Fan blade topological optimization method based on truss-continuum hybrid grid finite element model

Abstract

The invention provides a fan blade topological optimization method based on a truss-continuum hybrid grid finite element model, and belongs to the technical field of fan blade optimization design. According to the method, a quadrilateral unit is adopted to simulate a composite material base body in the fan blade, a truss unit is adopted to simulate reinforced fibers in the fan blade, a truss-continuum mixed mesh finite element model is constructed, topological optimization is performed on the basis of the truss-continuum mixed mesh finite element model, and therefore the composite material base body in the fan blade is simulated. The structural difference between the composite material matrix and the reinforced fibers is comprehensively considered, the optimization accuracy can be improved, and the expected requirement is met.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimized design of fan blades, and particularly relates to a topology optimization method for fan blades based on a truss-continuum hybrid mesh finite element model. Background Technique

[0002] As a core component of a wind turbine, the performance of a wind turbine blade directly affects the power generation efficiency, power generation cost, and service life. The design method of a wind turbine blade usually adopts topology optimization.

[0003] In related technologies, in the topology optimization process of a wind turbine blade, the design domain is directly considered as a continuum structure, and quadrilateral elements are used for mesh division. However, in the actual manufacturing process of a wind turbine blade, in addition to a composite matrix, it also includes a fiber structure for reinforcement. The fiber structure is arranged in a staggered manner in the composite matrix. The traditional mesh division form treats the fiber structure and the composite matrix as a whole, ignoring the structural differences between the fiber structure and the composite matrix itself, and the optimization result is difficult to meet the expected requirements.

[0004] Therefore, it is necessary to provide a topology optimization method for fan blades based on a truss-continuum hybrid mesh finite element model to solve the above problems. Summary of the Invention

[0005] The present invention provides a topology optimization method for fan blades based on a truss-continuum hybrid mesh finite element model. Quadrilateral elements are used to simulate the composite matrix in the fan blade, and truss elements are used to simulate the reinforcing fibers in the fan blade. A truss-continuum hybrid mesh finite element model is constructed, and topology optimization is carried out on the basis of the truss-continuum hybrid mesh finite element model. The structural differences between the composite matrix and the reinforcing fibers are comprehensively considered, which can improve the accuracy of optimization, meet the expected requirements, and effectively solve at least one technical problem involved in the background technique.

[0006] In order to solve the above technical problems, the present invention is implemented as follows:

[0007] A topology optimization method for fan blades based on a truss-continuum hybrid mesh finite element model includes the following steps:

[0008] Step S1, define the design domain of the fan blade, perform mesh division on the design domain, use quadrilateral continuum elements to simulate the composite matrix in the fan blade, use truss elements to simulate the reinforcing fibers in the fan blade, and construct a truss-continuum hybrid mesh;

[0009] Step S2, use the cross-sectional area of the truss element and the volume fraction of the continuum element as design variables, and use the minimum total compliance of the structure as the optimization goal to construct a truss-continuum hybrid mesh finite element model;

[0010] In step S3, perform finite element analysis on the truss-continuum hybrid mesh finite element model, update the design variables based on the calculated sensitivity, and iterate multiple times until the model converges or reaches the maximum number of iterations to complete the optimization process.

[0011] As a preferred improvement, step S1 specifically includes the following steps:

[0012] In step S11, define the design domain of the fan blade, divide the design domain into multiple super-element mesh modules, and each super-element mesh module includes multiple quadrilateral continuum elements to simulate the composite matrix in the fan blade with the continuum elements.

[0013] In step S12, construct truss elements by using the node interconnection method of adjacent two super-element mesh modules to simulate the reinforcing fibers in the fan blade with the truss elements.

[0014] In step S13, construct a truss-continuum hybrid mesh by using the displacement consistency of the shared nodes of the continuum elements and truss elements and the finite element shape function.

