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CN-121980661-A - Multistage self-supporting constraint topology optimization method and system combining projection and virtual pyramid

CN121980661ACN 121980661 ACN121980661 ACN 121980661ACN-121980661-A

Abstract

The invention discloses a multistage self-supporting constraint topology optimization method and system combining projection and virtual pyramid. The method comprises the steps of initializing a design domain and generating a non-uniform gradient initial density field, applying a total load vector overlapped by a bearing working condition and a guide load to define a key protection area, calculating projection supporting quantity of each grid unit and applying punishment, constructing a multi-layer virtual pyramid supporting domain which is downwards conical and expanded, calculating virtual pyramid supporting quantity and applying punishment, overlapping two punishment items to the sensitivity of which the original sensitivity is corrected, and iteratively updating design variables and carrying out protective correction on the key area until an optimized structure is converged and output. According to the invention, through a multistage self-supporting constraint mechanism, the overhang defect in the traditional topological optimization structure is effectively eliminated, a large amount of external supports are prevented from being added in additive manufacturing, the material consumption and the post-treatment difficulty are obviously reduced, and the cooperative promotion of the mechanical property and the manufacturability is realized.

Inventors

  • LIAO WENHE
  • HUANG JINGCHANG
  • LIU TINGTING
  • ZHANG CHANGDONG

Assignees

  • 南京理工大学

Dates

Publication Date
20260505
Application Date
20260308

Claims (10)

