab region, represents the frequency of the input external force, represents taking the real part of a complex number, for , indicating plural units, represents the external load vector, represents the conjugate transposed matrix of the external force, represents the displacement matrix of the collaborative optimization model, represents the stiffness matrix of the collaborative optimization model, represents the volume of the material in the reinforced area, The upper limit of the allowable material volume in the reinforced area, represents the p-norm condensed form of the maximum size constraint, Indicates geometric non-interference constraints, Indicates geometric-topological non-interference constraints, represents the pseudo-density value of the i-th entity element, represents the number of geometric non-interference constraints, represents the number of acoustic black holes in the slab region, Represents the number of solid elements in the stiffened area.

[0017] In the second aspect, an embodiment of the present application provides a modeling and topology optimization design device for a reinforced flat plate with an embedded acoustic black hole, comprising: an iterative execution module, which is used to iteratively execute the optimization steps until the optimization results meet the convergence conditions and obtain the optimal design variables; the optimization steps include: a modeling module, which is used to divide the design domain into units based on the defined design variables to construct a collaborative optimization model; wherein the reinforced area in the design domain is divided by solid units; the flat plate area in the design domain is divided by variable thickness shell units to simulate the acoustic black hole; a coupling module, which is used to couple the variable thickness shell units with the solid units to obtain a coupling unit, and determine its stiffness matrix; a constraint module, which is used to introduce a maximum size constraint and / or a geometric non-interference constraint and / or a geometric-topological non-interference constraint and / or a draft constraint into the design variables to optimize the collaborative optimization model; a solving module, which is used to solve the sensitivity of the design variables based on the optimization target in combination with the stiffness matrix, and obtain the optimization result of the optimized collaborative optimization model; if the optimization result does not meet the convergence conditions, the design variables are redefined based on the sensitivity, and the optimization step is executed.

[0018] In a third aspect, an embodiment of the present application provides a device, comprising: a processor; a memory for storing processor-executable instructions; when the processor executes the executable instructions, it implements the method described in the first aspect or any possible implementation method of the first aspect.

[0019] In a fourth aspect, an embodiment of the present application provides a non-volatile computer-readable storage medium, wherein the non-volatile computer-readable storage medium includes a medium for storing a computer program or instructions, which, when executed, enables the method described in the first aspect or any possible implementation method of the first aspect to be implemented.

[0020] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

[0021] The embodiment of the present application uses variable thickness shell elements to model the embedded acoustic black hole, which can avoid the problem of overall mesh changes caused by changes in the geometric variables of the acoustic black hole; by coupling the variable thickness shell elements with the solid elements, the seamless transition and effective connection between the solid elements and the variable thickness shell elements can be guaranteed; by introducing maximum size constraints and / or geometric non-interference constraints and / or geometric-topological non-interference constraints and / or draft constraints, the uniformity and stability of the structure can be guaranteed. The problem that the existing vibration reduction means are difficult to efficiently achieve lightweight vibration reduction design of thin-walled structures is solved. It can take into account both structural stiffness and medium and high frequency vibration and noise reduction characteristics to achieve structural-functional integrated design. Under the limitation of limited material volume fraction, the vibration reduction and noise reduction efficiency of the acoustic black hole is maximized through the collaborative optimization method of the flat plate area and the reinforced area, and the dynamic response of the structure is significantly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1 A flow chart of a method for modeling and topology optimization design of a reinforced flat plate with an embedded acoustic black hole provided in an embodiment of the present application;

[0024] Figure 2 A schematic diagram of the structure of a device for modeling and topology optimization design of a reinforced flat plate with an embedded acoustic black hole provided in an embodiment of the present application;

[0025] Figure 3 A schematic cross-sectional view of an acoustic black hole provided in an embodiment of the present application;

[0026] Figure 4 A thickness field cloud diagram describing an acoustic black hole provided in an embodiment of the present application;

[0027] Figure 5 A schematic diagram of a variable thickness shell element provided in an embodiment of the present application;

[0028] Figure 6 A schematic diagram of a coupled unit obtained by coupling a solid unit with a variable thickness shell unit provided in an embodiment of the present application;

[0029] Figure 7 A schematic diagram of the design domain, the reinforced area and the flat plate area provided in the embodiment of the present application;

[0030] Figure 8 A schematic diagram of a design domain boundary envelope circle in a flat plate region provided in an embodiment of the present application;

[0031] Fig. 9 A schematic diagram of the material suspension phenomenon to be prevented from occurring in the embodiments of the present application;

[0032] Fig.10 A schematic diagram of anisotropic filtering of a cylinder provided in an embodiment of the present application;

[0033] Fig.11 A schematic diagram of the maximum size constraint based on a cylindrical local constraint domain provided in an embodiment of the present application;

[0034] Fig.12 A schematic diagram of a uniform plate of uniform thickness excited by a base provided in an embodiment of the present application;

[0035] Fig.13 A frequency response curve diagram of a uniform flat plate of equal volume and uniform thickness under basic excitation provided as a control in an embodiment of the present application;

[0036] Fig.14 A frequency response curve of the average power of the external force when a uniform flat plate of equal volume and uniform thickness is excited by a foundation as a control provided in an embodiment of the present application;

[0037] Fig.15 The embodiments of the present application provide Fig.12 Example of the design results of a uniform plate of medium volume and uniform thickness at 810 Hz with only stiffening as the optimization objective, minimizing the average input power of the external force;

[0038] Fig.16 The embodiments of the present application provide Fig.12 An example of the collaborative optimization results of the reinforcement and acoustic black hole structure of a uniform plate of medium uniform thickness at 810 Hz with the optimization objective of minimizing the average input power of the external force;

[0039] Fig.17 A comparison chart of the whole plate dynamic response of the result of the reinforcement-only structure design provided in the embodiment of the present application and the collaborative optimization result of the reinforcement and acoustic black hole collaborative optimization of the present application. DETAILED DESCRIPTION

[0040] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are 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.

