CN112989648B - Flexible mechanism optimization design method for cooperative topological configuration and fiber path - Google Patents
Flexible mechanism optimization design method for cooperative topological configuration and fiber path Download PDFInfo
- Publication number
- CN112989648B CN112989648B CN202110154497.2A CN202110154497A CN112989648B CN 112989648 B CN112989648 B CN 112989648B CN 202110154497 A CN202110154497 A CN 202110154497A CN 112989648 B CN112989648 B CN 112989648B
- Authority
- CN
- China
- Prior art keywords
- fiber
- path
- design
- optimization
- flexible mechanism
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/04—Constraint-based CAD
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/26—Composites
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
- Moulding By Coating Moulds (AREA)
Abstract
The invention discloses a flexible mechanism optimization design method for coordinating a topological structure and a fiber path, which solves the problem of blindly selecting a fiber laying path by considering optimization of a continuous fiber path during topological optimization of the flexible mechanism structure; by adopting a polynomial to simulate a fiber path and indirectly optimizing the design idea of polynomial control coefficients, the problems of non-convex optimization and difficult processing of the fiber path are solved. The method fully considers the advantages of topology optimization and composite material design, and can fundamentally improve the deformation and the bearing capacity of the flexible mechanism.
Description
Technical Field
The invention belongs to the technical field of flexible mechanism configuration design, and particularly relates to a flexible mechanism optimization design method for coordinating topological configuration and a fiber path.
Background
The flexible mechanism is a novel mechanism proposed by Buens et al in 1968, and can realize the purposes of transferring motion, force and energy by means of elastic deformation of self materials. Compared with the traditional rigid mechanism, the rigid mechanism has the characteristics of compact structure, no need of assembly and lubrication, no clearance, easy integration and the like, and is widely applied to the fields of aerospace, micro-electro-mechanical systems, medical instruments and the like.
Through development of more than half a century, the current topological optimization method becomes a common method for designing flexible mechanisms, and the method performs finite element discretization on a design domain, and determines 'leaving' or 'deleting' of discrete units based on boundary conditions and design targets so as to achieve the purpose of optimally distributing materials. According to different modeling principles, topological optimization theories such as a homogenization method, a variable density method, a level set method and the like are formed, and the design approaches of the flexible mechanism are enriched.
The flexible mechanism designed by adopting isotropic materials can not reasonably distribute rigidity and stress according to the deformation and stress of the mechanism, and has the problem of difficult combination of deformation and bearing. Fiber reinforced composites have become an effective way to design flexible mechanisms due to their anisotropy and designability. However, 1) in the topology optimization of the flexible mechanism made of the composite material at present, a preset fiber path is taken as a research basis, so that certain blindness exists, and the further improvement of the performance of the flexible mechanism is limited. 2) In the existing fiber path and topology combined optimization design method, the discrete fiber angle is taken as a design variable, the non-convex problem exists in direct optimization, and the obtained fiber angle is in discrete distribution and cannot be directly used for processing and manufacturing. For example, the invention patent of china with the patent application number of 201910306542.4 "a method for fast collaborative optimization of a shell structure of a hybrid fiber composite material", which is optimized for hybrid fibers and is difficult to generate a continuous fiber path. Aiming at the curved fiber laying laminated plate, the invention fully utilizes the advantages of topological optimization and material designability, coordinates the topological configuration and the fiber path, fundamentally improves the performance of the flexible mechanism and obtains a continuous smooth fiber path.
Disclosure of Invention
The invention aims to provide a flexible mechanism optimization design method for coordinating topological configuration and a fiber path, and mainly solves the technical problem that the topological configuration and the fiber path of a flexible mechanism are difficult to be cooperatively optimized. The problem of blindly selecting a fiber laying path is solved by simultaneously considering the optimization of a continuous fiber path when the flexible mechanism configuration topology is optimized; by adopting a polynomial to simulate a fiber path and indirectly optimizing the design idea of polynomial control coefficients, the problems of non-convex optimization and difficult processing of the fiber path are solved. The method fully considers the advantages of topology optimization and composite material design, and can fundamentally improve the deformation and the bearing capacity of the flexible mechanism.
