CN118052095B - Full-scale parallel topology optimization method and system for solid-lattice hybrid configuration - Google Patents
Full-scale parallel topology optimization method and system for solid-lattice hybrid configuration Download PDFInfo
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Abstract
The invention belongs to the field of structural topology optimization design, and particularly discloses a full-scale parallel topology optimization method and system of a solid-lattice mixed configuration, wherein the method comprises the steps of constructing a level set function of a solid microstructure and a lattice microstructure, and obtaining a global parameterized level set function of the solid-lattice mixture by introducing control parameters; the method comprises the steps of carrying out a partial differential equation of a Hamiltonian-Jacobian equation to obtain a Chang Weifen equation, taking control parameters for controlling a solid structure and a lattice structure as double design variables, taking flexibility of a macroscopic structure as an objective function, establishing a topological optimization mathematical model with the solid structure volume and the macroscopic structure volume as double constraints, calculating sensitivity information, and solving the topological optimization model by adopting a gradient-based optimization algorithm. The invention can overcome the problem of insufficient mechanical properties of a pure entity macroscopic topological structure and a single lattice structure, realizes the configuration design of entity-lattice parallel optimization, and effectively improves the mechanical properties of the structure.
Description
Technical Field
The invention belongs to the field of structural topology optimization design, and particularly relates to a full-scale parallel topology optimization method and system of a solid-lattice hybrid configuration.
Background
The lattice structure is obtained through a periodic array of microstructures (lattice microstructures), has excellent mechanical properties such as low density, energy absorption, vibration reduction, heat dissipation, heat insulation and the like, and is widely applied to the design of key structures in the fields of aircrafts, rail transit, medical bone implants and the like. However, the problems of single function, insufficient mechanical property, complex coupling relation between mechanical property and macroscopic distribution and the like of the periodic lattice structure lead to insufficient application potential of the lattice structure, and the gap between the application potential and the application requirement of the actual functional structural member is larger.
The topology optimization method provides a powerful optimization tool for the mechanical property design of the lattice structure. The topology optimization method can perform parallel optimization on the macrostructure distribution and microstructure configuration of the lattice structure, and realize the design of functionally graded lattice, so that the mechanical property of the lattice structure is better than that of the periodic lattice structure. In terms of functionally graded lattice topology optimization, topology optimization methods can be classified into layer-by-layer optimization, domain-by-domain optimization and point-by-point optimization. Although the functionally graded lattice structure realizes relatively better design through the spatial configuration distribution of the variable density microstructure, in practical application, the mechanical property of the lattice structure is difficult to meet the design requirement of light and high-strength performance, and especially on the main force transmission path of the structure under the high-bearing working condition, the lattice structure cannot provide mechanical property similar to that of a solid material. On the other hand, the topological configuration of the pure solid structure can provide larger rigidity performance, but design conflicts are faced in the aspects of comprehensive performances such as light weight, robustness and buckling stability of the structure.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a full-scale parallel topology optimization method and system of a solid-lattice mixed configuration, and aims to realize cooperative regulation and control of a solid structure and a lattice structure topology configuration and effectively improve the mechanical property of the structure.
In order to achieve the above object, according to an aspect of the present invention, a full-scale parallel topology optimization method of a solid-lattice hybrid configuration is provided, including the following steps:
s1, introducing control parameters, constructing a level set function of an entity microstructure and a lattice microstructure on a unit cell, and further obtaining a global parameterized level set function of an entity-lattice hybrid structure;
S2, establishing a topological optimization mathematical model by taking control parameters for controlling the entity structure and the lattice structure as double design variables, taking the overall structure flexibility as an objective function and taking the entity structure volume and the macrostructure volume as double constraint conditions;
S3, introducing the global parameterized level set function into a partial differential equation of the Hamiltonian-Jacobian equation to obtain Chang Weifen equation;
S4, determining sensitivity columns of the objective function and the constraint condition on the design variables based on a normal differential equation to obtain sensitivity information;
and S5, solving the topological optimization model by adopting a gradient-based optimization algorithm based on sensitivity information to obtain double design variables, thereby determining the optimal entity-crystal mixed configuration.
