Optimization Design Method for a Lightweight Energy Absorbing and Vibration Damping Multifunctional Lattice Structure with Phononic Band Gap

Abstract

The present invention discloses an optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap, including: topologically optimizing and designing a new lightweight topological configuration based on the independent continuous mapping method; reconstructing the topological configuration into a parametric structure, and combining it with a chiral structure to rotate it into a three-dimensional cell structure with a phononic band gap; establishing a finite element model of the cell structure, and performing simulation analysis on the compression process, mode, and band gap of the cell; establishing a parameter optimization model with the geometric parameters of the cell structure as design variables, the maximum internal energy as the optimization objective, and the first natural frequency as the constraint; establishing a surrogate model of the internal energy and the first natural frequency with respect to the design variables based on the response surface method; and using a nonlinear quadratic programming algorithm to solve the parameter optimization model to obtain the optimal parameters of the cell. The method of the present invention can efficiently design a lightweight multifunctional lattice structure, shorten the structural design cycle, improve work efficiency, save design costs, and has very important application value for the design of lightweight energy-absorbing and vibration-damping lattice structures in fields such as aerospace.

Description

Technical Field

[0001] The present invention relates to the technical field of the design of buffer protection devices in the fields of aerospace and automobiles, and particularly relates to an optimized design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with phononic band gaps. Background Technique

[0002] Deep space exploration refers to the exploration and research of the external space environment of the Earth and celestial bodies by humans. Deep space exploration equipment has become a product of the world's technological forefront and market demand. Mars exploration is an important deep space exploration mission. Doing a good job in the preliminary work of deep space exploration missions and the structural design with scientific goals is a major demand in the current aerospace field. To ensure the stable landing of the detector on the planet's surface, the design of the landing buffer device is crucial. Currently, lattice structures are a type of new artificial design material with periodic or non-periodic arrangements of hole cell structures. Due to their characteristics such as light weight, high load-bearing capacity, and vibration damping, they have broad application prospects in buffer protection devices. In addition, lattice structures have high structural designability and programmability. Therefore, using them to replace traditional materials for the design of buffer devices can achieve the coordination of multiple functions, improve the structural efficiency, reduce the equipment mass, and thus reduce costs. The design of multifunctional lattice structures has interdisciplinary difficulties compared with single-performance lattice structures, such as large computational amounts, high complexity in modeling and solving, and prominent coupling effects. Therefore, a systematic structural design method needs to be developed to realize the design of multifunctional lattice structures. Summary of the Invention

[0003] The technical problem to be solved by the present invention is how to provide an optimized design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with phononic band gaps, which can avoid repeated modeling and calculation during the structural design process, shorten the design cycle, improve work efficiency, and save design costs.

[0004] To solve the above technical problem, the technical solution adopted by the present invention is: an optimized design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with phononic band gaps, comprising the following steps:

[0005] S1: Based on the ICM method, establish a lightweight topology optimization model with the minimum volume as the objective, the node displacement as the constraint, and the grid unit as the topology variable. Design the boundary conditions of the design domain and solve the topology optimization model. If it converges, obtain the cell topology configuration; if it does not converge, modify the topology optimization parameter settings until the result converges;

[0006] S2: Based on the topology optimization result of step S1, geometrically reconstruct the cell topology configuration into a parametric two-dimensional cell, and combine the chiral structure to perform rotational deformation on the two-dimensional cell to obtain a three-dimensional cell structure;

[0007] S3: Establish the three-dimensional cell finite element model obtained in step S2, perform quasi-static compression on the cell to obtain the internal energy of the structure during compression, perform modal analysis on the cell to obtain the natural frequency and vibration mode diagram of the structure, and perform band structure analysis and transmission characteristic analysis on the cell to obtain the phonon band gap characteristics of the structure;

[0008] S4: On the basis of step S3, establish a parameter optimization model with the maximum internal energy as the objective, the first-order natural frequency as the constraint, and the cell geometric parameters θ, R 2 and R 5 as the design variables, use the Latin hypercube sampling method to design sample points, fit the response surface functions E(x) and f 1 (x) of the internal energy and the first-order natural frequency with respect to the design variables and conduct accuracy tests;

[0009] S5: Adopt the nonlinear quadratic programming (NLPQL) algorithm, and on the basis of step S4, solve the parameter optimization model. If the iteration converges, the optimal cell geometric parameters can be obtained; if the solution does not converge, modify the parameter optimization model and the parameters until the optimization iteration converges;

[0010] S6: On the basis of step S5, assemble the parameter-optimized cells into a lattice structure in a dodecagon staggered arrangement.