The technical scheme adopted by the invention is as follows: a flexible mechanism optimization design method for coordinating topological configuration and fiber path comprises the following steps: boundary condition definition and initialization parameters
Setting a design area, boundary conditions, composite material mechanical properties and an initial fiber laying path of a flexible mechanism, setting input and output virtual spring stiffness, determining the filtering radius of a variable, carrying out finite element dispersion on the initial design area and the fiber path, and setting an initial variable of a globally convergent movement asymptotic algorithm;
step two: parametric description of a fiber placement reference path
Introducing a polynomial function to approximately describe a fiber placement reference path on a single layer, the parameterized polynomial function being:
wherein A is ω For the omega-th polynomial coefficient, X is a non-dimensionalized position coordinate whose value range is [ -1,1]Interval, n is the number of terms of the polynomial;
step three: construction of penalty model-based constitutive relation of curve fiber laying laminated plate
Through a discrete curve fiber path, the discrete units can be equivalent to linear fibers, the fiber direction of the discrete units is represented by the curve tangent direction at the central point of the units, the discrete units are equivalent to linear fiber laying laminated plates, and the constitutive relation of the discrete units i of the curve fiber laying laminated plates can be obtained according to the classical laminated plate theory;
step four: flexible mechanism optimization model for establishing cooperative topological configuration and fiber laying path
Respectively describing the structural topological shape and the fiber laying path by using the relative density of units and polynomial coefficients, and obtaining a flexible mechanism optimization model of the cooperative topology and the fiber laying path by taking the MSE (mean square error) of the flexible mechanism system as a design target and the volume as a constraint condition;
step five: finite element displacement field analysis
Combining the three layers of laminated plate constitutive relation and the plane quadrilateral unit, and the rigidity matrix k of the discrete unit i in finite element analysis i Is shown as
Wherein, B is a geometric matrix,
the integral stiffness matrix can be obtained by integrating the stiffness matrix of each unit for the constitutive relation of the discrete units i of the curve fiber laying laminated plate, wherein omega is the integral area of the discrete units, and the displacement field response of the structure can be realized by adopting a finite element programming technology;
step six: sensitivity analysis
According to the optimization model in the step four, a binding force balance equation and an accompanying load method, a target function f is obtained through derivation 0 (x) Sensitivity to design variables were respectively
Volume constraint function f 1 (x) The sensitivity to design variables can be directly derived as
Wherein, f 0 (x) And f 1 (x) Respectively representing the mutual strain energy and the volume constraint function, x i Representing the relative density of the i-th cell, p being a penalty factor, q i And u i Respectively representing displacement vectors at the ith unit node under the action of virtual load and actual load;
step seven: sensitivity filtering
Filtering the sensitivity of the objective function in the optimization model to the unit density to ensure the smoothness of the topological configuration without filtering the sensitivity of the polynomial coefficient;
step eight: design variable update
On the basis of obtaining the sensitivity of the flexible mechanism optimization model to design variables, simultaneously updating unit density design variables and polynomial coefficient variables by using a global convergent moving asymptote method to serve as initial values for next iteration;
step nine: iteration termination and result output
Taking the difference value of the iteration design variables of two adjacent times as a termination condition for judging optimization iteration, converging the optimization process when the termination condition is met, ending the iteration, and outputting the final unit density and polynomial coefficients; and if the termination condition is not met, returning to the step two, and continuing the optimization iteration until the termination condition is met.
The present invention is also characterized in that,
the constitutive relation of discrete units i of the three-step curve fiber placement laminated plate is
Wherein h is j Is the jth monolayer thickness, h is the total thickness of the curved fiber laminate, m is the total number of layers, E 1 、E 2 、G 12 、μ 12 、μ 21 Is the elastic constant of the material and is,
is the transpose matrix of the i unit on the j level, and the expression is
Wherein, the first and the second end of the pipe are connected with each other,
representing the center of the i cell on the j-th layer
A represents a polynomial coefficient vector;
based on a penalty model, the constitutive relation of the discrete units i of the symmetrical curve fiber laying laminated plate is
In the formula, x i Is the relative density on the ith cell and p is a penalty factor.