As a further preferred step S1, the global parameterized level set function is specifically:
Wherein phi (x, T) is a level set function of the solid structure, theta (x, T) is a level set function of the lattice structure, and T (T) and H (T) are control parameters of the solid structure and the lattice structure respectively, namely design variables; as a physical microstructure level set function with a volume fraction of 1, γ (x) is a lattice microstructure level set function with a predefined small volume fraction, C γ is the lattice microstructure level set function control coefficient, N (x) is a linear interpolation shape function, f (x, t) is a global parameterization level set function of a macro structure of a solid-lattice mixture, f (x, t) >0 region represents a position containing material in the structure, f (x, t) <0 region represents a blank position not containing material in the structure, f (x, t) =0 region represents a boundary region of material and void in the design domain, D represents a predefined whole design domain, Ω represents a junction evolution region in optimization,Representing the boundaries of the structure.
As a further preference, the control factorThe calculation of C γ is as follows:
as a further preferred step S2, the topology optimization mathematical model is specifically:
find:{T(t),H(t)}
Where J (f) is the overall compliance of the entity-lattice hybrid structure, ε and U are the strain fields and displacement fields of discrete units in the structure, B is the material equivalent elastic matrix, a Ф (U, V) is the functional of strain energy, l Ф (V) is the work done by external forces on virtual displacement, U is the displacement field of the structure, g (f) is the volume constraint function of the macrostructure, f (Φ) is the volume constraint function of the entity structure, ζ is the volume fraction constraint value of a given macrostructure, δ is the volume fraction constraint value of a given entity structure, V represents the initial complete volume of the design domain, Ω macro is the evolution region of the entity-lattice structure in optimization, Ω solid is the evolution region of the entity structure in optimization, T k (T) is the design variable of the entity structure on the kth unit cell, H k (T) is the design variable of the lattice structure on the kth unit cell, and m is the number of unit cells in the design domain.
As a further preferred, step S3, the resulting ordinary differential equation is as follows:
wherein t is a pseudo time, The normal speeds of boundary evolution of the solid structure and the lattice structure in the optimization process are respectively.
As a further preferred aspect, step S4, determining a sensitivity column of the objective function with respect to the design variable includes:
based on the ordinary differential equation, a normal velocity expression is determined and substituted into a sensitivity list of the objective function with respect to the pseudo time t, and the sensitivity list of the objective function with respect to the design variable is obtained as follows:
in the formula, The sensitivity of the variables for the objective function with respect to the physical structure is designed,The sensitivity of the objective function with respect to lattice structure design variables, delta is the derivative of the herceptin function with respect to the level set function, and G (f) is the node strain energy.
As a further preferred, step S4, the constraint on the sensitivity of the design variable is as follows:
in the formula, Sensitivity of the volume constraint function for macrostructure with respect to dual design variables,Sensitivity of the function to self-design variables is constrained for the physical structure volume.
As a further preferred aspect, the design domain dispersion is performed in advance, including:
dividing a design domain into a certain number of regular quadrilateral areas or regular hexahedral areas, matching each area with microstructure cells with corresponding sizes, and further dividing each area into fine grids to form a finite element analysis grid;
two sets of grids are obtained through the method so as to be matched with the entity microstructure and the lattice microstructure respectively, and two design variables are defined on nodes of the two sets of grids respectively.
As a further preferable mode, step S5, adopting a gradient-based optimization algorithm to solve the topological optimization model and carrying out iterative updating on the design variable, stopping iteration when meeting the convergence criterion, and taking the value of the double design variable at the moment as a final value;
The convergence criterion is:
Where σ is a given threshold, n max is a given maximum number of iterations, and J (Γ) n is the objective function value for the nth iteration.
According to another aspect of the present invention, there is provided a full-scale parallel topology optimization system of a solid-lattice hybrid configuration, comprising a processor for performing the full-scale parallel topology optimization method of a solid-lattice hybrid configuration described above.