[0011] The beneficial effects of adopting the above technical solutions are as follows: (1) The present invention provides a systematic lattice structure design framework combining topology optimization and parameter optimization. This framework is applicable to the optimization design of multifunctional lattice structures, including the complete process from conceptual design to detailed design, avoiding repeated modeling and calculation during the structure design process;

[0012] (2) On the one hand, this method performs topology optimization based on the ICM method to obtain an initial configuration of a new type of lightweight two-dimensional lattice structure cell; on the other hand, based on the response surface method, it accurately fits the functional relationship between mechanical properties and cell parameters and quickly obtains the optimal parameter values, providing a systematic and feasible method for the optimization design of new lattice structures, shortening the design cycle of lattice structures, improving work efficiency, and saving design costs. Description of the Drawings

[0013] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0014] Figure 1 is the flowchart of the optimization design method of the lattice structure described in the embodiment of the present invention;

[0015] Figure 2 are the configuration diagrams involved in the lattice structure design process;

[0016] Figure 3 is the cell compression load-displacement curve;

[0017] Figure 4 is the first-order modal vibration mode diagram of the unit cell;

[0018] Figure 5 is the phonon band gap energy band structure diagram and transmission characteristic diagram of the unit cell;

[0019] Figure 6 is the compression load-displacement curve diagram of the final lattice structure. Detailed implementation manners

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0021] Many specific details are set forth in the following description in order to provide a thorough understanding of the present invention, but the present invention may be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0022] As Figure 1 shown, the embodiments of the present invention disclose an optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phonon band gap, including the following steps:

[0023] The first step is to establish a lightweight topology optimization model based on the ICM method with displacement as the constraint and minimum volume as the objective. The topology optimization design domain is a rectangle of 14×10 mm 2 As Figure 2 shown, the grid side length is set to 0.1 mm, and there are a total of 14,000 grids. The method selects the structural material as aluminum alloy, with an elastic modulus of 72.4 GPa, a Poisson's ratio of 0.33, and a density of 2800 kg / m 3 . Fixed constraints are applied at the midpoints of the left and right sides of the design domain, and concentrated loads F = 1000 N are applied at the midpoints of the upper and lower sides and at a distance of 1 / 7 of the side length from the endpoints. The dual sequential quadratic programming algorithm is used to solve the optimization model.

[0024] The topology optimization model is:

[0025]

[0026] where t is the topology variable;

[0027] L is the number of topology variables, which is the number of grid cells, 14,000;

[0028] E L is the topological variable space;

[0029] V(t) is the structural volume;

[0030] u j (t) is the nodal displacement;

[0031] is the displacement constraint value;

[0032] t min is the lower limit of the topological variable;

[0033] In the second step, the geometric reconstruction of the irregular cell topological configuration is carried out into a parameterized two-dimensional cell, and the two-dimensional cell is rotationally deformed in combination with the chiral structure to obtain a three-dimensional cell structure, as Figure 2 shown. The geometric parameters of the cell and the chiral structure are shown in Table 1;

[0034] Table 1 Geometric parameters of two-dimensional cell and chiral structure

[0035]

[0036] In the third step, the finite element method is used to analyze the mechanical properties of the cell. First, the quasi-static compression analysis of the cell is carried out by using ABAQUS explicit dynamics to obtain the load-displacement curve of the cell compression process, as Figure 3 shown, and the internal energy at a compression ratio of 20% is extracted, which is 533.073 mJ; then the bottom of the cell is set as a fixed constraint for the modal analysis of the cell, and the first natural frequency value of the result is 7323.6 Hz, and the corresponding vibration mode diagram is as Figure 4 shown; finally, the phonon band gap characteristics of the lattice structure are verified by using COMSOL, and the energy band structure and transmission characteristic curve of the cell are analyzed, as Figure 5 shown. It can be seen from the figure that there are obvious high-frequency and wide-band band gap intervals.