The four-step cooperative topological configuration and fiber laying path flexible mechanism optimization model is
Wherein x is a design variable vector and represents relative density of units and polynomial coefficients, K is a whole stiffness matrix of the laminated plate, F is an external force vector, L is a virtual load vector, U and Q respectively represent node displacement vectors under the action of F and L, and V is 0 For the initial design region volume, g is the volume fraction, x i,min To allow a minimum in density, v i In order to optimize the volume of the i unit in iteration, n represents the number of polynomial terms, s represents the number of discrete units, and m represents the number of independent layers;
the seventh step is as follows:
filtered objective function versus density design variable x i Has a sensitivity of
In the formula, N e Is at the filter radius R min Set of cells in, H r Is a weighting factor.
The difference value of the variables of the two adjacent iterations in the step nine is used as the termination condition for judging the optimization iteration, and the constructed termination condition is
||x k+1 -x k ||≤ε (12)
In the formula, ε is an allowable threshold value, and the value is set to 0.01 to 0.001.
Step one the design area is 40 x 40mm.
Compared with the prior art, the invention has the following advantages and beneficial effects:
aiming at the problems of blindly selecting a fiber path, non-convex optimization, discrete fiber distribution and the like of the composite material flexible mechanism, the invention obtains the optimal topological configuration and the continuous fiber laying path of the flexible mechanism by cooperating topological optimization and fiber path design, thereby improving the performance of the flexible mechanism. By introducing a polynomial simulation fiber path and indirectly optimizing polynomial coefficients, the problem of non-convex optimization is solved, and a continuous smooth fiber path which can be used for processing is generated. The method provided by the invention can realize the integrated design of the composite material flexible mechanism, realize the collaborative optimization design of the structural topology and the fiber laying path, and improve the performance of the flexible mechanism to the maximum extent.
Drawings
FIG. 1 is a flow chart of an implementation of a method for optimally designing a compliant mechanism for coordinating a topological structure with a fiber path according to the present invention;
FIG. 2 is a schematic diagram of the present invention in which a laminate is laid down using a translation process;
FIG. 3 is a schematic illustration of a curvilinear fiber-placement laminate fiber discretization process of the present invention;
FIG. 4 is a schematic diagram of the flexible reverser co-optimized design area and boundary conditions of the present invention;
FIG. 5 is a diagram of the optimal topology of the curvilinear fiber placement flexible inverter of the present invention;
FIG. 6 (a) is a graph of a curvilinear fiber placement path on a first monolayer of the curvilinear fiber placement flexible inverter of the present invention;
FIG. 6 (b) is a graph of a curvilinear fiber placement path for a second monolayer of the curvilinear fiber placement flexibility inverter of the present invention.
Detailed Description
The invention will be described in detail with reference to the drawings and the detailed description
In order to make the process problems solved, the process schemes adopted and the process effects achieved by the present invention clearer, the present invention will be further described in detail with reference to the accompanying drawings and examples.
Fig. 1 is an implementation flowchart of a flexible mechanism optimization design method for coordinating a topological structure and a fiber path provided by the invention. The optimization design method mainly comprises the following steps: 1) Defining and initializing boundary conditions; 2) A parametric approximation of the fiber placement reference path; 3) Constructing a penalty model-based constitutive relation of curve fiber laying laminated plates; 4) Establishing a flexible mechanism optimization model of the cooperative topology and the fiber laying path; 5) Analyzing a finite element displacement field; 6) Analyzing a target function and sensitivity; 7) Sensitivity filtering; 8) Updating a design variable; 9) And (5) iteration termination and output. The method is characterized in that a parameterized polynomial function is used for simulating a fiber path, coefficients of the fiber path are used as design variables, a flexible mechanism optimization model of a cooperative topology and the fiber path is constructed by combining cell density, and synchronous optimization of a topology configuration and a continuous fiber path can be realized by indirectly optimizing the polynomial coefficients and the cell density. The method comprises the following specific steps:
the first step is as follows: boundary condition definition and initialization parameters
Setting a design area, boundary conditions, composite material mechanical properties and an initial fiber laying path of a flexible mechanism, setting input and output virtual spring stiffness, determining a filtering radius of a variable, carrying out finite element dispersion on the initial design area and the fiber path, and setting an initial variable of a global convergent moving asymptotic algorithm (GCMMA).