In general, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the invention constructs a parameterized level set function by introducing double design variables, completes decoupling of a Hamilton-Jacobi partial differential equation, establishes double constraints of a macroscopic structure volume and a solid structure volume, realizes cooperative regulation and control of a solid structure and a lattice structure topological configuration, obtains a configuration design of a solid-lattice mixture, avoids a parallel optimization process of a splitting entity and a lattice structure, can overcome the problem of insufficient mechanical properties of a pure solid macroscopic topological structure and a single lattice structure, effectively improves the mechanical properties of the structure, and provides a new method for expanding the design freedom degree and engineering application range of the lattice structure.
2. According to the invention, the topological configuration regulation and control and geometric boundary continuity of the preset microstructure are converted into design variables to be embedded into an optimization framework, and the continuous distribution of the entity structure in the design domain and the gradient distribution of the lattice microstructure are ensured based on the full-scale finite element, so that the continuous transition of the geometric boundary of the entity structure and the lattice structure is ensured. Compared with the adoption of the entity-uniform lattice design, the entity-gradient lattice mixing innovative configuration provided by the invention expands the design space and the design freedom degree, and can greatly improve the mechanical property of the structure.
3. According to the invention, through constructing the volume double constraint of the macrostructure and the volume double constraint of the solid structure, the flexible cooperative regulation and control of the volume proportion of the solid structure and the lattice structure in the design domain is realized, namely under any given double volume constraint, the mechanical property of the optimized structure can be accurately regulated and controlled, the corresponding solid-lattice configuration is obtained, the reasonable distribution and parallel design of the two structural configurations in space are ensured, and a new thought is provided for the mechanical property improvement of the light high-strength structure. The invention can better balance the comprehensive elements of light weight, rigidity, robustness, buckling stability and the like of the structure, and provides a feasible structural innovation design technical scheme for customized performance design requirements and engineering application requirements.
Drawings
FIG. 1 is a flow chart of a full-scale parallel topology optimization method of a solid-lattice hybrid configuration provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of design domain dispersion and dual design variable definition in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a hybrid design of a physical and lattice microstructure according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the two-dimensional cantilever structure design domain of embodiment 1 of the present invention;
FIG. 5 is a schematic diagram of the entity and lattice optimization configuration of the cantilever structure in example 1 of the present invention, wherein (a) is a configuration diagram of the entity structure in the macrostructure, (b) is a gradient lattice distribution configuration diagram of X-shaped unit cells in the macrostructure, and (c) is an optimized entity-lattice mixture configuration diagram;
fig. 6 (a) and (b) are graphs of the objective function and the volume fraction optimization iteration in example 1 of the present invention;
FIGS. 7 (a) - (f) are diagrams of optimized configurations of cantilever beams under different parameters in embodiment 1 of the present invention;
FIG. 8 is a schematic diagram of the structural design domain of a two-dimensional Michell beam in example 2 of the present invention;
FIG. 9 is a schematic diagram of Michell Liang Shiti and a lattice optimization configuration in example 2 of the present invention, wherein (a) is a physical structure configuration diagram in a macroscopic structure, (b) is an X-shaped unit cell gradient lattice distribution configuration diagram in a macroscopic structure, and (c) is an optimized physical-lattice mixture configuration diagram;
fig. 10 (a) and (b) are graphs of the objective function and the volume fraction optimization iteration in example 2 of the present invention;
FIG. 11 is a schematic diagram of the design domain of a three-dimensional MBB beam structure in example 3 of the present invention;
FIG. 12 is a schematic diagram of the MBB Liang Shiti and the lattice optimization configuration in example 3 of the present invention, wherein (a) is a physical structure configuration diagram in a macrostructure, (b) is a body centered cubic unit cell gradient lattice distribution configuration diagram in a macrostructure, and (c) is an optimized physical-lattice mixture configuration diagram;
fig. 13 (a) and (b) are graphs of the objective function and the volume fraction optimization iteration in example 3 of the present invention.