[0041] The following describes some of the techniques involved in the embodiments of the present application to facilitate understanding, and they should be considered as merely exemplary. Therefore, it should be appreciated by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present application. Similarly, for the sake of clarity and conciseness, some descriptions of well-known functions and structures are omitted in the following description.

[0042] Figure 1 1 is a flow chart of a method for modeling and topology optimization design of a reinforced flat plate with an embedded acoustic black hole provided in an embodiment of the present application, including steps 101 to 107. Among them, Figure 1 This is only an execution order shown in the embodiment of the present application, and does not represent the only execution order of the embedded acoustic black hole reinforced flat plate modeling and topology optimization design method. In the case that the final result can be achieved, Figure 1 The steps shown may be performed in parallel or reversed.

[0043] Step 101: Based on the defined design variables, the design domain is divided into units to construct a collaborative optimization model. The reinforced area in the design domain is divided with solid units. The flat plate area in the design domain is divided with variable thickness shell units to simulate the acoustic black hole. The design variables include topological variables and geometric variables. The topological variables include the material density of each solid unit in the reinforced area. The geometric variables include the position and radius of the acoustic black hole in the flat plate area.

[0044] In the embodiment of the present application, taking a uniform flat plate as an example, from a spatial point of view, the ribs are arranged on the reinforced uniform flat plate, and the acoustic black hole is embedded inside the reinforced uniform flat plate. In terms of design type, the reinforcement layout belongs to topological design, and the size and layout of the acoustic black hole belong to parameter design. The present application efficiently solves the problem of coordinated optimization of the reinforcement layout on the uniform flat plate and the size and layout of the acoustic black hole in the uniform flat plate through a modeling and topological optimization design method of a reinforced flat plate with an embedded acoustic black hole.

[0045] Specifically, Figure 7 As shown, a geometric model of a uniform plate is constructed, and the design domain of the uniform plate (hereinafter referred to as the uniform plate refers to the geometric model of the uniform plate) is divided into two layers, the upper layer is the reinforced area, and the lower layer is the flat plate area.

[0046] After determining the reinforced area and the flat plate area, use finite element analysis software (such as ANSYS, Abaqus, etc.) to divide them into units.

[0047] like Figure 7As shown in the figure, the reinforced area (i.e., topological design domain) is used to simulate the reinforced layout of the uniform plate. Using solid elements to divide the reinforced area can more accurately capture the details of the reinforced part and provide more accurate results in subsequent analysis and optimization. The flat plate area (i.e., geometric design domain) is used to simulate the acoustic black hole layout of the uniform plate. Using variable thickness shell elements (i.e., Figure 7 The flat plate area is divided by the shell unit in the structure so that the acoustic black hole only affects the thickness of the variable thickness shell unit, thereby avoiding the problem of mesh changes caused by changes in its geometric variables. The shapes of the solid unit and the variable thickness shell unit here are defined by those skilled in the art according to needs, and can be tetrahedrons, hexahedrons, etc., and are not specifically limited here.

[0048] In the embodiment of the present application, the cross-sectional thickness variation of the acoustic black hole is projected as a thickness field on a plane. Based on the thickness field, all nodes on the flat plate region are traversed to determine the thickness of each node in the flat plate region. The variable thickness shell unit is determined according to the thickness of each node in the flat plate region, and the acoustic black hole is simulated based on the variable thickness shell unit.

[0049] In an embodiment of the present application, the flat plate area of ​​the design domain is divided by variable thickness shell units to simulate the acoustic black hole. In the flat plate area, the thickness of the acoustic black hole is variable, the thickness of the uniform plate outside the acoustic black hole is fixed, and its thickness within the boundary of the acoustic black hole gradually changes from the cutoff thickness to the thickness of the uniform plate, as follows.

[0050] like Figure 3 and Figure 4 As shown in the collaborative optimization design process, the cutoff thickness of the acoustic black hole, that is, the thickness at the thinnest point, is a fixed value, and the thickness of the internal plate where the acoustic black hole is located is a function of the radius, that is, ,in, represents the thickness of the inner plate of an acoustic black hole as a function of radius, represents the radius variable of the acoustic black hole from any point on the inner plate of the uniform flat plate to the center of the acoustic black hole, represents the cutoff thickness of the acoustic black hole, For example, take 2, Figure 3 Middle vertical axis represents the thickness. The design variables in the flat plate region are the geometric variables of the acoustic black hole (the radius of the acoustic black hole With location ), the geometric relationship is: .in, represents the thickness of the inner plate of an acoustic black hole as a function of radius, represents the cutoff thickness of the acoustic black hole, represents the geometric relationship between the internal plate thickness and radius of an acoustic black hole, represents the radius of the acoustic black hole in the flat plate region (the radius of the circle used to represent the acoustic black hole in the flat plate region), represents the thickness of the uniform plate within the flat plate region.