The second step is that: parametric approximate description of a fiber placement reference path
A polynomial function was introduced to approximately describe the fiber placement reference path on a single layer, spreading the entire initial laminate design area according to the reference path in a translational method, as shown in fig. 2. The method achieves the purpose of adjusting the fiber path by indirectly optimizing the coefficients of the polynomial, reduces the design scale, and solves the non-convex problem of directly optimizing the fiber angle. Assume that the introduced parameterized polynomial function is:
in the formula, A ω Is the coefficient of the omega-th multi-form, X is the position coordinate of the horizontal non-dimensionalization, and the value range after the non-dimensionalization is [ -1,1]And n is the number of terms of the selected polynomial. Other fiber paths over the initial laminate design area may be obtained by translating the reference path described above.
The third step: construction of penalty model-based constitutive relation of curve fiber laying laminated plate
For a curved fiber-laid laminate, the constitutive relation varies with position, and through the discrete topological configuration region and the fiber path, the discrete units can be equivalent to straight-line fibers, and the tangential direction of the curve at the central point of the unit approximately represents the fiber direction of the discrete units, and the process principle is shown in fig. 3. For the discrete laminated plate, the discrete units are equivalent to a linear fiber laying laminated plate, and according to the classical laminated plate theory, the constitutive relation of the discrete units i of the curve fiber laying laminated plate can be obtained as
In the formula, h j Is the jth monolayer thickness, h is the total thickness of the curved fiber laminate, m is the total number of layers, E 1 、E 2 、G 12 、μ 12 、μ 21 Is the elastic constant of the material.
Is the transpose matrix of the i unit on the j layer, the value of which is related to the fiber angle on each layer unit, the slope of the curve at the center of the unit is used to represent the fiber direction, the expression of the transpose matrix is
In the formula (I), the compound is shown in the specification,
representing the center of the i cell on the j-th layer
Is the slope of the polynomial coefficient vector A and position
The function of (2) can be obtained by differentiating the formula (1).
According to the idea of a variable density method, converting a discrete optimization problem into a continuous problem through punishment on the density of a unit, wherein the constitutive relation of a symmetrical curve fiber laying laminated plate unit i based on a punishment model is
In the formula, x i Is the relative density at the i-th cell, p is a penalty factor, D i The constitutive relation of the original material (not punished) can be obtained by the formula (2).
The fourth step: flexible mechanism optimization model for establishing cooperative topology and fiber laying path
The symmetrical variable stiffness laminated plate laid by the symmetrical curve is taken as a research object, and the structural topological shape and the fiber laying path are respectively described by using the unit relative density and the polynomial coefficient. With the flexible mechanism system Mutual Strain (MSE) as a design target and the volume as a constraint condition, the flexible mechanism optimization model of the cooperative topology and the fiber placement path is as follows:
wherein x is a design variable vector and represents relative density of units and polynomial coefficients, K is a whole stiffness matrix of the laminated plate, F is an external force vector, L is a virtual load vector, U and Q respectively represent node displacement vectors under the action of F and L, and V is 0 For the initial design region volume, g is the volume fraction, x i,min To allow the density to be minimizedValue v i To optimize the i-cell volume in the iteration, n represents the number of polynomial terms, s represents the number of discrete cells, and m represents the number of independent layers.
The fifth step: finite element displacement field analysis
Finite element analysis is an effective means for obtaining a structural displacement field, an integral rigidity matrix K is generated by integrating a unit rigidity matrix and combines the sheet constitutive relation and a plane quadrilateral unit, and a rigidity matrix K of a unit i in the finite element analysis i Is shown as
Wherein, B is a geometric matrix, and omega is a discrete unit integration area. The rigidity matrix of each unit is integrated to obtain an integral rigidity matrix, and the displacement field response of the structure can be realized by adopting a finite element programming technology.