[0015] As a preferred improvement, taking the cross-sectional area ρ t of the truss element as the design variable, the stiffness matrix of the truss element is expressed as:

[0016] In the formula, represents the stiffness matrix of truss element e1; represents the design variable of truss element e1; represents the stress of truss element e1; η t represents the penalty parameter of the truss element; represents the stiffness matrix of truss element e1; E t represents the Young's modulus of the truss element;

[0017] Taking the volume fraction ρ c of the continuum element as the design variable, the stiffness matrix of the continuum element is expressed as:

[0018]

[0019] In the formula, represents the stiffness matrix of continuum element e2; represents the design variable of continuum element e2; represents the stress of continuum element e2; η c represents the penalty parameter of the continuum element; represents the minimum threshold of the design variable of continuum element e2; Denote the stiffness matrix of the continuum element e2; D(g) denotes the constitutive stiffness tensor of the continuum element e2; Denote the basic components of the standard strain-displacement tensor, satisfying ε = Bu, where ε represents the strain of the continuum element e2, and u represents the displacement of the element e2; T represents the transpose matrix; V2 represents the volume of the continuum element e2.

[0020] As a preferred improvement, the approximate value D of the stiffness tensor of the continuum element e2 p is defined in the principal stress coordinate system as follows:

[0021]

[0022] In the formula, D11 and D22 respectively denote the modulus values in the first and second principal directions, ν eff denotes the Poisson's ratio of the isotropic material;

[0023] Since the elastic modulus of the isotropic material is not equal in the compression and tension states, D ij (i = 1, 2; j = 1, 2) depends on the principal normal stress σ of the material ci , and it is necessary to introduce an if operator to represent it, as shown below:

[0024]

[0025] In the formula, ν i denotes the Poisson's ratio, ν ct denotes the elastic modulus under tensile load, and ν1, ν2 are used to calculate the equivalent elastic modulus ν eff ;

[0026] Introduce the Sigmoid function to construct the smoothed D 11 、D 22 expressions, which are expressed as:

[0027]

[0028] In the formula, E tc and E tt are the Young's moduli of the material under compression and tension; ν tc and ν tt are the Poisson's ratios of the isotropic material under compression and tension, ν tt = ν tc E tt / E tc , so as to ensure the symmetry of D p ; is the set influence factor;

[0029] The principal stress σ i and the direction θ of the principal plane are calculated in the following standard manner:

[0030]

[0031] Wherein, σ x and σ y both represent the normal stress in the global coordinate system, and τ xy represents the shear stress in the global coordinate system;

[0032] The constitutive stiffness tensor of the continuum element e2 is defined in the principal coordinate system and then transformed into the global coordinate system using the following formula:

[0033] D = Q T D P Q;

[0034] Wherein, Q represents the transformation tensor and is expressed as:

[0035]

[0036] As a preferred improvement, the topology optimization model is expressed as:

[0037]

[0038] Wherein, f(g) represents the structural response function, F represents the load vector applied to the structure, U represents the structural displacement, Ω t and Ω c represent the design domains of the truss and the continuum respectively, V represents the volume constraint value, and are the length of the truss element and the volume of the continuum element respectively, and K(g) represents the global stiffness matrix;

[0039]

[0040] The beneficial effects of the present invention are as follows:

[0041] The composite material matrix in the fan blade is simulated by quadrilateral elements, and the reinforcing fibers in the fan blade are simulated by truss elements to construct a truss-continuum hybrid mesh finite element model. Topology optimization is carried out on the basis of the truss-continuum hybrid mesh finite element model, taking into account the structural differences between the composite material matrix and the reinforcing fibers, which can improve the accuracy of the optimization and meet the expected requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts, where:

[0043] Figure 1 Schematic diagram showing the design domain in Embodiment 1;

[0044] Figure 2 Schematic diagram of the truss - continuum hybrid mesh in Embodiment 1;

[0045] Figure 3 Schematic diagram showing the optimization result in Embodiment 1. Detailed implementation manner

[0046] Next, in combination with the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0047] This implementation manner provides a topology optimization method for a wind turbine blade based on a truss - continuum hybrid mesh finite element model, including the following steps:

[0048] Step S1, define the design domain of the wind turbine blade, perform mesh division on the design domain, simulate the composite matrix in the wind turbine blade with quadrilateral continuum elements, simulate the reinforcing fibers in the wind turbine blade with truss elements, and construct a truss - continuum hybrid mesh;

[0049] Step S1 specifically includes the following steps:

[0050] Step S11, define the design domain of the wind turbine blade, divide the design domain into multiple super - element mesh modules, each super - element mesh module includes multiple quadrilateral continuum elements, and simulate the composite matrix in the wind turbine blade with the continuum elements;

[0051] Step S12, construct truss elements by using the node interconnection method of adjacent two super - element mesh modules, and simulate the reinforcing fibers in the wind turbine blade with the truss elements;

[0052] Step S13, construct a truss - continuum hybrid mesh by using the displacement consistency of the shared nodes of the continuum elements and the truss elements and the finite - element shape function.