[0051] The cross-sectional thickness change of the acoustic black hole is projected into a thickness field on the plane (i.e., the plane where the flat plate region is located), and the corresponding thickness is assigned to the variable thickness shell unit to simulate the distribution of the acoustic black hole on the flat plate region, such as Figure 3 As shown. The characteristic function is used to describe the position of the acoustic black hole for a circle of any radius in the flat plate region of the uniform flat plate. The characteristic function is as follows:

[0052] (1)

[0053] In the formula, represents the characteristic function, Represents any node in the flat area The position vector of , represents the horizontal and vertical coordinates of any node in the plate area, represents the radius of the acoustic black hole in the slab region.

[0054] Among them, the characteristic function describes the boundary of an acoustic black hole. Within the boundary of an acoustic black hole, , outside the boundary of the acoustic black hole, The function values ​​inside and outside the boundary of the acoustic black hole are mapped to 1 and 0 through the characteristic projection function, as follows:

[0055] (2)

[0056] In the formula, represents the characteristic projection function of the acoustic black hole on the plane (i.e., the plane where the flat plate region is located), Represents any node in the flat area The position vector of represents the coordinates of the center of the projection of the acoustic black hole on the plane, Represents the projection parameters, which are used to control the feature projection function The steepness of the change at the boundary is set to 10 for example in this application. represents the characteristic function.

[0057] The thickness of an acoustic black hole is given by a power function along the radial direction of the circle Description, where is the cutoff thickness of the acoustic black hole. Assume that there are acoustic black hole, then The thickness formula of a point near an acoustic black hole can be expressed as:

[0058] (3)

[0059] In the formula, Indicates the first The thickness of a point near an acoustic black hole, Indicates The characteristic projection function of an acoustic black hole on a plane, Represents any node in the flat area The position vector of A power function representing the thickness of an acoustic black hole, Indicates The coordinates of the center of the projection of an acoustic black hole on the plane, represents the thickness of the uniform plate in the flat plate region, represents the thickness of the inner plate of an acoustic black hole as a function of radius, represents the cutoff thickness of the acoustic black hole, represents the geometric relationship between the thickness of the inner plate of an acoustic black hole and its radius, represents the radius of the acoustic black hole in the flat plate region, m represents the power of the function, and here m is 2.

[0060] In addition, this application takes into account the existence of the cutoff thickness. The acoustic black hole cannot completely absorb the incident elastic wave. It is also necessary to paste damping material in the corresponding acoustic black hole area to reduce the reflection of the elastic wave and dissipate the accumulated vibration energy to achieve the purpose of vibration reduction. Therefore, this application simulates pasting damping material by setting a larger damping loss factor in the acoustic black hole area to simplify the damping modeling. The damping loss factor at an acoustic black hole is expressed in formula (4) as follows:

[0061] (4)

[0062] In the formula, Indicates the area of ​​the plate The damping loss factor of any point near an acoustic black hole is, Indicates The characteristic projection function of an acoustic black hole on a plane, Indicates The characteristic function of an acoustic black hole, Indicates The damping loss factor inside an acoustic black hole, is the damping loss factor of the initial material in the flat plate region.

[0063] Considering the distribution of all acoustic black holes based on formulas (3) and (4), the thickness of any node of the variable thickness shell element in the flat plate region is as follows:

[0064] (5)

[0065] The damping loss factor of any node in the flat plate area is as follows (6):

[0066] (6)

[0067] In the formula, represents the thickness of any node in the plate region, Indicates The characteristic projection function of an acoustic black hole on a plane, Represents any node in the flat area The position vector of A power function representing the thickness of an acoustic black hole, Indicates The coordinates of the center of the projection of an acoustic black hole on the plane, represents the thickness of the uniform plate in the flat plate region, represents the total number of acoustic black holes distributed in the flat plate region, represents the damping loss factor at any point in the plate region, Indicates The damping loss factor inside an acoustic black hole, is the damping loss factor of the initial material in the flat plate region.

[0068] After the plate area is divided into units, the coordinates of the nodes of the variable thickness shell element are substituted into formulas (5) and (6) to calculate the thickness of the corresponding strain thickness shell element nodes in the plate area. After traversing all the variable thickness shell element nodes, the variable thickness shell element can be obtained, such as Figure 5 As shown in the figure, the embedded acoustic black hole is modeled by using variable thickness shell elements. , , and Represents a variable thickness shell element node.

[0069] It should be noted that in order to reduce the numerical error caused by the thickness deviation of the variable thickness shell element, a finer grid is required. The size of the variable thickness shell element in this application does not exceed , represents the radius of the acoustic black hole in the slab region.

[0070] Step 102: Couple the variable thickness shell element with the solid element to obtain a coupled element, and determine its stiffness matrix. In an embodiment of the present application, if the reinforced area is divided into a single layer by the solid element, the solid element nodes on the contact surface of the solid element are determined, and the variable thickness shell element nodes on the contact surface of the variable thickness shell element are matched to determine the coupling nodes. Based on the coupling nodes, the degrees of freedom of the solid element nodes and the variable thickness shell element nodes are coupled to obtain a coupled element.