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 full-scale parallel topology optimization method of the entity-lattice mixed configuration provided by the embodiment of the invention, as shown in fig. 1, comprises the following steps:
S1, constructing a bivariate parameterized level set function;
Entity and microstructure level set functions constructed based on an implicit modeling method are established by introducing double control parameters T k (T) and T k (T) to establish bivariate level set functions phi k (x, T) and theta k (x, T) of local unit cells, and are defined as follows:
Where the coefficients T k (T) and H k (T) are control parameters with respect to the pseudo-time T, i.e. design variables in the subsequent optimization process. T k (T) represents a design variable of the physical microstructure on the kth unit cell, H k (T) represents a design variable of the lattice microstructure on the kth unit cell, As a physical microstructure level set function with a volume fraction of 1, γ (x) is a lattice microstructure level set function with a predefined small volume fraction,For the physical microstructure level set function control coefficients, C γ is the lattice microstructure level set function control coefficient, and N (x) is a linear interpolation shape function. Regulation and control coefficientAnd C γ is defined as follows:
The level set function f k (x, t) of the local unit cell in the kth entity-lattice hybrid structure form in the discrete design domain is obtained by a boolean operation summing operation according to the defined bivariate level set function, the boolean operation summing operation being defined as follows:
Гk(x,t)＝max(Φk(x,t),θk(x,t))
the microstructure unit cells (i.e., the solid microstructure or the lattice microstructure) are assembled to obtain the whole solid structure or lattice structure. Then, according to the level set function of the local unit cell, a parameterized level set function of the whole structure is obtained, and the parameterized level set function is defined as follows:
Wherein phi (x, T) is a parameterized level set function of the solid structure, θ (x, T) is a parameterized level set function of the lattice structure, T (T) is a global design variable of the solid structure, H (T) is a global design variable of the lattice structure, r (x, T) is a macrostructure level set function of the solid-lattice mixture, the r (x, T) >0 region represents the location of the material contained in the structure, the r (x, T) <0 region represents the blank location of the material not contained in the structure, r (x, T) =0 represents the boundary region of the material and voids in the design domain, D represents the predefined whole design domain, Ω represents the junction evolution region in the optimization, Representing the boundaries of the structure.
Specifically, for a two-dimensional structure, one cell has 4 nodes, the dimensions T k (T) and H k (T) are both 4×1, and for a three-dimensional structure, one cell has 8 nodes, the dimensions T k (T) and H k (T) are both 8×1.
Specifically, the volume fraction of the lattice microstructure unit is predefined before optimization, and the volume fraction can be changed between 0 and 1 or can be predefined at will within a range of 0 to 1. The predefined small volume fraction is 0.06 in this embodiment.
Further, for the dual design variables, design domain discretization is performed:
Design domain discretization is to divide the design domain into a number of regular quadrilateral regions (two-dimensional structures) or regular hexahedral regions (three-dimensional structures) for matching microstructural cells of corresponding dimensions, each region being further divided into fine grids to form a finite element analysis grid. The actual design domain actually comprises 2 sets of virtual grid matching entity structures and lattice structures with the same scale after being discretized, design variables (control parameters) are respectively defined on nodes of the 2 sets of virtual grids, and the two sets of design variables are written into a column vector form, wherein the definition is as follows:
T(t)=[T1(t) T2(t) T3(t) … Tm(t)]T
H(t)=[H1(t) H2(t) H3(t) … Hm(t)]T
Wherein T (T) and H (T) represent design variables of the predefined entity and lattice microstructure, m is the number of the design variables and corresponds to the number of unit cells nodes in the design domain, and the control parameters T k (T) and H k (T) of the unit cells are obtained from the T (T) and the H (T).
S2, establishing a multi-constraint topological optimization mathematical model;
The topological optimization mathematical model with the solid structure and the macroscopic structure volume as double constraints is established by taking control parameters for controlling the solid structure and the lattice structure as design variables and taking structural flexibility minimization (rigidity maximization) as an objective function, and the method comprises the following steps:
find:{T(t),H(t)}
Wherein J (f) is the compliance of the entity-lattice hybrid structure, is set as dimensionless values, epsilon and U are the strain field and displacement field of the structure, B is the material equivalent elastic matrix, a Ф(u,v)＝lФ (v) is the weak form of the elastic equilibrium equation, a Ф (U, v) is the strain energy functional, l Ф (v) is the work done by external force on the virtual displacement, U is the displacement field of the structure, g (f) is the volume constraint function of the macrostructure, f (phi) is the volume constraint function of the entity structure, zeta is the volume fraction constraint value of the given macrostructure, delta is the volume fraction constraint value of the given entity structure, Representing the initial complete volume of the design domain, Ω macro being the region of evolution of the entity-lattice structure in the optimization, Ω solid being the region of evolution of the entity structure in the optimization.