And a sixth step: objective function and sensitivity analysis
The actual displacement and the accompanying displacement field of the structure can be obtained through finite element analysis, and the target f of the flexible mechanism can be directly obtained according to the function expression of mutual strain 0 (x) The function value of (1). The density of the cells varies during the optimization, and the constraint f is obtained by integrating all the cells 1 (x) The function value of (1).
According to the relation of the optimization model, the binding force balance equation and the accompanying load method, the objective function f is obtained through derivation 0 (x) Sensitivity to design variables are respectively
In the formula, q i And u i Respectively represents a displacement vector at the ith unit node under the action of a virtual load and an actual load, k i Is the ith unit stiffness matrix without penalty, and the expression is
k i ＝∫∫ Ω B T D i (A,X)BhdΩ (8)
Combining equations (2) and (8), the cell stiffness matrix k can be obtained by derivation i And finally, obtaining the sensitivity information of the flexible mechanism target function to all design variables for the sensitivity information of the polynomial coefficient design variable A.
Volume constraint function f 1 (x) For density design variable x i Can be directly derived as
The polynomial coefficient design variable A does not affect the change of the unit volume, so the sensitivity of the volume constraint function to the phase in the optimization process is as follows:
the seventh step: sensitivity filtering
Sensitivity filtering techniques are used to ensure the existence of topology optimization solutions, avoiding the appearance of checkerboard topology results. Filtered objective function versus density design variable x i Has a sensitivity of
Wherein Ne is at the filter radius R min Set of cells in, H r Is a weighting factor.
Eighth step: design variable update
On the basis of obtaining the sensitivity of the flexible mechanism optimization model to the design variables, a global convergent moving asymptote method (GCMMA) is utilized to update the cell density design variables and the polynomial coefficient variables at the same time to serve as initial values used in the next iteration.
The ninth step: iteration termination and result output
Taking the difference value of the design variables of two adjacent iterations as a termination condition for judging optimization iteration, and constructing the termination condition
||x k+1 -x k ||≤ε (12)
In the formula, ε is an allowable threshold value, and its value is usually set to 0.01 to 0.001. When the termination condition is met, the optimization process converges, the iteration is finished, and the final unit density and polynomial coefficients are output; and if the termination condition is not met, returning to the second step, and continuing optimization iteration until the termination condition is met.
Referring to fig. 4 to 6 (b), the present invention takes a flexible reverser as an example to perform an optimized design of a cooperative topological configuration and a fiber path, and the specific implementation is as follows:
the initial design domain and boundary conditions of the flexible reverser are shown in FIG. 4, the design domain is a 40X 40mm area, the two ends of the left side are fixed, and the input force F is in =20N for the left-end intermediate position, the desired volume constraint is 30%, and the virtual stiffness factor k in ＝0.1，k out =0.1, filter radius R min =1.6, the design area is discretized into 80 × 80 finite element units, the laminate being investigated with equal-thickness symmetrical curve fiber-laid. Assuming that glass fiber reinforced epoxy resin is selected as a layering material, the engineering elastic constants are respectively as follows: e 1 ＝39GPa，E 2 ＝8.4GPa，G 12 ＝4.2GPa，μ 12 =0.26. The initial cell density design variables were x =0.3, the polynomial coefficient term n =8, and the initial polynomial coefficient value a =0.1, assuming a total number of plies of the symmetric laminate was 4.
Based on the established collaborative optimization design method, the flexible reverser is optimally designed under the action of initial conditions, and fig. 5 shows the obtained optimal topological configuration of the flexible reverser mechanism. Secondly, the topological structure material is distributed uniformly and reasonably, the phenomenon of single-point linkage does not occur, the topological structure material is consistent with the optimization result obtained by the isotropic material, and the effectiveness of the flexible reverser structure is demonstrated.
Fig. 6 (a), (b) are the optimal fiber placement paths obtained according to the co-optimization, since the composite material laminate is a symmetrical laminate, and thus only half of the lay-up paths are independent of each other, the optimal fiber placement paths are shown only on 2 single layers, and the rest of the lay-up paths are symmetrical to the optimal fiber placement paths. As can be seen from the fiber laying path, the fiber path is smoothly and continuously distributed in the flexible reverser, and the generated fiber path can be suitable for the translation laying mode of the automatic tape laying machine.