[0071] like Figure 6 As shown in the figure, specifically, the connection between the solid element and the variable thickness shell element is realized by the unit common node method. Since the degrees of freedom of the solid element and the variable thickness shell element are different, it is necessary to consider the coupling problem of the two elements at the connection. The solid element node has three degrees of freedom , the variable thickness shell element node has 6 degrees of freedom Among them, the degrees of freedom of the nodes of the variable thickness shell element are and degrees of freedom of the solid element nodes Therefore, according to the matching relationship between the unit node degrees of freedom, the stiffness matrix of the coupling unit can be obtained:

[0072] (7)

[0073] In the formula, Represents the 36×36 stiffness matrix of the coupling element, where the upper left side of the stiffness matrix Represents the 6×6 node stiffness matrix of the coupling node. Figure 6 As shown, the variable thickness shell elements 1, 2, 3, and 4 of the shell element (i.e., variable thickness shell element) in the figure are coupling nodes determined on the contact surface of the variable thickness shell element, and the solid element nodes 1, 2, 3, and 4 in the figure are coupling nodes determined on the contact surface of the solid element. The coupling nodes of the variable thickness shell element and the solid element are coupled to obtain the coupling element and the coupling nodes 1, 2, 3, and 4, and the remaining nodes are non-coupling nodes.

[0074] The stiffness matrix combination of the variable thickness shell element and the solid element at the coupling node is written as follows (8):

[0075] (8)

[0076] Among them, m, n = 1, 2, 3, 4.

[0077] In formula (7) The 3×3 node stiffness matrix representing the solid element nodes that are not involved in the coupling can be written as the following formula (9):

[0078] (9)

[0079] Where, when m=5,...,8, n=1,...,8. When n=5,...,8, m=1,...,8. represents the three degrees of freedom of the solid element node, represents the 6 degrees of freedom of the nodes of the variable thickness shell element, is the stiffness characteristic information in the stiffness matrix of the unit node corresponding to the direction of the degree of freedom, and m and n represent the number of rows and columns of the matrix.

[0080] In the embodiment of the present application, if the reinforced area is divided into multiple layers by the solid element, the solid element nodes on the contact surface of the solid element in contact with the variable thickness shell element in the reinforced area are determined, and the variable thickness shell element nodes on the contact surface of the variable thickness shell element are matched to determine the coupling nodes. Based on the coupling nodes, the degrees of freedom of the solid element nodes and the variable thickness shell element nodes are coupled to obtain the coupling unit.

[0081] Specifically, when the reinforced area is divided into multiple layers of solid elements to simulate the structure of the reinforced layout, only the solid elements in the bottom layer are coupled with the variable thickness shell elements, and the stiffness matrices of the remaining solid elements remain unchanged. At this time, the stiffness matrix of the uniform plate is obtained by assembling the stiffness matrix of the coupled elements. and the stiffness matrix of the remaining solid elements (Stiffness matrix of the entity element of the non-coupled node) is obtained, as shown in formula (10):

[0082] (10)

[0083] In the formula, represents the stiffness matrix of the uniform plate as a whole (including the stiffened area and the flat plate area), represents the stiffness matrix of the variable thickness shell element, represents the stiffness matrix of the solid element, represents the stiffness matrix of the coupled element, represents the stiffness matrix of the remaining solid elements that do not participate in the coupling, , and are the number of variable thickness shell elements, the number of solid elements and the number of coupled elements, , Indicates an incremental variable starting from 1.

[0084] Step 103: Introducing maximum size constraints and / or geometric non-interference constraints and / or geometric-topological non-interference constraints and / or draft constraints into the design variables to optimize the collaborative optimization model.

[0085] In an embodiment of the present application, a maximum size constraint is introduced into the design variables of the collaborative optimization model to avoid material accumulation in the topological optimization results of the reinforcement layout.

[0086] Specifically, the solid elements in the reinforced area Neighborhood Introducing the volume ratio as The pore volume of the neighborhood The physical feature size within is limited, as shown in formula (11):

[0087] (11)

[0088] It should be noted that the maximum size constraint in this application is the physical density field after Heaviside filtering. Applied, so the unit physical density is used in the formula.

[0089] Moreover, formula (11) can only control the solid element The maximum characteristic size in the neighborhood. If you need to impose size constraints on the entire structure, you need to traverse all the entity units. In order to reduce the number of constraints, the p-norm is used to condense the local size constraints. In order to reduce the nonlinearity of the condensed global size constraints and improve the calculation accuracy of the condensation function, firstly, the formula (11) is biased, as shown in the following formula (12):

[0090] (12)

[0091] The global maximum size constraint expression after condensation is as shown in equation (13):

[0092] (13)

[0093] In the formula, represents the p-norm condensed form of the maximum size constraint, represents the entire reinforced area, is the p-norm agglomeration factor, represents the pore volume, Represents solid element Neighborhood of Represents neighborhood The entity feature size constraint formula within, Represents the neighborhood after bias processing The entity feature size constraint formula within, Represents neighborhood The A solid unit, Represents neighborhood The The volume of a solid unit, Represents neighborhood In The material density of a solid element after Heaviside filtering.