S3, decoupling a Hamilton-Jacobi (Hamilton-Jacobi) partial differential equation;
the level set function is dynamically changing over the pseudo-time t, and the process of structural topology optimization can be described as a process of dynamically changing the level set function over time. Thus, its dynamic model is expressed as:
Differentiating the pseudo time t by two sides of the equation to obtain a partial differential equation of the Hamilton-Jacobi type:
considering normal velocity v n = v n, and normal vector n is defined as Thus, a Hamilton-Jacobi partial differential equation is obtained:
The global parameterized level set function of the defined entity structure and lattice structure is brought into the original Hamilton-Jacobi differential equation, and the partial differential equation is converted into a normal differential equation, and the expression is as follows:
the normal velocity mathematical expression can be obtained:
s4, structural finite element analysis and sensitivity information calculation;
And defining a finite element analysis grid with the same number according to the number of the discrete units, applying constraint and load according to given boundary conditions, carrying out finite element analysis to obtain a strain field and a displacement field of the structure, further calculating strain energy of the units, and converting the strain energy into node strain energy G (gamma) of unit cells.
And further determining a sensitivity information calculation mode:
(1) The sensitivity of the objective function with respect to the two sets of design variables is listed as:
the normal speeds in the step S2 are respectively brought into the following conditions:
According to the chain law:
the sensitivity of the objective function to the two sets of design variables is tabulated by comparing the above formulas:
in the formula, The sensitivity of the variables for the objective function with respect to the physical structure is designed,For the sensitivity of the objective function to lattice structure design variables, δ is the derivative of the herceptin function to the level set function.
(2) The sensitivity of the constraint function with respect to the two sets of design variables is listed as:
in the formula, Sensitivity for macrostructure volume constraints with respect to dual design variables,Sensitivity to self design variables for physical structure volume constraints.
S5, solving an optimization model and updating double design variables;
based on the sensitivity information, a gradient-based optimization algorithm is adopted to solve the topological optimization model, design variable updating is carried out, in the solving process, when the convergence criterion is not met, the step S3 is returned, when the convergence criterion is met, iteration is stopped, and the double design variable value at the moment is used as a final value.
Further, a double optimization criterion method is adopted for solving, and a mobile asymptote optimization algorithm can also be adopted for model solving.
Further, the convergence criterion is defined as follows for reaching a given threshold or for reaching a maximum number of iterations:
Where σ is a given threshold, n max represents a given maximum number of iterations, and J (Γ) n is the objective function value for the nth iteration.
The following are specific examples:
Example 1
The optimized structure is a two-dimensional cantilever beam, and as shown in fig. 4, the two-dimensional cantilever beam has the dimensions of L×H=400×200, the left side of the design domain structure is fixed, the lower right corner applies a vertical downward concentrated load F=1N, the design domain comprises 20×10 single cells, and the single cell size is 20×20. The optimization was performed using solid unit cells and X-shaped unit cells. The entity-lattice parallel topology optimization method provided by the invention is adopted to develop the two-dimensional cantilever beam optimization design. The objective function is structural rigidity maximization (flexibility minimization), macroscopic structure volume fraction constraint is 0.5, physical structure volume fraction constraint is 0.3, and lattice structure is freely optimized under macroscopic volume constraint. After 57 steps of iteration, the optimization is finished, and the topological optimization configuration design of the mixture of the entity and the lattice is obtained as shown in fig. 5, wherein the entity structure is continuously distributed, and the lattice structure is in gradient distribution. The structural flexibility converged to 177.65, the macrostructure volume fraction converged to 0.5, and the physical structure volume fraction converged to 0.3. From the iteration curve of fig. 6, the algorithm exhibits better convergence, and both constraints satisfy the given set value.