In summary, the invention provides a flexible mechanism optimization design method for coordinating topology configuration and fiber path. Firstly, introducing a polynomial function approximate simulation fiber laying path, and equally-effective linear fiber laying on a unit through a discrete fiber path to obtain a unit constitutive relation of a curve fiber laying composite material laminated plate; simultaneously, topology optimization and fiber placement are considered, a flexible mechanism cooperative topology and fiber path optimization model is established by taking the unit density and the polynomial function as design variables, the solution scale is reduced, and the non-convex problem of cooperative optimization is solved; the sensitivity of the strain energy to the design variable is deduced by using an adjoint matrix method; the design variables are updated by using a GCMMA algorithm based on gradient information, the optimal topological configuration and the optimal fiber laying path of the flexible mechanism are synchronously realized, the advantages of material design and topological optimization are fundamentally exerted, and a continuous and smooth fiber path is provided for automatic fiber laying equipment.
Claims (4)
1. A flexible mechanism optimization design method for coordinating topological configuration and fiber path is characterized by comprising the following specific steps:
the method comprises the following steps: boundary condition definition and initialization parameters
Setting a design area, boundary conditions, composite material mechanical properties and an initial fiber laying path of a flexible mechanism, setting input and output virtual spring stiffness, determining the filtering radius of a variable, carrying out finite element dispersion on the initial design area and the fiber path, and setting an initial variable of a globally convergent movement asymptotic algorithm;
step two: parametric description of a fiber placement reference path
Introducing a polynomial function to approximately describe a fiber placement reference path on the single layer, the parameterized polynomial function being:
wherein A is ω For the omega-th polynomial coefficient, X is a non-dimensionalized position coordinate whose value range is [ -1,1]Interval, n is the number of terms of the polynomial;
step three: construction of penalty model-based constitutive relation of curve fiber laying laminated plate
Through a discrete curve fiber path, the discrete units can be equivalent to straight line fibers, the fiber direction of the discrete units is represented by the curve tangent direction at the central point of the units, the discrete units are equivalent to straight line fiber laying laminated plates, and the constitutive relation of discrete units i of the curve fiber laying laminated plates can be obtained according to the classical laminated plate theory;
the constitutive relation of discrete units i of the step three-curve fiber laying laminated plate is
Wherein h is j Is a single layer thickness, h is a total thickness of the curved fiber laminate, m is a total number of layers, E 1 、E 2 、G 12 、μ 12 、μ 21 Is the elastic constant of the material and is,
is the transpose matrix of the i unit on the j layer, and the expression is
Wherein the content of the first and second substances,
representing the center of the i cell on the j-th layer
A represents a polynomial coefficient vector;
based on a penalty model, the constitutive relation of the discrete units i of the symmetrical curve fiber laying laminated plate is
In the formula, x i Is the relative density on the ith cell, p is a penalty factor;
step four: flexible mechanism optimization model for establishing cooperative topology and fiber laying path
Respectively describing the structural topological shape and the fiber laying path by using the unit relative density and the polynomial coefficient, and obtaining a flexible mechanism optimization model of the cooperative topology and the fiber laying path by taking the flexible mechanism system mutual strain MSE as a design target and the volume as a constraint condition;
the four-step cooperative topology and fiber laying path flexible mechanism optimization model is
Wherein, x is a design variable vector representing relative density of units and polynomial coefficients, K is a whole rigidity matrix of the laminated plate, F is an external force vector, L is a virtual load vector, U and Q respectively represent node displacement vectors under the action of F and L, and V 0 For the initial design region volume, g is the volume fraction, x i,min To allow a minimum in density, v i In order to optimize the volume of the i unit in iteration, n represents the number of polynomial terms, s represents the number of discrete units, and m represents the number of independent layers;
step five: finite element displacement field analysis