[0094] The local volume constraint neighborhood of the coupling unit based on the maximum size of the density field is a circle (two-dimensional) or a sphere (three-dimensional), but this neighborhood shape is not suitable for the design of reinforced structures. According to the structural characteristics of the uniform plate to be reinforced, this application will Take the diameter as The cylindrical local constraint domain of the cylinder is Fig.11 shown.

[0095] In the embodiment of the present application, geometric-topological non-interference constraints can also be introduced into the design variables to realize the non-interference constraints of the acoustic black hole structure represented by the variable thickness shell unit and the solid unit reinforced structure.

[0096] Specifically, since the acoustic black hole structure and the reinforced structure are located in different design domains, there will be interference between the reinforced structure and the acoustic black hole structure during the collaborative optimization process, that is, there are both acoustic black holes and reinforced structures at the same position of the coupling unit. In order to avoid this problem, this application adopts the idea of ​​maximum size constraint to introduce porosity in the spatial neighborhood of the acoustic black hole. , controls the material distribution in the neighborhood, as shown in formula (14):

[0097] (14)

[0098] In the formula, Indicates geometric-topological non-interference constraints, Represents solid element Neighborhood of represents the porosity introduced in the spatial neighborhood of the acoustic black hole, Represents neighborhood The A solid unit, Represents neighborhood In The material density of the solid element after Heaviside filtering. Spatial neighborhood The size of is taken as the same radius as the corresponding acoustic black hole, and the cylinder that penetrates the reinforced region is as follows: Fig.11 As shown. When the value of is close to 0, the control space neighborhood is filled with material. When the value of is close to 1, avoid distributing materials in the spatial neighborhood. , to avoid the distribution of reinforcing materials at the acoustic black hole, that is, to achieve geometric-topological non-interference constraints.

[0099] In the embodiment of the present application, an envelope circle may be established around each acoustic black hole to achieve geometric non-interference constraints. A draft constraint is introduced into the collaborative optimization model to eliminate the hanging phenomenon of the material in the collaborative optimization model.

[0100] Specifically, in order to find the optimal layout of the collaborative optimization model to reduce the overall dynamic response, the geometric position and radius of the acoustic black hole are continuously updated. When there are multiple acoustic black holes on the flat plate area, the boundaries between the updated acoustic black holes may overlap. When coordinating the positions of the acoustic black holes on the flat plate area, this interference must be prevented. In addition, it is also necessary to ensure that the acoustic black hole is located within the flat plate area as a whole, that is, the boundary of the acoustic black hole does not interfere with the design domain boundary of the uniform flat plate as a whole.

[0101] like Figure 8 As shown, the present application uses an envelope circle to handle the above geometric non-interference constraints. First, a set of envelope circles are used to describe the boundaries of the design domain of the acoustic black hole and the uniform flat plate as a whole. Among them, the boundary of the two-dimensional acoustic black hole on the flat plate area can be directly expressed by the circle equation By calculating the distance between the centers of the envelope circle, it can be determined whether the boundary of the design domain between the acoustic black holes or between the acoustic black hole and the uniform flat plate generates interference. Finally, the geometric non-interference constraint between the acoustic black holes is realized by constraining the distance between the centers of the envelope circle, as shown in the following formula (15):

[0102] (15)

[0103] In the formula, Indicates geometric non-interference constraints, and Respectively represent and The coordinates of the center of the enveloping circle, Indicates and The distance between the centers of the enveloping circles, and Respectively represent i and j The radius of the enveloping circle. In the circle equation, and represents the position coordinates of any node in the flat plate area, and Representing an acoustic black hole The coordinates of the center of the circle, It is the radius of the acoustic black hole in the flat plate region. Those skilled in the art should realize that the envelope circle here includes the envelope circle of the acoustic black hole and the envelope circle of the design domain boundary.

[0104] In particular, during the optimization process, the value on the right side of formula (15) can be appropriately reduced to adjust the distance between acoustic black holes.

[0105] The present application also introduces a draft constraint to eliminate the material hanging phenomenon in the reinforced area in the collaborative optimization model. The schematic diagram of the material hanging phenomenon to be prevented provided in the embodiment of the present application is as follows: Fig. 9 Here, it is achieved by filtering the anisotropic design variable field of the reinforcement area, as shown in Fig.10 As shown in the figure, xy is the plane where the flat plate area is located. represents the pseudo-density value of the i-th entity element, represents the design density of the solid element, Indicates the filter radius of the cylindrical neighborhood.

[0106] For example, in the topological reinforcement structure design based on the density method, when the plate-shell structure is subjected to an out-of-plane force, the topological optimization result is likely to have a suspended structure, and the material in the topological optimization result will be accumulated on the upper and lower surfaces of the plate-shell structure while there is no material in the middle layer. This phenomenon is not conducive to the generation of the reinforcement layout. Fig.10 The anisotropic filtering of the element design variable field shown achieves the same element density control effect as the draft constraint. The specific expression (16) is as follows:

[0107] (16)

[0108] In the formula, represents the draft constraint, , Represents the entity element The center coordinates and volume of Represents solid element In is the set of solid units within the cylindrical neighborhood of the filter radius, Represents the solid element in the cylindrical neighborhood Design density The weight of It represents the relaxed two-dimensional Euclidean distance, that is, the projection distance of the center of the solid element in the xy plane (the plane where the uniform plate is located).