To further illustrate the applicability and stability of the method of the present invention, the volume constraints of the solid structure (Vol_solid) were varied, set to Vol_solid 0, 0.1, 0.2, 0.3, 0.4, 0.5, respectively, and the macrostructure volume fractions (Vol_macro) were all set to 0.5, and optimization was performed according to the 6 sets of constraints described above. The results are shown in fig. 7, and clear and correct configuration design can be obtained under each group of constraint conditions, so that the effectiveness of the method provided by the invention is verified. As the volume fraction of solid structures in the design domain increases, the lower the compliance value (Comp) of the structure, i.e., the higher the stiffness of the structure. But the pure solid structure design without considering the lattice is poor in robustness and buckling instability easily occurs.
Example 2
The optimization structure is a two-dimensional Michell beam, as shown in fig. 8, the Michell beam has the dimensions of L×H=600X200, the left lower corner and the right lower corner of the design domain structure are provided with simple branches and fixed constraints, the central part of the lower boundary is applied with a vertical downward concentrated load F=1N, the design domain comprises 30×10 single cells, and the optimization is carried out by adopting solid single cells and X-shaped single cells. And after the optimization is finished, the topological optimization configuration design of the mixture of the entity and the lattice is obtained, the entity structure is continuously distributed, and the lattice structure is in gradient distribution as shown in fig. 9. After 57 iterations, the structural flexibility converged to 28.48, the macrostructure volume fraction converged to 0.5, and the physical structure volume fraction converged to 0.3, and the iteration curve is shown in fig. 10. Different structural examples verify the applicability and stability of the full-scale parallel topology optimization method of the entity-lattice mixed configuration design.
Example 3
The optimized structure is a three-dimensional MBB beam, as shown in fig. 11, the MBB beam has dimensions of l×h×w=280×70×42, the bottom of the left side and the right side of the design domain is a fixed and simply supported, and a vertically downward military load f=10n is applied to the middle position of the top. The design domain comprises 20 multiplied by 5 multiplied by 3 single cells, and the single cell size is selected from three-dimensional solid single cells and body-centered cubic single cells, and the size is 14 multiplied by 14. After 67 iterations, the optimization is finished, and the topological optimization configuration design of the mixture of the entity and the lattice is obtained, wherein the entity structure is continuously distributed, and the lattice structure is in gradient distribution, as shown in fig. 12. The structural flexibility converged to 492007.88, the macrostructure volume fraction converged to 0.5, and the physical structure volume fraction converged to 0.3, and the iteration curve is shown in fig. 13.
The three-dimensional calculation example shows that the method still has better applicability and stability in the topological optimization process of the three-dimensional structure.
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 full-scale parallel topology optimization method of the entity-lattice mixed configuration is characterized by comprising the following steps of:
s1, introducing control parameters, constructing a level set function of an entity microstructure and a lattice microstructure on a unit cell, and further obtaining a global parameterized level set function of an entity-lattice hybrid structure;
the global parameterized level set function is specifically:
Wherein phi (x, T) is a level set function of the solid structure, theta (x, T) is a level set function of the lattice structure, and T (T) and H (T) are control parameters of the solid structure and the lattice structure respectively, namely design variables; as a physical microstructure level set function with a volume fraction of 1, γ (x) is a lattice microstructure level set function with a predefined small volume fraction, For the physical microstructure level set function control coefficients, C γ is the lattice microstructure level set function control coefficients, N (x) is a linear interpolation shape function, f (x, t) is a global parameterization level set function of the macro structure of the physical-lattice mixture, f (x, t) >0 region represents the position of the material contained in the structure, f (x, t) <0 region represents the blank position of the material not contained in the structure, f (x, t) =0 region represents the boundary region of the material and the cavity in the design domain, D represents the predefined whole design domain, Ω represents the structure region in the optimization,Representing the boundaries of the structure;
S2, establishing a topological optimization mathematical model by taking control parameters for controlling the entity structure and the lattice structure as double design variables, taking the overall structure flexibility as an objective function and taking the entity structure volume and the macrostructure volume as double constraint conditions;
S3, introducing the global parameterized level set function into a partial differential equation of the Hamiltonian-Jacobian equation to obtain Chang Weifen equation;
S4, determining sensitivity columns of the objective function and the constraint condition on the design variables based on a normal differential equation to obtain sensitivity information;
and S5, solving the topological optimization model by adopting a gradient-based optimization algorithm based on sensitivity information to obtain double design variables, thereby determining the optimal entity-crystal mixed configuration.
