Search

CN-121983191-A - Gradient method-based two-dimensional phonon crystal multi-target topology optimization method

CN121983191ACN 121983191 ACN121983191 ACN 121983191ACN-121983191-A

Abstract

The invention discloses a gradient method-based two-dimensional photonic crystal multi-objective topological optimization method which comprises the steps of constructing a finite element analysis model of a photonic crystal, taking the relative density of units as a design variable, parameterizing material properties by adopting a material interpolation model, acquiring discrete characteristic frequency data and performing smooth processing, constructing a multi-objective optimization problem, wherein the objective of the multi-objective optimization problem is to simultaneously maximize band gap width and minimize structural flexibility or simultaneously maximize band gap width and minimize thermal flexibility, respectively calculating the sensitivity of each objective function to the design variable, performing normalization processing, carrying out weighted fusion on the normalized sensitivity, filtering and historical averaging on a sensitivity field to smooth an updating process, using a Heaiside projection to obtain a clear topological structure, updating the design variable based on an optimal criterion method, and iteratively optimizing until the optimal topological configuration is output by meeting a preset convergence criterion. The invention obviously improves the design efficiency of the comprehensive performance of the phonon crystal.

Inventors

  • WANG YINGJUN
  • YANG JINGQI

Assignees

  • 华南理工大学

Dates

Publication Date
20260505
Application Date
20251224

Claims (10)

  1. 1. The two-dimensional phononic crystal multi-target topological optimization method based on the gradient method is characterized by comprising the following steps of: constructing a finite element analysis model of phonon crystal, taking the relative density of units as a design variable, and parameterizing the material property by adopting a material interpolation model; Discrete characteristic frequency data are obtained, and smoothing processing is carried out on the discrete characteristic frequency; Constructing a multi-objective optimization problem with the objective of simultaneously maximizing the bandgap width and minimizing the structural compliance, or simultaneously maximizing the bandgap width and minimizing the thermal compliance; Respectively calculating the sensitivity of each objective function to the design variable, and carrying out normalization processing on the sensitivity sequence of each objective function; weighting and fusing the normalized sensitivity through a preset weight coefficient to form a unified comprehensive sensitivity field; filtering and historical averaging the sensitivity field to smooth the update process, using the Heaviside projection to obtain a clear topology; updating the design variables based on an optimal criterion method; And presetting a convergence criterion, and iteratively optimizing until the preset convergence criterion is met to output an optimal topological configuration.
  2. 2. The gradient-based two-dimensional photonic crystal multi-target topological optimization method according to claim 1, wherein the finite element analysis model comprises a wave equation finite element model and a finite element model for structural mechanics analysis or steady-state thermal conduction analysis.
  3. 3. The gradient method-based two-dimensional photonic crystal multi-target topological optimization method according to claim 2, wherein the constructing of the finite element analysis model of the photonic crystal specifically comprises: setting a two-dimensional phonon crystal unit cell design domain, adopting a two-phase material system, setting material volume fraction constraint, establishing a wave equation finite element model under periodic boundary conditions based on the Bloch theorem, selecting adjacent band gap serial numbers to be optimized, setting boundary conditions and loads required by structural flexibility or thermal flexibility optimization, and simultaneously establishing a finite element model for structural mechanical analysis or steady-state thermal conduction analysis.
  4. 4. The gradient-method-based two-dimensional photonic crystal multi-target topological optimization method according to claim 1, wherein the material property is parameterized by adopting a material interpolation model, and specifically comprising: the material interpolation model adopts a linear interpolation mode in band gap calculation; An exponential penalty model of elastic modulus is adopted in the analysis of the structural flexibility; An exponential penalty model for thermal conductivity is employed in the thermal compliance analysis.
  5. 5. The gradient-method-based two-dimensional photonic crystal multi-target topological optimization method according to claim 4, wherein the material properties comprise a prune coefficient, an elastic modulus, a mass density and a thermal conductivity.
  6. 6. The gradient-method-based two-dimensional photonic crystal multi-target topology optimization method according to claim 1, wherein smoothing is performed on discrete characteristic frequencies, and specifically comprising: and smoothing the discrete characteristic frequency based on a KS function, wherein the KS function adopts a lower bound aggregation form when processing the band gap lower limit frequency, and adopts an upper bound aggregation form when processing the band gap upper limit frequency.
  7. 7. The gradient-method-based two-dimensional photonic crystal multi-objective topology optimization method of claim 1, wherein the calculating of the sensitivity of each objective function to the design variable comprises: and respectively calculating the sensitivity of the band gap target, the structural flexibility target and the thermal flexibility target to the design variable, solving the band gap sensitivity by adopting an analytical method based on the derivative of the characteristic value, and solving the structural flexibility sensitivity and the thermal flexibility sensitivity by adopting an accompanying variable method.
  8. 8. The gradient-method-based two-dimensional photonic crystal multi-target topology optimization method of claim 7, wherein the normalizing process is performed on the sensitivity sequence of each objective function, and specifically comprises: Carrying out logarithmic transformation based on 10 on the band gap original sensitivity value, and mapping the transformed numerical value to a [0,1] interval by a maximum value-minimum value normalization method; structural flexibility sensitivity and thermal flexibility sensitivity are mapped to [0,1] using a maximum-minimum normalization method.
  9. 9. The gradient method-based two-dimensional photonic crystal multi-objective topological optimization method according to claim 1, wherein the optimization criterion method introduces a movement limiting mechanism in the process of updating the design variables, and the damping coefficient is determined according to the nonlinearity degree of the optimization problem by setting the damping coefficient to limit the maximum variation amplitude of the design variables in a single iteration.
  10. 10. The gradient method-based two-dimensional photonic crystal multi-target topological optimization method is characterized in that a linear filtering method based on convolution operation is adopted for filtering a sensitivity field, the filtering radius and the unit size are kept in a fixed proportion, and a weight function is determined according to the distance between the centers of the units; The Heaviside projection adopts a continuous and differentiable approximate step function, and the definition degree of the material boundary formation is controlled by adjusting projection parameters.