[0053] Specifically, in this embodiment, in order to reduce the complexity of the final mixed mesh finite element model, a relative node spacing of n:1, where n > 1, is adopted, that is, one node is selected as a shared node every n nodes of the truss structure for the connection between trusses and the force transfer between meshes. The establishment range of the truss element is limited within two adjacent super-element mesh modules to reduce the complexity of the initial truss structure. In the truss-continuum composite structure, the continuum element has good compressive performance, and the truss element is embedded between the continuum elements and has good tensile performance, so that the structure formed by the combination of the two has good compressive and tensile performance.

[0054] Step S2: Using the cross-sectional area of the truss element and the volume fraction of the continuum element as design variables, and with the minimum total compliance of the structure as the optimization objective, a truss-continuum mixed mesh finite element model is constructed.

[0055] Taking the cross-sectional area ρ of the truss element t as the design variable, the stiffness matrix of the truss element is expressed as:

[0056] In the formula, represents the stiffness matrix of the truss element e1; represents the design variable of the truss element e1; represents the stress of the truss element e1; η t represents the penalty parameter of the truss element; represents the stiffness matrix of the truss element e1; E t represents the Young's modulus of the truss element;

[0057] Taking the volume fraction ρ of the continuum element c as the design variable, the stiffness matrix of the continuum element is expressed as:

[0058]

[0059] In the formula, represents the stiffness matrix of the continuum element e2; represents the design variable of the continuum element e2; represents the stress of the continuum element e2; η c represents the penalty parameter of the continuum element; represents the minimum threshold of the design variable of the continuum element e2; represents the stiffness matrix of the continuum element e2; D(g) represents the constitutive stiffness tensor of the continuum element e2; represents the basic component of the standard strain-displacement tensor, satisfying ε = Bu, where ε represents the strain of the continuum element e2, u represents the displacement of the element e2; T represents the transpose matrix; V2 represents the volume of the continuum element e2.

[0060] Approximation value D of the stiffness tensor of the continuum element e2 p Is defined in the principal stress coordinate system as follows:

[0061]

[0062] Where D11 and D22 represent the modulus values in the first and second principal directions respectively, and ν eff Represents the Poisson's ratio of the isotropic material;

[0063] Since the elastic modulus of the isotropic material is not equal in the compression and tension states, D ij (i = 1, 2; j = 1, 2) depends on the principal normal stress σ ci Of the material and an if operator needs to be introduced to represent it, as shown below:

[0064]

[0065] Where ν i Represents the Poisson's ratio, ν ct Represents the elastic modulus under tensile load, and ν1, ν2 are used to calculate the equivalent elastic modulus ν eff .

[0066] The use of the if operator makes the constitutive stiffness tensor matrix of the continuum element e2 non-smooth, resulting in difficulties in solving the sensitivity of the structural flexibility and reducing the topological optimization calculation efficiency. To solve this problem, the present application further introduces the Sigmoid function to construct a smoothed D 11 And D 22 Expressions, which are expressed as:

[0067]

[0068] Where E tc And E tt Are the Young's moduli of the material under compression and tension; ν tc And ν tt Are the Poisson's ratios of the isotropic material under compression and tension, and ν tt = ν tc E tt / E tc To ensure the symmetry of D p ; Is the set influence factor.

[0069] The principal stress σ i And the direction θ of the principal plane are calculated in the following standard way:

[0070]

[0071] Where σ x, σ y both represent the normal stress in the global coordinate system, and τ xy represents the shear stress in the global coordinate system.

[0072] The constitutive stiffness tensor of the continuum element e2 is defined in the principal coordinate system and then transformed to the global coordinate system using the following formula:

[0073] D = Q T D P Q;

[0074] where Q represents the transformation tensor and is expressed as:

[0075]

[0076] Then, the topology optimization model is expressed as:

[0077]

[0078] where f(g) represents the structural response function, F represents the load vector applied to the structure, U represents the structural displacement, Ω t , Ω c represent the design domains of the truss and continuum respectively, V represents the volume constraint value, and are the length of the truss element and the volume of the continuum element respectively, and K(g) represents the global stiffness matrix;

[0079]

[0080] Step S3: Perform finite element analysis on the truss-continuum hybrid mesh finite element model, update the design variables based on the calculated sensitivities, and iterate multiple times until the model converges or reaches the maximum number of iterations to complete the optimization process.