[0109] Step 104: Solve the sensitivity of the design variables based on the optimization target combined with the stiffness matrix, and obtain the optimization results of the optimized collaborative optimization model. In the embodiment of the present application, the optimization target is exemplarily set to minimize the average external force input power. Considering the given material usage, geometric constraints and process constraints, based on the constraints, a collaborative optimization mathematical model is established with the goal of minimizing the average external force input power, as shown in the following formula (17):

[0110] , (17)

[0111] In the formula, represents the average external input power, Pseudo-density vector representing the material density of the solid elements in the stiffened region, A vector set of geometric variables representing the acoustic black hole in the slab region, represents the frequency of the input external force, represents taking the real part of a complex number, for , indicating plural units, represents the external load vector, represents the conjugate transposed matrix of the external force, represents the displacement matrix of the collaborative optimization model, represents the stiffness matrix of the collaborative optimization model, represents the volume of the material in the reinforced area, The upper limit of the allowable material volume in the reinforced area, represents the p-norm condensed form of the maximum size constraint, Indicates geometric non-interference constraints, Indicates geometric-topological non-interference constraints, represents the pseudo-density value of the i-th entity element, represents the number of geometric non-interference constraints, represents the number of acoustic black holes in the slab region, Represents the number of solid elements in the stiffened area.

[0112] Step 105: Determine whether the optimization result meets the convergence condition. In the embodiment of the present application, based on the sensitivity of the design variables calculated in step 104 and the optimization result (i.e., the average external force input power), it is determined whether the optimization result meets the convergence condition. The convergence condition here is exemplarily set to that the obtained optimization result meets the design requirements so that the average external force input power is minimized. Or the difference between the optimization result calculated this time and the optimization result calculated last time is less than a set threshold value (e.g., 0.001). Those skilled in the art may also set the convergence condition here according to actual needs, which shall not be regarded as a limitation on the scope of protection of the present application.

[0113] If the optimization result does not meet the convergence condition, step 106 is executed until the convergence condition is met. If the optimization result meets the convergence condition, step 107 is executed.

[0114] Step 106: Redefine the design variables based on the sensitivity. In the embodiment of the present application, the design variables are modified based on the calculated sensitivity, and steps 101 to 105 are performed again.

[0115] Step 107: Obtaining optimal design variables. Specifically, the optimal design variables obtained at this time can maximize the vibration reduction and noise reduction efficiency of the acoustic black hole under the limitation of limited material volume, and significantly reduce the dynamic response of the structure.

[0116] In the embodiments of the present application, the specific implementation steps of the present application are described in detail by taking a topology optimization example of a uniform flat plate with an embedded acoustic black hole, as follows.

[0117] The first step is to establish Fig.12 The uniform plate with uniform thickness of 1m×1m×0.005m is used as the design object. The four corners of the uniform plate are fixed and subjected to simple harmonic foundation excitation. The material properties of the uniform plate include: Young's modulus is 210GPa, density is 7850kg / m³, Poisson's ratio is 0.3, damping loss factor is 0.05, and reinforcement height is 0.015m. Due to the symmetry of the structure, only the lower right 1 / 4 of the uniform plate is taken for optimization design. Among them, the reinforcement area is divided by solid elements, and the flat plate area is divided by variable thickness shell elements. The unit size is 0.01m, and the geometric model of the uniform plate is divided into 7500 solid elements and 2500 variable thickness shell elements.

[0118] The second step is to analyze the dynamic response of the uniform flat plate structure of equal volume and uniform thickness under the same working condition as a comparison of the collaborative optimization results of this application. In order to ensure that the weight of the uniform flat plate of equal volume and uniform thickness with only the reinforced structure design and the uniform flat plate with embedded acoustic black hole in the collaborative optimization of this application is consistent, the thickness of the uniform plate in the flat plate area is taken as 0.008m. Fig.13 and Fig.14They are the frequency response curve of a uniform plate of equal volume and uniform thickness under foundation excitation and the frequency response curve of the average power of the external force when a uniform plate of equal volume and uniform thickness is excited by the foundation.

[0119] In the third step, the material volume ratio of the reinforced area is set to 0.2, and the maximum size constraint of the reinforced structure is set to 0.08m. At the same time, the maximum size constraint, geometric non-interference constraint, geometric-topological non-interference constraint and draft constraint are introduced.

[0120] The fourth step is to minimize the average external force power of the system at 810Hz as the optimization goal, coordinately optimize the topological variables and geometric variables, establish a collaborative optimization mathematical model based on the optimization goal and the stiffness matrix, and solve the sensitivity of each design variable of the uniform plate. If the design variables meet the preset convergence conditions, the optimal design variables are output. If the preset convergence conditions are not met, the design variables are modified and iterated, and finally the following is obtained: Fig.16 The collaborative optimization results shown are Fig.15 represents the optimization result of a uniform plate with only the stiffened structure designed. Fig.16 It represents the collaborative optimization results of the acoustic black hole and reinforced structure design. The green circles represent the distribution results of the acoustic black hole.