[0037] In the fourth step, a parameter optimization model is established with the maximum internal energy as the objective, the first natural frequency as the constraint, and the cell geometric parameters θ, R 2 and R 5 as the design variables; the Latin hypercube sampling method is used to design sample points, and the response surface functions E(x) and f 1 (x) of the internal energy and the first natural frequency with respect to the design variables are fitted and tested.

[0038] The parameter optimization model is:

[0039]

[0040] where x is the design variable vector;

[0041] E Tis the design variable space;

[0042] T is the number of design variables, and its value is 3;

[0043] E(x) is the objective function of the internal energy with respect to the design variables;

[0044] f 1 (x) is the constraint function of the first natural frequency with respect to the design variables;

[0045] f 1 is the constraint value of the first natural frequency;

[0046] x i is the design variable, which are the cell geometric parameters θ, R 2 and R 5 ;

[0047] x i are the upper and lower limits of the design variables.

[0048] The parameters of the sample points randomly generated in the method and the mechanical property responses are shown in Table 2. In the method, the design variables θ, R 2 and R 5 have the value ranges of 0° ≤ θ ≤ 90°, 7.5° ≤ θ ≤ 22.5° and 5° ≤ θ ≤ 11°, respectively.

[0049] Table 2 Sample Points

[0050]

[0051] Use a ternary cubic polynomial to fit the display functional relationships of the internal energy and the first natural frequency with respect to the design variables θ, R 2 and R 5 . Assume that g'(x) is the approximate explicit expression of the true response function g(x), and its basic form is:

[0052]

[0053] where β 0 , β i , β ii , β ij are the undetermined constant coefficients of each term. The final expressions for the maximum internal energy and the first natural frequency are:

[0054]

[0055]

[0056] In the formula, f 1 (θ, R 2 , R 5 ) and E(θ, R2 , R 5 ) are the internal energy and the first-order natural frequency with respect to the design variables θ, R 2 and R 5 of the response surface response function. The multiple correlation coefficient and the modified multiple correlation coefficient of the internal energy are 0.991 and 0.975 respectively, and the root mean square error is 0.082; the multiple correlation coefficient and the modified multiple correlation coefficient of the internal energy are 0.986 and 0.961 respectively, and the root mean square error is 0.0974.

[0057] Step 5: Use the NLPQL algorithm to solve the parameter optimization model. The constraint value of the first-order natural frequency is set to 7700 Hz. For the final optimization result of the method cell, the parameter θ is 50.716°, R 2 is 21.52°, R 5 is 9.791°; the internal energy is 596.114 mJ, an increase of 11.8%, and the first-order natural frequency is 7700 Hz, meeting the constraint conditions. Use ABAQUS to re-establish the model with the optimized parameters for finite element analysis. The final numerical analysis results of the first-order natural frequency and the internal energy are 7517.5 Hz and 595.312 mJ respectively, and the errors are 2.37% and 0.13% respectively. Since the result of solving the parameter optimization model by the method converges, the process of modifying the parameter optimization settings in the lattice structure design flowchart is not reflected. If the solution of the parameter optimization model does not converge, then modify the first-order natural frequency in the constraint conditions of the parameter optimization model in Step 4 (increase or decrease) until the calculation converges.