Combining the step three-layer plywood constitutive relation and the planar quadrilateral unit, the rigidity of the discrete unit i in finite element analysisMatrix array
Is shown as
Wherein, B is a geometric matrix,
the method is characterized in that the method is a constitutive relation of discrete units i of a curve fiber laying laminated board, omega is a discrete unit integral area, an integral stiffness matrix can be obtained by integrating stiffness matrixes of all units, and the displacement field response of the structure can be realized by adopting a finite element programming technology;
step six: sensitivity analysis
According to the optimization model in the step four, a binding force balance equation and an accompanying load method, a target function f is obtained through derivation 0 (x) Sensitivity to design variables are respectively
Volume constraint function f 1 (x) The sensitivity to design variables can be directly derived as
Wherein k is i Is the ith penalized cell stiffness matrix, f 0 (x) And f 1 (x) Respectively representing the mutual strain energy and the volume constraint function, x i Representing the relative density of the i-th cell, p is a penalty factor, q i And u i Respectively representing displacement vectors at unit nodes under the action of virtual load and actual load;
step seven: sensitivity filtering
Filtering the sensitivity of the objective function in the optimization model to the unit density to ensure the smoothness of the topological configuration without filtering the sensitivity of the polynomial coefficient;
step eight: design variable update
On the basis of obtaining the sensitivity of the flexible mechanism optimization model to the design variables, simultaneously updating the unit density design variables and the polynomial coefficient variables by using a global convergent moving asymptote method to serve as initial values for next iteration;
step nine: iteration termination and result output
Taking the difference value of the two adjacent iteration design variables as the termination condition for judging the optimization iteration, converging the optimization process when the termination condition is met, ending the iteration, and outputting the final unit density and polynomial coefficient; and if the termination condition is not met, returning to the step two, and continuing the optimization iteration until the termination condition is met.
2. The method for optimally designing the flexible mechanism for coordinating the topological structure with the fiber path according to the claim 1, wherein the seventh step is as follows:
filtered objective function versus density design variable x i Has a sensitivity of
In the formula, N e Is at the filter radius R min Set of cells in, H r Is a weighting factor.
3. The method for optimally designing the flexible mechanism of the cooperative topological structure and the fiber path according to claim 1, wherein a difference value of two adjacent iteration design variables in the step nine is used as a termination condition for judging optimization iteration, and the constructed termination condition is that
||x k+1 -x k ||≤ε (12)
In the formula, ε is an allowable threshold value, and the value is set to 0.01 to 0.001.
4. The method for optimally designing a flexible mechanism with cooperative topological structure and fiber path as claimed in claim 1, wherein, in the step one, the design area is 40 x 40mm.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110154497.2A CN112989648B (en) | 2021-02-04 | 2021-02-04 | Flexible mechanism optimization design method for cooperative topological configuration and fiber path |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110154497.2A CN112989648B (en) | 2021-02-04 | 2021-02-04 | Flexible mechanism optimization design method for cooperative topological configuration and fiber path |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112989648A CN112989648A (en) | 2021-06-18 |
| CN112989648B true CN112989648B (en) | 2022-11-25 |
Family
ID=76346923
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110154497.2A Active CN112989648B (en) | 2021-02-04 | 2021-02-04 | Flexible mechanism optimization design method for cooperative topological configuration and fiber path |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112989648B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113442441B (en) * | 2021-07-30 | 2022-05-06 | 西安交通大学 | Continuous fiber 3D printing path planning method based on parallel optimization of fiber orientation and structure |
| CN114595617B (en) * | 2022-05-10 | 2022-07-22 | 山东科技大学 | Design method of micro-pulse laser radar light path parameter topological structure |
| CN117195666B (en) * | 2023-11-08 | 2024-03-01 | 江西应用科技学院 | Part lightweight manufacturing method and system based on SLM technology |