[0121] The fifth step is to compare the collaborative optimization results of the reinforced structure design of this application with the acoustic black hole structure ( Fig.16 Results for a uniform plate designed for both an acoustic black hole and a stiffened structure) compared to a uniform plate designed for a stiffened structure only ( Fig.15 The vibration reduction effect of the uniform plate with only reinforced structure design in the Fig.17 As shown, it can be clearly seen that compared with the design method of the uniform flat plate with only a reinforced structure design (red curve), the collaborative optimization result of the present application (green curve) suppresses the vibration of the flat plate in a wide frequency range of 300-2000 Hz, and achieves a better vibration reduction effect after 1200 Hz through the acoustic black hole structure, proving the effectiveness of the design method proposed in the present invention.

[0122] Although the present application provides method operation steps such as embodiments or flow charts, more or fewer operation steps may be included based on conventional or non-creative labor. The order of steps listed in this embodiment is only one way of executing the order of many steps and does not represent the only execution order. When the actual device or client product is executed, it can be executed in the order of the method shown in this embodiment or the accompanying drawings or in parallel (for example, in a parallel processor or multi-threaded processing environment).

[0123] like Figure 2As shown, the embodiment of the present application also provides an embedded acoustic black hole reinforced flat plate modeling and topology optimization design device 200. The device includes: an iterative execution module 201, a modeling module 202, a coupling module 203, a constraint module 204 and a solution module 205, as follows.

[0124] The iterative execution module 201 is used to iteratively execute the optimization steps until the optimization result meets the convergence condition and the optimal design variables are obtained.

[0125] The iterative execution module 201 integrates a modeling module 202 , a coupling module 203 , a constraint module 204 and a solving module 205 .

[0126] The modeling module 202 is used to divide the design domain into units based on the defined design variables to construct a collaborative optimization model. The reinforced area in the design domain is divided by solid units. The flat plate area in the design domain is divided by variable thickness shell units to simulate the acoustic black hole.

[0127] The coupling module 203 is used to couple the variable thickness shell element with the solid element to obtain a coupled element and determine its stiffness matrix.

[0128] The constraint module 204 is used to introduce maximum size constraints and / or geometric non-interference constraints and / or geometric-topological non-interference constraints and / or draft constraints into the design variables to optimize the collaborative optimization model.

[0129] The solution module 205 is used to solve the sensitivity of the design variables based on the optimization target combined with the stiffness matrix, and obtain the optimization results of the optimized collaborative optimization model. If the optimization results do not meet the convergence conditions, the design variables are redefined based on the sensitivity and the optimization steps are performed.

[0130] Some modules in the apparatus described in the present application can be described in the general context of computer executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc. that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0131] The devices or modules described in the above application embodiments can be implemented by computer chips or entities, or by products with certain functions. For the convenience of description, the above devices are described in various modules according to their functions. When implementing the embodiments of the present application, the functions of each module can be implemented in the same or multiple software and / or hardware. Of course, the module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0132] The methods, devices or modules described in this application can be implemented in the form of computer-readable program codes. The controller can be implemented in any appropriate manner. For example, the controller can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program codes (such as software or firmware) that can be executed by the (micro)processor, logic gates, switches, application-specific integrated circuits (English: Application Specific Integrated Circuit; Abbreviation: ASIC), programmable logic controllers and embedded microcontrollers. Examples of controllers include but are not limited to the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20 and Silicone Labs C8051F320. The memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art also know that in addition to implementing the controller in the form of pure computer-readable program codes, the controller can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, this controller can be considered as a hardware component, and the devices included in it for implementing various functions can also be regarded as structures within the hardware component. Or even, the means for realizing various functions may be regarded as both a software module for realizing the method and a structure within a hardware component.

[0133] An embodiment of the present application further provides a device, comprising: a processor; a memory for storing processor executable instructions; when the processor executes the executable instructions, the method described in the embodiment of the present application is implemented.

[0134] In addition, each functional module in each embodiment of the present invention may be integrated into one processing module, or each module may exist independently, or two or more modules may be integrated into one module.

[0135] The above storage media include but are not limited to random access memory (RAM), read-only memory (ROM), cache, hard disk drive (HDD) or memory card. The memory can be used to store computer program instructions.

[0136] Through the description of the above implementation methods, it can be known that those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary hardware. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, or can be embodied in the implementation process of data migration.

[0137] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. All or part of this application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc.

[0138] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit the present application. Although the present application has been described in detail with reference to the aforementioned embodiments, a person of ordinary skill in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A modeling and topology optimization design method for a reinforced flat plate with an embedded acoustic black hole, characterized in that: include: Iterate the optimization steps until the optimization results meet the convergence conditions and obtain the optimal design variables; The optimization step comprises: The design domain is divided into units based on the defined design variables to construct a collaborative optimization model; wherein the reinforced area in the design domain is divided by solid units; and the flat plate area in the design domain is divided by variable thickness shell units to simulate an acoustic black hole; Couple the variable thickness shell element and the solid element to obtain a coupled element, and determine its stiffness matrix; Introducing a maximum size constraint and / or a geometric non-interference constraint and / or a geometric-topological non-interference constraint and / or a draft constraint into the design variables to optimize the collaborative optimization model; Solving the sensitivity of the design variables based on the optimization target and the stiffness matrix, and obtaining the optimization result of the optimized collaborative optimization model; If the optimization result does not meet the convergence condition, the design variables are redefined based on the sensitivity, and the optimization step is performed.