[0081] The processes of finite element analysis and optimization adopt the existing technologies in the field, and specifically include the following steps:

[0082] (1) Initialize the design variables ρ t and ρ c ;

[0083] (2) Solve the linear elastic problem K(ρ t = 200 GPa)d = F for the truss elements, and all continuum elements (E t , ρ c ) are isotropic (i.e., all elements are fully stiff); c = 24.9 GPa)

[0084] (3) Update the truss element stiffness matrix and the continuum element stiffness matrix, and solve K(ρt , ρ c , σ t , σ c ) d = F;

[0085] (4) Calculate the sensitivity and update the design variable ρ based on the gradient-based optimizer t and ρ c ;

[0086] (5) Iterate multiple times until the model converges or reaches the maximum number of iterations to complete the optimization process.

[0087] Example 1

[0088] The design domain of the fan blade provided in this example is as Figure 1 shown. The structural dimensions of the design domain are 480 mm × 120 mm. The load F acts on the midpoint of the lower side line of the structure, with a magnitude of 10 N and a direction vertically downward; fixed constraints are applied to the lower left and lower right vertices of the structure.

[0089] Perform mesh element division on the structure, as Figure 2 shown. For the continuum structure, 480 × 120 plane quadrilateral finite element units are used for division. For the truss structure, 1 node out of every 20 continuum element nodes is taken as a shared node, and the quadrilateral area divided by the shared nodes is called the super-element mesh module, that is, 480 × 120 continuum elements are divided into 24 × 6 super-element mesh modules.

[0090] It should be noted that:

[0091] To reduce the complexity of the truss structure design domain, the connection of each shared node does not exceed the range of adjacent two super-element mesh modules, and each super-element contains 30 × 30 quadrilateral continuum elements.

[0092] During the design process, different optimization results are obtained by changing the elastic modulus value of the material, and the influence of different parameters on the results is explored. To simplify the description and calculation, this example of the present invention mainly considers two-dimensional problems, and only gives different optimization results after changing the elastic modulus of the matrix material, that is, changing the ratio of the tensile elastic modulus to the compressive elastic modulus of the matrix material. However, the above criteria can be extended to the research of three-dimensional problems and different optimization results can be obtained by changing other parameters without any obstacles.

[0093] In this example, by fixing the elastic modulus of the truss element and taking the compression modulus E of the continuum element cc = 2.5×10 4 Mpa, R cTake 2.5, 12.5, 25, and 125 respectively, and the corresponding tensile moduli are 1×104 Mpa, 2×103 Mpa, 1×103 Mpa, and 5×102 Mpa. Optimize them respectively using the optimization method provided by this application, and the optimization results are as Figure 3 shown.

[0094] The following conclusions can be drawn from the optimization results:

[0095] First, clear topological optimization results can be obtained under each working condition. The upper part of the structure mainly bears compressive loads and distributes more matrix materials, while the lower part of the structure mainly bears tensile loads and distributes more reinforcing fiber materials;

[0096] Second, when other parameters are the same, as R c increases, the tensile modulus of the continuum element decreases, and the objective function of the optimization result increases accordingly. This is because as the elastic modulus decreases, the overall stiffness of the structure decreases, and the compliance value, that is, the objective function, increases accordingly;

[0097] Third, as R c increases, the number and cross-sectional area of the strut structures formed by the matrix materials in the lower part of the structure decrease, and more matrix materials move closer to the upper part of the structure; on the contrary, the distributed reinforcing fiber materials in the upper part decrease, and more move closer to the lower part of the structure;

[0098] The above results verify the feasibility of the optimization method provided by this application. The optimization results show that the optimization method proposed by the present invention can solve the non-linearity problem of the elastic modulus of bimodulus materials to a certain extent.

[0099] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the claims of the present invention, and all of them belong to the protection scope of the present invention.