Description

Gradient method-based two-dimensional phonon crystal multi-target topology optimization method Technical Field The invention relates to the technical field of phonon crystal topology optimization, in particular to a two-dimensional phonon crystal multi-target topology optimization method based on a gradient method. Background The phononic crystal is an artificial material with a periodic structure, can regulate and control the propagation behavior of elastic waves, and has wide application in the fields of vibration suppression, acoustic wave diversion, acoustic stealth and the like. The traditional phonon crystal design depends on experience or trial and error methods, and other physical properties such as structural rigidity or heat conduction performance are difficult to consider while the band gap performance is ensured. With the continuous increase of the requirements of engineering application on the multifunctionality of materials, how to realize cooperative optimization between wide band gap and good mechanical/thermal properties has become a key problem to be solved urgently. Topology optimization can realize the optimal configuration of structural performance by optimizing the spatial distribution of materials in a design domain. However, there is a complex coupling relation between the band gap characteristics of phonon crystals and targets such as structural flexibility and thermal flexibility, and the traditional single-target optimization method is difficult to realize balanced design of multiple physical properties. In addition, the non-smoothness of the band gap objective function and the numerical instability phenomenon in the multi-objective sensitivity integration process limit the further application of the topology optimization in phonon crystal multi-performance collaborative design. In the prior art, although research attempts are made to apply topological optimization to phonon crystal design, most of the prior art focuses on optimization of single band gap performance, and comprehensive consideration of multiple physical field performance is lacking. Phononic crystal structures in the aerospace field, for example, need to possess both excellent vibration isolation properties (wide bandgap) and sufficient structural rigidity (low structural compliance) to withstand mechanical loads, or good heat dissipation properties (low thermal compliance) to prevent overheating of the device. If the band gap width is simply pursued, the rigidity of the structure is often too low or the thermal performance is often deteriorated, and vice versa, a topological optimization framework capable of effectively cooperatively optimizing multiple performances such as the band gap of the phonon crystal and mechanics/heat is lacked, so that the comprehensive performance of the designed structure is poor and is difficult to directly apply to a complex multi-physical field environment. Therefore, there is an urgent need to develop a method capable of efficiently and stably implementing multi-objective topology optimization of phononic crystals, so as to meet the design requirements of modern engineering on multifunctional materials. Disclosure of Invention In order to overcome the defects and shortcomings in the prior art, the invention provides a two-dimensional photonic crystal multi-target topological optimization method based on a gradient method, a photonic crystal multi-physical-property multi-target topological optimization frame is constructed, and the elastic band gap and the structure/thermal flexibility of the photonic crystal are synchronously optimized through a gradient optimization algorithm, so that the design efficiency of the comprehensive performance of the photonic crystal is remarkably improved. In order to achieve the above purpose, the present invention adopts the following technical scheme: The invention provides a two-dimensional phonon crystal multi-target topology optimization method based on a gradient method, which comprises the following steps: constructing a finite element analysis model of phonon crystal, taking the relative density of units as a design variable, and parameterizing the material property by adopting a material interpolation model; Discrete characteristic frequency data are obtained, and smoothing processing is carried out on the discrete characteristic frequency; Constructing a multi-objective optimization problem with the objective of simultaneously maximizing the bandgap width and minimizing the structural compliance, or simultaneously maximizing the bandgap width and minimizing the thermal compliance; Respectively calculating the sensitivity of each objective function to the design variable, and carrying out normalization processing on the sensitivity sequence of each objective function; weighting and fusing the normalized sensitivity through a preset weight coefficient to form a unified comprehensive sensitivity field; filtering and historical averaging the se