2. The method according to claim 1, characterized in that The design variables include topological variables and geometric variables; The topological variables include the material density of each solid element in the reinforcement area; The geometric variables include the position and radius of the acoustic black hole in the flat plate region.

3. The method according to claim 1, characterized in that The flat plate region in the design domain is divided by variable thickness shell elements to simulate the acoustic black hole, including: Project the cross-sectional thickness variation of the acoustic black hole into a thickness field on a plane; Based on the thickness field, traverse all nodes on the flat plate region to determine the thickness of each node in the flat plate region; The variable thickness shell element is determined according to the thickness of each node in the flat plate region, and an acoustic black hole is simulated based on the variable thickness shell element.

4. The method according to claim 3, characterized in that: The calculation formula for traversing all nodes on the flat plate region to determine the thickness of each node in the flat plate region based on the thickness field is as follows: ； In the formula, represents the thickness of any node in the plate region, Indicates The characteristic projection function of an acoustic black hole on a plane, Represents any node in the flat area The position vector of A power function representing the thickness of an acoustic black hole, Indicates The coordinates of the center of the projection of an acoustic black hole on the plane where the flat plate region is located, represents the thickness of the uniform plate in the flat plate region, Represents the total number of acoustic black holes distributed on the flat plate area.

5. The method according to claim 1, characterized in that The step of coupling the variable thickness shell element and the solid element to obtain a coupled element comprises: If the reinforced area is divided into a single layer by the solid element, then determine the solid element nodes on the contact surface of the solid element, and match the variable thickness shell element nodes on the contact surface of the variable thickness shell element to determine the coupling nodes; Based on the coupling node, the degrees of freedom of the solid unit node and the variable thickness shell unit node are coupled to obtain a coupling unit.

6. The method according to claim 1, characterized in that The step of coupling the variable thickness shell element and the solid element to obtain a coupled element comprises: If the reinforced area is divided into multiple layers by the solid element, then determine the solid element nodes on the contact surface of the solid element in the reinforced area that contacts the variable thickness shell element, and match the variable thickness shell element nodes on the contact surface of the variable thickness shell element to determine the coupling nodes; Based on the coupling node, the degrees of freedom of the solid unit node and the variable thickness shell unit node are coupled to obtain a coupling unit.

7. The method according to claim 1, characterized in that The obtaining of the optimized result of the collaborative optimization model after optimization includes: Based on the constraints, a collaborative optimization mathematical model is established with minimizing the average external force input power as the optimization goal, as follows: ， ； In the formula, represents the average external input power, a pseudo-density vector representing the material density of the solid element in the reinforced region, A vector set of geometric variables representing the acoustic black hole in the slab region, represents the frequency of the input external force, represents taking the real part of a complex number, for , indicating plural units, represents the external load vector, represents the conjugate transposed matrix of the external force, represents the displacement matrix of the collaborative optimization model, represents the stiffness matrix of the collaborative optimization model, represents the volume of the material in the reinforced area, The upper limit of the allowable material volume in the reinforced area, represents the p-norm condensed form of the maximum size constraint, Indicates geometric non-interference constraints, Indicates geometric-topological non-interference constraints, represents the pseudo-density value of the i-th entity element, represents the number of geometric non-interference constraints, represents the number of acoustic black holes in the slab region, Represents the number of solid elements in the stiffened area.

8. A device for modeling and topology optimization design of a reinforced flat plate with an embedded acoustic black hole, characterized in that: include: Iterative execution module, used to iteratively execute optimization steps until the optimization results meet the convergence conditions and obtain the optimal design variables; The optimization step comprises: A modeling module, for performing unit division on the design domain based on the defined design variables to construct a collaborative optimization model; wherein the reinforced area in the design domain is divided by solid elements; and the flat plate area in the design domain is divided by variable thickness shell elements to simulate an acoustic black hole; A coupling module, used for coupling the variable thickness shell element with the solid element to obtain a coupled element, and determining its stiffness matrix; A constraint module, used for introducing a maximum size constraint and / or a geometric non-interference constraint and / or a geometric-topological non-interference constraint and / or a draft constraint into the design variables to optimize the collaborative optimization model; A solution module, used for solving the sensitivity of the design variables based on the optimization target in combination with the stiffness matrix, and obtaining the optimization result of the optimized collaborative optimization model; If the optimization result does not meet the convergence condition, the design variables are redefined based on the sensitivity, and the optimization step is performed.

9. A device for executing a method for modeling and topology optimization of a reinforced flat plate with an embedded acoustic black hole, characterized in that: include: processor; a memory for storing processor-executable instructions; When the processor executes the executable instructions, the method according to any one of claims 1 to 7 is implemented.

10. A non-volatile computer-readable storage medium, characterized in that: The device comprises a computer program or an instruction for storing the computer program or the instruction, which, when executed, enables the method according to any one of claims 1 to 7 to be implemented.

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