Claims

1. A topology optimization method for a wind turbine blade based on a truss-continuum hybrid mesh finite element model, characterized in that, It includes the following steps: Step S1: Define the design domain of the fan blade, perform mesh division on the design domain, simulate the composite matrix in the fan blade with quadrilateral continuum elements, simulate the reinforcing fibers in the fan blade with truss elements, and construct a truss-continuum hybrid mesh; Step S2: Use the cross-sectional area of the truss element and the volume fraction of the continuum element as design variables, and construct a truss-continuum hybrid mesh finite element model with the minimum total compliance of the structure as the optimization goal; Step S3: Perform finite element analysis on the truss-continuum hybrid mesh finite element model, update the design variables based on the calculated sensitivity, and iterate multiple times until the model converges or reaches the maximum number of iterations to complete the optimization process.

2. The topology optimization method of the fan blade based on the truss-continuum hybrid mesh finite element model according to claim 1, wherein, Step S1 specifically includes the following steps: Step S11: Define the design domain of the fan blade, divide the design domain into multiple super-element mesh modules, each super-element mesh module includes multiple quadrilateral continuum elements, and simulate the composite matrix in the fan blade with continuum elements; Step S12: Construct truss elements by using the node interconnection method of two adjacent super-element mesh modules, and simulate the reinforcing fibers in the fan blade with truss elements; Step S13: Construct a truss-continuum hybrid mesh by using the displacement consistency of the shared nodes of the continuum elements and the truss elements and the finite element shape function.

3. The fan blade topology optimization method based on the truss-continuum hybrid mesh finite element model according to claim 1, wherein Taking the cross-sectional area ρ of the truss element t as the design variable, the stiffness matrix of the truss element is expressed as: In the formula, represents the stiffness matrix of truss element e1; represents the design variable of truss element e1; represents the stress of truss element e1; η t represents the penalty parameter of the truss element; represents the stiffness matrix of truss element e1; E t represents the Young's modulus of the truss element; Taking the volume fraction ρ of the continuum element c as the design variable, the stiffness matrix of the continuum element is expressed as: In the formula, represents the stiffness matrix of the continuum element e2; represents the design variable of the continuum element e2; represents the stress of the continuum element e2; η c represents the penalty parameter of the continuum element; represents the minimum threshold of the design variable of the continuum element e2; represents the stiffness matrix of the continuum element e2; D(g) represents the constitutive stiffness tensor of the continuum element e2; represents the basic components of the standard strain-displacement tensor, satisfying ε = Bu, where ε represents the strain of the continuum element e2, u represents the displacement of the element e2; T represents the transpose matrix; V2 represents the volume of the continuum element e2.

4. The method for topologically optimizing a fan blade based on a truss-continuum hybrid mesh finite element model according to claim 3, wherein Approximated stiffness tensor D of continuum element e2 p Defined in the principal stress coordinate system as follows: where D11 and D22 respectively represent the modulus values in the first and second principal directions, and ν eff represents the Poisson's ratio of the isotropic material; Since the elastic modulus of an isotropic material is not equal in compression and tension states, D ij (i = 1, 2; j = 1, 2) depends on the principal normal stress σ ci of the material, and an if operator needs to be introduced to represent it as follows: where ν i denotes the Poisson's ratio, ν ct denotes the elastic modulus under tensile load, and ν1, ν2 are used to calculate the equivalent elastic modulus ν eff ; Introduce the Sigmoid function to construct a smoothed D 11 and D 22 expressions, expressed as: Where, E tc and E tt are the Young's moduli during material compression and tension; ν tc and ν tt are the Poisson's ratios during compression and tension of the isotropic material, ν tt = ν tc E tt / E tc , so as to ensure the symmetry of D p ; is the set influence factor; Principal stress σ i and the direction θ of the principal plane are calculated in the following standard manner: where, σ x , σ y both represent the normal stresses in the global coordinate system, and τ xy represents the shear stress in the global coordinate system; The constitutive stiffness tensor of the continuum element e2 is defined in the principal coordinate system and then transformed into the global coordinate system using the following formula: D = Q T D P Q; In the formula, Q represents the transformation tensor, expressed as:

5. The topology optimization method of the fan blade based on the truss-continuum hybrid mesh finite element model according to claim 4, characterized in that The topology optimization model is expressed as: In the formula, f(g) represents the structural response function, F represents the load vector applied to the structure, U represents the structural displacement, Ω t , Ω c respectively represent the design domains of the truss and the continuum, V represents the volume constraint value, and are respectively the length of the truss element and the volume of the continuum element, and K(g) represents the global stiffness matrix;

Images