| CN117892414B (en) * | 2024-03-18 | 2024-05-24 | 华东交通大学 | Structural robustness topology optimization design method for anisotropic material under simple harmonic excitation |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107220461A (en) * | 2017-06-26 | 2017-09-29 | 大连理工大学 | A kind of variation rigidity composite panel shell structure effectively optimizing method |
| CN108038324A (en) * | 2017-12-21 | 2018-05-15 | 北京航空航天大学 | A kind of Continuum Structure bi-material layers Topology Optimization Method towards anisotropic material |
| CN111723457A (en) * | 2020-05-08 | 2020-09-29 | 华中科技大学 | Level set method for optimization design of fiber curve laying variable-stiffness structure |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11084223B2 (en) * | 2018-08-20 | 2021-08-10 | Lawrence Livermore National Security, Llc | Optimal toolpath generation system and method for additively manufactured composite materials |
-
2021
- 2021-02-04 CN CN202110154497.2A patent/CN112989648B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107220461A (en) * | 2017-06-26 | 2017-09-29 | 大连理工大学 | A kind of variation rigidity composite panel shell structure effectively optimizing method |
| CN108038324A (en) * | 2017-12-21 | 2018-05-15 | 北京航空航天大学 | A kind of Continuum Structure bi-material layers Topology Optimization Method towards anisotropic material |
| CN111723457A (en) * | 2020-05-08 | 2020-09-29 | 华中科技大学 | Level set method for optimization design of fiber curve laying variable-stiffness structure |
Non-Patent Citations (3)
| Title |
|---|
| Optimal fiber orientation and topology design for compliant mechanisms with fiber-reinforced composites;Tong Xinxing等;《Proceedings of Institution of Mechanical Engineers》;20171231;全文 * |
| 基于改进离散材料插值格式的复合材料结构优化设计;段尊义等;《航空学报》;20121225(第12期);全文 * |
| 考虑不确定性的柔性机构拓扑优化设计;罗阳军等;《机械工程学报》;20110105(第01期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112989648A (en) | 2021-06-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112989648B (en) | Flexible mechanism optimization design method for cooperative topological configuration and fiber path | |
| CN107220461B (en) | A kind of variation rigidity composite panel shell structure effectively optimizing method | |
| Henry et al. | Smart morphing wing: optimization of distributed piezoelectric actuation | |
| CN110083900B (en) | Rapid collaborative optimization method for hybrid fiber composite material plate shell structure | |
| CN108829914B (en) | Structure and process integrated design method of FRP structural member | |
| Liguori et al. | An isogeometric framework for the optimal design of variable stiffness shells undergoing large deformations | |
| Dayyani et al. | Multi-objective optimization for the geometry of trapezoidal corrugated morphing skins | |
| CN112507587A (en) | Variable-stiffness composite material structure optimization design method oriented to compression stability | |
| CN111723457B (en) | Level set method for optimization design of fiber curve laying variable-stiffness structure | |
| Dillinger et al. | Static aeroelastic stiffness optimization of a forward swept composite wing with CFD-corrected aero loads | |
| Ma et al. | Generative design of stiffened plates based on homogenization method | |
| Günay et al. | Stresses in thin-walled composite laminated box-beams with curvilinear fibers: Antisymmetric and symmetric fiber paths | |
| Muramatsu et al. | Distributed-parametric optimization approach for free-orientation of laminated shell structures with anisotropic materials | |
| CN115295097A (en) | Fiber reinforced composite multi-material multi-scale variable stiffness optimization design method considering additive manufacturing | |
| Stegmann | Analysis and optimization of laminated composite shell structures | |
| Hui et al. | A data-driven CUF-based beam model based on the tree-search algorithm | |
| CN112765731B (en) | Method for optimizing aeroelasticity of curved fiber composite structure by considering local buckling | |
| Ahmed et al. | An efficient facet shell element with layerwise mechanics for coupled electromechanical response of piezolaminated smart shells | |
| Iannotta et al. | A mechanical analysis of variable angle-tow composite plates through variable kinematics models based on Carrera’s unified formulation | |
| Dong et al. | Topology optimization of multi-gradient composite | |
| CN115906586A (en) | Variable-stiffness optimal design method of porous composite material considering additive manufacturing continuity | |
| Wu et al. | An integrated approach to shape and laminate stacking sequence optimization of free-form FRP shells | |
| Weaver et al. | Optimisation of variable stiffness plates | |
| CN113515850A (en) | Fiber-reinforced composite material structure layout optimization design method considering fiber continuity | |
| Stanford et al. | Aeroelastic tailoring via tow steered composites |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |