CN117690532A - Topology optimization design method and system for fiber reinforced composite structure with variable thickness skin - Google Patents
Topology optimization design method and system for fiber reinforced composite structure with variable thickness skin Download PDFInfo
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Abstract
The invention belongs to the technical field of material structure optimization, and discloses a topology optimization design method and system for a fiber reinforced composite structure with a variable thickness skin, wherein the method comprises the following steps: dividing the mesh of the fiber reinforced composite structure with the outer skin, and defining two groups of Boolean parameters for representing filling materials in the mesh; processing the two groups of Boolean parameters to obtain a first derivative variable and a second derivative variable and Young modulus; correcting the stiffness matrix of the material by adopting the Young modulus to obtain a global stiffness matrix and a global structural displacement matrix; obtaining a filtered radius variable field of each unit based on the structural displacement matrix; and obtaining the local volume fraction of each unit fiber material, and carrying out iterative optimization by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility as an objective function to obtain the structural parameters of the composite structure. The parallel optimization taking the skin material, the matrix material and the fiber material into consideration simultaneously can be realized.
Description
Technical Field
The invention belongs to the technical field of material structure optimization, and particularly relates to a topology optimization design method and system for a fiber reinforced composite structure of a variable-thickness skin.
Background
Fiber Reinforced Composites (FRCs) are composed of a matrix material and fibrous inclusions, which have a higher stiffness to weight ratio than conventional metal materials, and are now widely used in the automotive, robotic, medical, aerospace and aerospace industries. In recent years, with the development of additive manufacturing technologies represented by Fused Deposition Modeling (FDM), metal Additive Manufacturing (MAM), and the like, the manufacturing difficulty of fiber reinforced composite materials with spatially-varying continuous fiber paths has been solved, thereby bringing a considerable degree of design freedom to novel design methods.
FRCs may be designed using long (i.e., continuous) fibers or short fibers; the former is preferred in mission critical applications due to its excellent material properties, dimensional stability and robustness in terms of fiber orientation and bonding, and the latter can serve as a geometric transition when the matrix topology is significantly changed, matching long fibers to improve the mechanical properties of the composite structure. In order for long fiber FRCs to be effective, concurrent optimization of matrix topology, fiber spacing, and fiber orientation must be performed simultaneously in design terms. However, the optimization of the fiber angle of each finite element mesh is a non-convexity problem, not only is the calculation very computationally intensive, but the resulting fiber angle tends to be discontinuous and difficult to use in subsequent manufacturing. The structural conditions in application are often quite complex, and the matrix material and the fiber material are subject to corrosion risk, so that special skin features are required to further enhance structural performance and also to provide corrosion resistance.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a topological optimization design method and a topological optimization design system for a fiber reinforced composite structure of a variable-thickness skin, which can realize parallel optimization by simultaneously considering a skin material, a matrix material and a fiber material, and can generate a continuous fiber path in a full-scale frame for direct use in manufacturing.
In order to achieve the above object, according to one aspect of the present invention, there is provided a topology optimization design method of a fiber reinforced composite structure of a variable thickness skin, the method comprising: s1: dividing a grid of the fiber reinforced composite structure with the outer skin, and defining two sets of Boolean parameters for representing filling materials in the grid, wherein one set of Boolean parameters is used for representing skin parameters and matrix parameters, the other set of Boolean parameters is used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials; s2: carrying out blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing the skin structure, and carrying out blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing the fiber structure; s3: obtaining Young modulus of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters; s4: correcting the stiffness matrix of the material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix; s5: obtaining a filtered radius variable field driven by displacement information in each unit based on the structural displacement matrix; s6: obtaining a local volume fraction of the fibrous material of each unit by taking the second derivative variable as a parameter, and simultaneously presetting an upper limit and a lower limit of the local volume fraction to construct a local volume constraint; and constructing the integral volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters; s7: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
Preferably, in step S4, the stiffness matrix of the material in each unit is corrected by using the young' S modulus to obtain a material stiffness matrix of each unit, the material stiffness matrix of each unit is assembled to obtain a global stiffness matrix, and finite element analysis is performed on the global stiffness matrix to obtain a global structural displacement matrix.
Preferably, in step S3, the young 'S modulus of the filling material is interpolated by SIMP method to obtain the young' S modulus of the composite structure.
Preferably, step S7 further includes obtaining sensitivity information of the objective function and the constraint function, and updating two sets of boolean parameters by using a moving asymptote method based on the sensitivity information to obtain structural parameters of the composite structure.
Preferably, in step S5, the filtered radius variable field R 2 The expression of (2) is:
wherein R is min Is a preset minimum skin thickness; r is R max For a preset maximum skin thickness, ue is the arithmetic mean of the displacements of the four nodes of the grid cell e,for designing the maximum value of the grid cell displacement in the domain +.>Is the minimum value of the grid cell displacement in the design domain.
Preferably, the local volume fraction V is:
where Se is the set of all grid cells e in the neighborhood of grid cells, δ i Is the coordinates of the centroid of grid cell i, delta e Is the coordinates of the centroid of grid cell e, ζ i For the second derivative variable of the grid cell i, i.e. the pseudo-density field characterizing the fibre distribution, R 2 Filtering a radius variable field;
the local volume constraint comprises a maximum m of the local volume constraint V 1 And a minimum value m of the local volume constraint V 2 Wherein:
wherein the local volume fraction of each subdomain is aggregated into a single constraint using a p-norm, N is the number of meshing, V e For the local volume fraction of the neighborhood of element e,lambda is lambda 1 a，/>Lambda is lambda 2 a，λ 1 、λ 2 As coefficients, a is a local volume fraction constraint;
overall volume constraint m 3 The method comprises the following steps:
wherein ρ is 1 、ρ 2 And ρ 3 Represents the density, mu and fiber material of the skin material, the matrix material and the fiber material respectivelyFor the first derivative variable, ζ is the second derivative variable, frac is the upper volume fraction limit of the composite structure.
Preferably, the objective function is:
wherein W is the whole design domain, C (x, y) is the compliance of the composite structure, u i For a displacement matrix of four nodes per grid cell, k (x, y) is the material stiffness matrix of each grid cell.
In another aspect, the present application provides a system for implementing the above-mentioned method for topology optimization design of a fiber-reinforced composite structure with a variable thickness skin, where the system includes: partitioning and definition module: the method comprises the steps of carrying out grid division on a fiber reinforced composite structure with an outer skin, and defining two groups of Boolean parameters for representing filling materials in the grid, wherein one group of Boolean parameters are used for representing skin parameters, the other group of Boolean parameters are used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials; the processing module is used for: the method comprises the steps of performing blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing a skin structure, and performing blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing a fiber structure; a first acquisition module: obtaining Young's modulus of the fiber reinforced composite structure of the outer skin by taking the first derivative variable and the second derivative variable as parameters; and a second acquisition module: the method comprises the steps of correcting a stiffness matrix of a material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix; and a third acquisition module: obtaining a filtered radius variable field in each cell driven by displacement information based on the structural displacement matrix; a fourth acquisition module: obtaining a local volume fraction of the fibrous material of each unit with the second derivative variable as a parameter, while specifying upper and lower limits of the local volume fraction to construct a local volume constraint; and constructing the integral volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters; and a solving module: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
The third aspect of the application provides a fiber reinforced composite structure with a variable-thickness skin, which is designed by adopting the fiber reinforced composite structure topology optimization design method with the variable-thickness skin.
In general, compared with the prior art, the fiber reinforced composite structure topology optimization design method and system for the variable-thickness skin mainly have the following beneficial effects:
1. the integrated topology optimization framework of the skin fiber reinforced composite structure is established by uniformly considering the skin material, the matrix material and the fiber material, and the two groups of Boolean parameters are adopted for characterization, so that the calculation cost is saved, the variable field of the filter radius for controlling the thickness of the skin is constructed, and further, the variable field can be directly driven by displacement information obtained by finite element analysis.
2. The fiber path optimization method established on the full-scale topological optimization framework can obtain fiber distribution with spatial variation and continuous paths by utilizing local volume constraint, and the problem of fiber angle dispersion caused by a scale separation design method is avoided.
3. The topological optimization framework provided by the application can optimize three geometric characteristics of solid topology, fiber morphology and skin thickness in parallel, and the problems of complex design process, limited optimality and the like caused by serial and repeated optimization are avoided. And the three characteristics are controlled by optimizing parameters such as total volume fraction, local volume fraction, preset skin maximum/minimum thickness control and the like, so that a designer can conveniently regulate and control according to engineering requirements.
4. The application provides a brand new fiber composite structure configuration, wherein the coating is wrapped on the outer full size of the matrix material, so that the wear resistance, corrosion resistance and fatigue resistance of the composite structure can be effectively improved, and the inner matrix material and the fiber material are protected to prolong the service life of the composite structure.
Drawings
FIG. 1 is a schematic step diagram of a fiber reinforced composite structure topology optimization design method for a variable thickness skin of the present application;
FIG. 2 is a schematic diagram of the modeling of a fiber reinforced composite structure of the variable thickness skin of the present application;
FIG. 3 is a flow chart of a method of topology optimization design of a fiber reinforced composite structure of the variable thickness skin of the present application;
FIG. 4 is a cantilever beam of an embodiment of the present application;
fig. 5 is a fiber reinforced composite structure with a variable thickness skin, as referred to in the examples of this application.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention provides a fiber reinforced composite structure topology optimization design method of a variable-thickness skin, which mainly comprises the following steps S1-S7 as shown in figures 1 and 3.
S1: the method comprises the steps of meshing a fiber reinforced composite structure with an outer skin, and defining two sets of Boolean parameters representing filling materials in the mesh, wherein one set of Boolean parameters is used for representing skin parameters and matrix parameters, the other set of Boolean parameters is used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials.
Each grid cell can be filled with one of a void, a skin material, a matrix material or a fiber material, and due to the special modeling property of the material model in the application, the filling state of each cell can be described only by designing two groups of design variables x and y, and particularly the generation process of the skin material, the matrix material and the fiber material is shown in fig. 2.
S2: and carrying out blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing the skin structure, and carrying out blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing the fiber structure.
The process of blurring and projecting the Boolean parameter x is as follows:
blurring process:
the projection process comprises the following steps:
blurring process:
the projection process comprises the following steps:
the process of blurring and projecting the Boolean parameter y is as follows:
blurring process:
the projection process comprises the following steps:
wherein mu andin order to be dependent on the first derivative variable of x, ζ is dependent on the second derivative variable of y, ρ 1 、ρ 2 And ρ 3 Representing the densities of the outer skin material, the matrix material and the fibre material, respectively, beta is increased stepwise from 1 to 128 in the optimization iteration. In the present embodiment, the projection threshold η 1 The value is 0.5, and the projection threshold value eta 2 Take a value of 0.95 so that the corrosion density field generates an outer skin, R 1 And R is 3 Is the filter radius of two groups of variable fields x and y, R 2 The variable field of the filter radius for controlling the thickness of the outer skin is driven by displacement information obtained by finite element analysis.
The material model of the fiber-reinforced composite structure with the outer skin can then be expressed as:
wherein ρ is shell 、ρ matrix And ρ fiber Representing the density fields of the outer skin material, the matrix material and the fibre material, respectively.
S3: and taking the first derivative variable and the second derivative variable as parameters to obtain the Young modulus of the fiber reinforced composite structure with the outer skin.
In a further preferred scheme, the young modulus E of the composite structure is obtained by interpolating the young modulus of the filling material by adopting a SIMP (Solid Isotropic Material with Penalization, punished solid isotropic material) method, and the specific formula is as follows:
wherein E is 1 、E 2 And E is 3 Young's modulus of the outer skin material, the matrix material and the fiber material respectively, E in order to avoid matrix singularity min Take 10 in the present application -9 Gamma is a penalty for intermediate density, and in this application gamma has a value of 3.
S4: and correcting the stiffness matrix of the material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix.
The Young modulus is adopted to correct the rigidity matrix of the material in each unit to obtain the material rigidity matrix of each unit, the material rigidity matrix of each unit is assembled to obtain a global rigidity matrix, and finite element analysis is carried out on the global rigidity matrix to obtain a global structural displacement matrix.
S5: and obtaining a filtered radius variable field driven by displacement information in each unit based on the structural displacement matrix.
Calculating the filter radius of each grid cell sub-pair variable field mu for optimizing the thickness of the outer skin, and driving the filter radius variable field R by displacement 2 The expression of (2) is:
wherein R is min Is a preset minimum skin thickness; r is R max For a preset maximum skin thickness, U e Is the arithmetic mean of the displacements of the four nodes of the grid cell e,for designing the maximum value of the grid cell displacement in the domain +.>Is the minimum value of the grid cell displacement in the design domain.
S6: obtaining a local volume fraction of the fibrous material of each unit by taking the second derivative variable as a parameter, and simultaneously presetting an upper limit and a lower limit of the local volume fraction to construct a local volume constraint; and constructing the overall volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters.
Directly optimizing fiber paths in a full-scale topological optimization model based on local volume constraint, wherein the local volume fraction of fiber materials of each subdomain of a pseudo-density field xi for representing fiber distribution is as follows:
where Se is the set of all grid cells e in the neighborhood of grid cells, δ i Is the coordinates of the centroid of grid cell i, delta e Is the coordinates of the centroid of grid cell e, ζ i For the second derivative variable of the grid cell i, i.e. the pseudo-density field characterizing the fibre distribution, R 2 Filtering a radius variable field;
the local volume constraint comprises a maximum m of the local volume constraint V 1 And a minimum value m of the local volume constraint V 2 Wherein:
wherein the local volume fraction of each subdomain is aggregated into a single constraint using a p-norm, N is the number of meshing, V e For the local volume fraction of the neighborhood of element e,lambda is lambda 1 a，/>Lambda is lambda 2 a，λ 1 、λ 2 As coefficients, a is a local volume fraction constraint;
the optimization framework proposed in the present application comprises two volume constraints, an overall volume fraction of the fiber reinforced composite structure and a local volume fraction of the fiber material of each neighborhood, wherein the overall volume constraint m of the fiber reinforced composite structure 3 The method comprises the following steps:
wherein ρ is 1 、ρ 2 And ρ 3 Represents the density, mu and fiber material of the skin material, the matrix material and the fiber material respectivelyFor the first derivative variable, ζ is the second derivative variable, frac is the upper volume fraction limit of the composite structure.
S7: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
The objective function is:
wherein W is the whole design domain, C (x, y)Is the flexibility of the composite structure, mu i For the displacement matrix of the four nodes of the ith grid cell, k (x, y) is the material stiffness matrix of each grid cell.
And step S7, acquiring sensitivity information of an objective function and a constraint function, and updating two groups of Boolean parameters by a moving asymptote method based on the sensitivity information to acquire structural parameters of the composite structure.
k 0 For a cell stiffness matrix with a material density of "1", the sensitivity of the objective function is:
wherein:
the sensitivity of the constraint function is:
the sensitivity is derived according to the chain rule, where the sensitivity of the intermediate variable is given by:
based on the obtained sensitivity information of the objective function and the constraint function, two groups of design variables are updated by using a moving asymptote method. Judging whether convergence is carried out after each updating, and if the convergence is carried out, directly outputting two groups of pseudo-density fields of the skin fiber reinforced composite structure and the optimal layout of skin materials, matrix materials and fiber materials; if not, returning to step S2.
Examples
As shown in fig. 4 to 5, the cantilever beam calculation example is used to explain the method according to the present invention in detail. To simplify the problem, the values used in the calculations are dimensionless. The initial design domain is a cantilever beam with length l=20 and width w=10 as shown in fig. 4, the center of the right side of the beam has a concentrated force f=1 vertically downward, and the left side of the beam is applied with a fixed constraint. The design domain is divided into 200×400Q 4 units, the young modulus of the skin material is 2, the young modulus of the matrix material is 1, and the young modulus of the fiber material is 15. The poisson's ratio of each material was 0.3. The allowed maximum thickness of the skin is 4, the minimum thickness is 2, the influencing radius R2 of the local volume constraint of the fiber material is 7, the upper limit of the local volume fraction is 0.25, and the upper limit of the volume fraction of the macrostructure is 0.6.
The optimized fiber reinforced composite structure with variable thickness skin is shown in fig. 5, the thickness of the outer skin is driven by the structural displacement field, and the trend that the thickness of the outer skin of the structure shown in fig. 5 gradually increases from left to right can be seen, because the deformation of the cantilever beam gradually increases from left to right, which is consistent with the engineering experience of people. In addition, the continuous long fibers are naturally distributed in the matrix material, which fibers are almost parallel in the main force transfer area. The fiber intersection phenomenon occurs when the macroscopic physical topology is obviously changed, because the corresponding local maximum stress direction in the region is obviously changed, and the fiber morphology needs to be changed in a transition way in cooperation with the change of the macroscopic geometric topology characteristics so as to meet the requirement of local reinforcement. Compared with the traditional fiber reinforcement method, the method provided by the invention can realize parallel optimization of the matrix material and the fiber material, and the fiber material is continuously distributed in a full-scale topological optimization frame. In addition, the invention can also design the outer skin with variable thickness to prevent the base material and the fiber from being corroded, the thickness of the skin is driven by the structural displacement information, and the design freedom degree is further expanded.
The second aspect of the present application provides a system for implementing the above-mentioned method for topology optimization design of a fiber-reinforced composite structure with a variable thickness skin, the system comprising:
partitioning and definition module: the method comprises the steps of carrying out grid division on a fiber reinforced composite structure with an outer skin, and defining two sets of Boolean parameters for representing filling materials in the grid, wherein one set of Boolean parameters is used for representing skin parameters and matrix parameters, the other set of Boolean parameters is used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials;
the processing module is used for: the method comprises the steps of performing blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing a skin structure, and performing blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing a fiber structure;
a first acquisition module: obtaining Young's modulus of the fiber reinforced composite structure of the outer skin by taking the first derivative variable and the second derivative variable as parameters;
and a second acquisition module: the method comprises the steps of correcting a stiffness matrix of a material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix;
and a third acquisition module: obtaining a filtered radius variable field in each cell driven by displacement information based on the structural displacement matrix;
a fourth acquisition module: obtaining a local volume fraction of the fibrous material of each unit by taking the second derivative variable as a parameter, and simultaneously presetting an upper limit and a lower limit of the local volume fraction to construct a local volume constraint; and constructing the integral volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters;
and a solving module: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
The third aspect of the application provides a fiber reinforced composite structure with a variable-thickness skin, which is designed by adopting the fiber reinforced composite structure topology optimization design method with the variable-thickness skin.
According to the fiber reinforced composite structure topology optimization design method and system for the variable-thickness skin, disclosed by the invention, the skin material, the matrix material and the fiber material are uniformly considered and optimized in the same model, so that parallel optimization of different characteristics is realized. The thickness of the skin is driven by displacement of the macroscopic structure, the thickness of the skin is increased at the place with large deformation to prevent corrosion and abrasion, and the thickness of the skin is reduced at the place with small deformation to reduce the cost. Meanwhile, continuous fiber paths can be directly generated in the full-scale topological optimization framework, so that scale separation is avoided, and subsequent manufacturing of the fiber reinforced composite structure is facilitated.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The topological optimization design method of the fiber reinforced composite structure with the variable thickness skin is characterized by comprising the following steps of:
s1: dividing a grid of the fiber reinforced composite structure with the outer skin, and defining two sets of Boolean parameters for representing filling materials in the grid, wherein one set of Boolean parameters is used for representing skin parameters and matrix parameters, the other set of Boolean parameters is used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials;
s2: carrying out blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing the skin structure, and carrying out blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing the fiber structure;
s3: obtaining Young modulus of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters;
s4: correcting the stiffness matrix of the material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix;
s5: obtaining a filtered radius variable field driven by displacement information in each unit based on the structural displacement matrix;
s6: obtaining a local volume fraction of the fibrous material of each unit by taking the second derivative variable as a parameter, and simultaneously presetting an upper limit and a lower limit of the local volume fraction to construct a local volume constraint; and constructing the integral volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters;
s7: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
2. The method according to claim 1, wherein step S4 is specifically that the young' S modulus is adopted to correct the stiffness matrix of the material in each unit to obtain a material stiffness matrix of each unit, the material stiffness matrix of each unit is assembled to obtain a global stiffness matrix, and finite element analysis is performed on the global stiffness matrix to obtain a global structural displacement matrix.
3. The method according to claim 1, wherein in step S3, the young 'S modulus of the composite structure is obtained by interpolating the young' S modulus of the filler material by SIMP method.
4. The method according to claim 1, wherein step S7 further comprises obtaining sensitivity information of the objective function and the constraint function, and updating two sets of boolean parameters by a moving asymptote method based on the sensitivity information to obtain the structural parameters of the composite structure.
5. The method according to claim 1, wherein in step S5, the filtered radius variable field R 2 The expression of (2) is:
wherein R is min Is a preset minimum skin thickness; r is R max For a preset maximum skin thickness, U e Is the arithmetic mean of the displacements of the four nodes of the grid cell e,for designing the maximum value of the grid cell displacement in the domain +.>Is the minimum value of the grid cell displacement in the design domain.
6. The method according to claim 1 or 5, wherein the local volume fraction V is:
where Se is the set of all grid cells e in the neighborhood of grid cells, δ i Is the coordinates of the centroid of grid cell i, delta e Is the coordinates of the centroid of grid cell e, ζ i For the second derivative variable of the grid cell i, i.e. the pseudo-density field characterizing the fibre distribution, R 2 Filtering a radius variable field;
the local volume constraint comprises a maximum m of the local volume constraint V 1 And a minimum value m of the local volume constraint V 2 Wherein:
wherein the local volume fraction of each subdomain is aggregated into a single constraint using a p-norm, N is the number of meshing, V e For the local volume fraction of the neighborhood of element e,lambda is lambda 1 a，/>Lambda is lambda 2 a，λ 1 、λ 2 As coefficients, a is a local volume fraction constraint;
overall volume constraint m 3 The method comprises the following steps:
wherein ρ is 1 、ρ 2 And ρ 3 Represents the density, mu and fiber material of the skin material, the matrix material and the fiber material respectivelyFor the first derivative variable, ζ is the second derivative variable, frac is the upper volume fraction limit of the composite structure.
7. The method of claim 1, wherein the objective function is:
wherein W is the whole design domain, C (x, y) is the compliance of the composite structure, u i For a displacement matrix of four nodes per grid cell, k (x, y) is the material stiffness matrix of each grid cell.
8. A system for implementing the method for topologically optimizing a fiber reinforced composite structure of a variable thickness skin according to any one of claims 1 to 7, said system comprising:
partitioning and definition module: the method comprises the steps of carrying out grid division on a fiber reinforced composite structure with an outer skin, and defining two groups of Boolean parameters for representing filling materials in the grid, wherein one group of Boolean parameters are used for representing skin parameters, the other group of Boolean parameters are used for representing fiber parameters, and the filling materials comprise one of gaps, skin materials, matrix materials and fiber materials;
the processing module is used for: the method comprises the steps of performing blurring and projection processing on one group of Boolean parameters to obtain a first derivative variable representing a skin structure, and performing blurring and projection processing on the other group of Boolean variables to obtain a second derivative variable representing a fiber structure;
a first acquisition module: obtaining Young's modulus of the fiber reinforced composite structure of the outer skin by taking the first derivative variable and the second derivative variable as parameters;
and a second acquisition module: the method comprises the steps of correcting a stiffness matrix of a material by adopting the Young modulus to obtain a global stiffness matrix, and carrying out finite element analysis on the global stiffness matrix to obtain a global structural displacement matrix;
and a third acquisition module: obtaining a filtered radius variable field in each cell driven by displacement information based on the structural displacement matrix;
a fourth acquisition module: obtaining a local volume fraction of the fibrous material of each unit with the second derivative variable as a parameter, while specifying upper and lower limits of the local volume fraction to construct a local volume constraint; and constructing the integral volume constraint of the fiber reinforced composite structure with the outer skin by taking the first derivative variable and the second derivative variable as parameters;
and a solving module: and carrying out iterative optimization solving by taking the local volume constraint and the whole volume constraint as constraints and taking the structural flexibility of the fiber reinforced composite structure with the outer skin as an objective function to obtain the structural parameters of the composite structure.
9. The fiber reinforced composite structure with the variable thickness skin is characterized in that the fiber reinforced composite structure is designed by adopting the topological optimization design method of the variable thickness skin according to any one of claims 1 to 7.
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