[0058] Step 6: Assemble the parameter-optimized cells into a 3×3×3 lattice structure in a dodecagon staggered arrangement. Assemble the lattice structure in this arrangement so that its internal energy is a multiple of the internal energy of the cell, realizing the programmability from the cell to the lattice structure. Use ABAQUS to obtain the internal energy of the single-layer 3×3 lattice structure compressed by 20% in this arrangement, with a value of 4890.19 mJ, which is close to the sum of the internal energies of 9 single cells, 4797.66 mJ, with an error of 1.93%, within the acceptable range. Perform quasi-static compression on the finally obtained lattice structure to obtain its load-displacement curve, as Figure 6 shown, and the deformation of each layer is basically the same during the compression process.

[0059] As described above, only some specific implementation manners in the present invention are provided, but the protection scope of the present invention is not limited thereto. Any equivalent changes, modifications, equal-proportion enlargements or reductions made in accordance with the design spirit of the present invention should be covered within the protection scope of the present invention.

Claims

1. An optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap, characterized in that, it includes the following steps: S1: Based on the ICM method, establish a lightweight topology optimization model with the minimum volume as the objective, the node displacement as the constraint, and the grid element as the topology variable. Design and solve the topology optimization model for the design domain boundary conditions. If it converges, obtain the cell topology configuration; if it does not converge, modify the topology optimization parameter settings until the result converges. S2: Based on the topology optimization result of step S1, geometrically reconstruct the cell topology configuration into a parametric two-dimensional cell, and combine the chiral structure to perform rotational deformation on the two-dimensional cell to obtain a three-dimensional cell structure. S3: Establish a finite element model of the three-dimensional cell obtained in step S2, perform quasi-static compression on the cell to obtain the internal energy of the structure during the compression process, perform modal analysis on the cell to obtain the natural frequency and vibration mode diagram of the structure, and perform band structure analysis and transmission characteristic analysis on the cell to obtain the phononic band gap characteristics of the structure. S4: On the basis of step S3, establish a parameter optimization model with the maximum internal energy as the objective, the first natural frequency as the constraint, and the cell geometric parameters θ, R 2 and R 5 as the design variables. Use the Latin hypercube sampling method to design sample points, fit the response surface functions E(x) and f 1 (x) of the internal energy and the first natural frequency with respect to the design variables and conduct accuracy tests; S5: Adopt the nonlinear quadratic programming NLPQL algorithm. On the basis of step S4, solve the parameter optimization model. If the iteration converges, obtain the optimal cell geometric parameters; if the solution does not converge, modify the parameter optimization model and parameters until the optimization iteration converges. S6: Assemble the parameter-optimized cells into a lattice structure in a dodecagon staggered arrangement manner on the basis of step S5.

2. The optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap according to claim 1, characterized in that: The topology optimization model in step S1 is as follows: In the formula, t is the topology variable; L is the number of topology variables, that is, the number of grid elements 14000; E L is the topological variable space; V(t) is the structure volume; u j (t) is the nodal displacement; is the displacement constraint value; t min is the lower limit of the topological variable.

3. The optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap according to claim 1, characterized in that: The parameter optimization model in step S4 is as follows: In the formula, x is the design variable vector; E T is the design variable space; T is the number of design variables, and the value is 3; E(x) is the objective function of the internal energy with respect to the design variable; f 1 (x) is the constraint function of the first natural frequency with respect to the design variables; f 1 is the first-order natural frequency constraint value; x i are design variables, which are the cellular geometric parameters θ and R 2 and R 5 ; x i are the upper and lower limits of the design variables.

4. The optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap according to claim 3, characterized in that: The basic form of the response function of the internal energy and the first-order natural frequency with respect to the design variable in step S4 is: Among them, β 0 , β i , β ii , β ij are undetermined constant coefficients for each term.

5. The optimization design method for a lightweight energy-absorbing and vibration-damping multifunctional lattice structure with a phononic band gap according to claim 4, characterized in that: In the step S4, the specific expressions E(x) and f 1 (x) of the internal energy and the first-order natural frequency are as follows: where f 1 (θ, R 2 , R 5 ) and E(θ, R 2 , R 5 ) are the response surface response functions of the internal energy and the first-order natural frequency with respect to the design variables θ, R 2 and R 5 .

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