2. The method for full-scale parallel topological optimization of entity-lattice mixed configuration according to claim 1, wherein the control coefficients areThe calculation of C γ is as follows:
3. The method for full-scale parallel topological optimization of a solid-lattice hybrid configuration according to claim 1, wherein in step S2, the topological optimization mathematical model is specifically:
find:{T(t),H(t)}
min:
s.t:
Wherein J (f) is the overall compliance of the entity-lattice hybrid structure, ε and U are the strain fields and displacement fields of discrete units in the structure, B is the material equivalent elastic matrix, a Ф (U, v) is the functional of strain energy, l Ф (v) is the work done by external force on virtual displacement, U is the displacement field of the structure, g (f) is the volume constraint function of the macrostructure, f (Φ) is the volume constraint function of the entity structure, ζ is the volume fraction constraint value of a given macrostructure, δ is the volume fraction constraint value of a given entity structure, Representing the initial complete volume of the design domain, Ω macro being the region of evolution of the entity-lattice structure in optimization, Ω solid being the region of evolution of the entity structure in optimization, T k (T) representing the design variables of the entity structure on the kth unit cell, H k (T) representing the design variables of the lattice structure on the kth unit cell, m being the number of unit cells in the design domain.
4. A method of full-scale parallel topology optimization of a hybrid entity-lattice configuration of claim 3, wherein, in step S3, the resulting ordinary differential equation is as follows:
wherein t is a pseudo time, The normal speeds of boundary evolution of the solid structure and the lattice structure in the optimization process are respectively.
5. The method for full-scale parallel topology optimization of a hybrid entity-lattice configuration of claim 4, wherein step S4, determining a sensitivity column of an objective function with respect to a design variable, comprises:
based on the ordinary differential equation, a normal velocity expression is determined and substituted into a sensitivity list of the objective function with respect to the pseudo time t, and the sensitivity list of the objective function with respect to the design variable is obtained as follows:
in the formula, The sensitivity of the variables for the objective function with respect to the physical structure is designed,The sensitivity of the objective function with respect to lattice structure design variables, delta is the derivative of the herceptin function with respect to the level set function, and G (f) is the node strain energy.
6. The method for full-scale parallel topological optimization of a solid-lattice hybrid configuration according to claim 5, wherein in step S4, the sensitivity of the constraint on the design variables is as follows:
in the formula, Sensitivity of the volume constraint function for macrostructure with respect to dual design variables,Sensitivity of the function to self-design variables is constrained for the physical structure volume.
7. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration of claim 1, wherein design domain discretization is performed in advance, comprising:
dividing a design domain into a certain number of regular quadrilateral areas or regular hexahedral areas, matching each area with microstructure cells with corresponding sizes, and further dividing each area into fine grids to form a finite element analysis grid;
two sets of grids are obtained through the method so as to be matched with the entity microstructure and the lattice microstructure respectively, and two design variables are defined on nodes of the two sets of grids respectively.
8. The full-scale parallel topology optimization method of a solid-lattice hybrid configuration of any one of claims 1-7, wherein step S5, a gradient-based optimization algorithm is adopted to solve a topology optimization model, and design variables are iteratively updated;
The convergence criterion is:
Or n is greater than or equal to n max
Where σ is a given threshold, n max is a given maximum number of iterations, and J (Γ) n is the objective function value for the nth iteration.
9. A full-scale parallel topology optimization system of a hybrid entity-lattice configuration, comprising a processor configured to perform the full-scale parallel topology optimization method of a hybrid entity-lattice configuration of any one of claims 1-8.
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