  1. 1. A multistage self-supporting constraint topology optimization method combining projection and virtual pyramid is characterized by comprising the following steps: S1, initializing a design domain of a beam structure, dispersing the design domain into grid cells, giving different initial density values to each grid cell according to position coordinates of each grid cell, and introducing a boundary effect function to locally correct the initial density values of each grid cell to generate a non-uniform gradient initial density field comprising a uniform distribution region and a gradient region; S2, applying a total load vector generated by superposition of a bearing working condition and a guide load with a preset amplitude on an initial density field, and defining a key area for keeping the density of a material at a preset position of a design domain; S3, calculating the projection supporting quantity of each grid cell according to the density value of other grid cells in the projection coverage area of the grid cell, and when the projection supporting quantity is lower than a preset projection supporting quantity threshold value, applying punishment to the grid cell and recording the punishment as a projection supporting punishment item; S4, after projection support penalty items are applied, constructing a multi-layer pyramid support domain which is downwards conical and expanded for each grid unit, calculating virtual pyramid support quantity, and when the virtual pyramid support quantity does not meet a preset support layer number mode and a support density threshold value, applying cross-layer penalty to the grid unit, and recording as a virtual pyramid penalty item; S5, overlapping the projection support penalty term and the virtual pyramid penalty term to the original sensitivity according to a preset sequence to obtain corrected sensitivity, wherein the sensitivity is the partial derivative of the cantilever structure flexibility on the grid cell density value; and S6, updating the density value of each grid cell by using the corrected sensitivity, performing protective correction on the density value of the grid cells in the key area, and repeating the steps S3 to S5 until the optimization converges and outputting the optimized structure of the beam structure.
  2. 2. The method for multi-stage self-supporting constrained topology optimization combining projection and virtual pyramid as claimed in claim 1, wherein in step S1, the specific process of generating the non-uniform gradient initial density field is as follows: setting a target volume fraction Total layer number of structure Determining the layer height of 30% at the bottom as uniformly distributed region and the layer height of 70% at the upper as gradient region, for the first Layer grid cell, initial density of The calculation formula is as follows: Wherein, the Representing the distance of the grid cell to the active area boundary; Representing a boundary effect function; Representing a contraction factor function; represent the first Base density of the layer.
  3. 3. The multistage self-supporting constrained topology optimization method combining projection and virtual pyramid as claimed in claim 1, wherein in step S3, the calculation formula of the projection supporting quantity of the grid unit is: Wherein, the Representing the projected support amount of the grid cell; To support grid cells in an area Density variable of (2); Representing a projected support area; As a gaussian weight function.
  4. 4. The method of claim 1, wherein in step S4, the multi-layered pyramid support domain is based on a maximum overhang angle Determination of the first Cross-sectional area of layer pyramid The method meets the following conditions: Cross-layer importance weighting The calculation formula is as follows: Layer number of pyramids The selection criteria are: Virtual pyramid support The calculation formula of (2) is as follows: Wherein, the Is the weight attenuation coefficient; a weighted cumulative total of all supporting grid cell densities within the layer L pyramidal projection cross-section; representing the calculation cost brought by the layer; a benefit/cost threshold for acceptance; The representation is located at the first A spatial collection of all support grid cells within the layer virtual pyramid; Is a Gaussian weight function; To support grid cells in an area Density variable of (a).
  5. 5. The multistage self-supporting constraint topology optimization method combining projection and virtual pyramid as claimed in claim 1, wherein in step S4, the preset supporting layer number mode and supporting density threshold value adopt a stage-by-stage adjustment strategy, and in the optimization iteration process, when the iteration step number reaches a preset intermediate node or the standard function change rate of adjacent step numbers is stabilized in a preset range, the layer number switching is triggered, the supporting layer number is sequentially reduced, the supporting density threshold value is synchronously increased, and the supporting constraint is gradually transited from a front-stage multilayer search mode to a later-stage single-layer path mode.
  6. 6. The multistage self-supporting constrained topology optimization method combining projection and virtual pyramid as claimed in claim 1, wherein in step S5, the projection supporting penalty term and virtual pyramid penalty term are superimposed to the original sensitivity according to a preset sequence to obtain the corrected sensitivity, and the specific process is as follows: First overlapping projection region support punishment item Re-overlaying virtual pyramid penalty term Sensitivity after correction The calculation formula of (2) is as follows: Wherein, the Is the flexibility of the cantilever structure For design variable grid cell density The partial derivative of (a), i.e. the sensitivity.
  7. 7. The multistage self-supporting constrained topology optimization method combining projection and virtual pyramid as claimed in claim 1, wherein in step S6, the density value of grid cells in the key area is subjected to protective correction, and a specific calculation formula is as follows: Wherein, the Is shown in the first In the sub-optimization iteration step, the coordinates are as follows Final density value of grid cells subjected to protective correction; Is shown in the first In the sub-optimization iteration step, the coordinates before the protective correction is not performed and are obtained based on the sensitivity after the correction just updated Is a grid cell density value of (1); Represents the first Minimum density threshold within layer critical protection areas.
  8. 8. A multi-stage self-supporting constrained topology optimization system combining projection and virtual pyramids, comprising: The initialization and pretreatment module is used for initializing a design domain of the beam structure and dispersing the design domain into grid cells; according to the position coordinates of each grid unit, giving different initial density values, introducing a boundary effect function to locally correct the initial density values of each grid unit, and generating a non-uniform gradient initial density field comprising a uniform distribution area and a gradient area; The projection support constraint application module is used for calculating the projection support quantity of each grid unit according to the density value of other grid units in the projection coverage area of the grid unit, and when the projection support quantity is lower than a preset projection support quantity threshold value, punishment is applied to the grid unit and recorded as a projection support punishment item; The virtual pyramid constraint applying module is used for constructing a multi-layer pyramid supporting domain which is downwards conical and expanded for each grid unit after the projection supporting penalty term is applied, calculating the virtual pyramid supporting quantity of the multi-layer pyramid supporting domain, and applying cross-layer penalty to the grid unit when the virtual pyramid supporting quantity does not meet a preset supporting layer number mode and supporting density threshold value, and recording the cross-layer penalty as the virtual pyramid penalty term; The sensitivity correction module is used for superposing the projection support penalty term and the virtual pyramid penalty term to the original sensitivity according to a preset sequence to obtain corrected sensitivity, wherein the sensitivity is the partial derivative of the cantilever structure flexibility on the grid cell density value; The iterative optimization module is used for updating the density value of each grid cell by utilizing the corrected sensitivity, carrying out protective correction on the density value of the grid cells in the key area, and repeatedly executing the steps of projection support constraint application, virtual pyramid constraint application and sensitivity correction until the preset convergence condition is met, and outputting an optimized structure of the beam structure.
  9. 9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements a multi-level self-supporting constrained topology optimization method combining projection and virtual pyramid as claimed in any one of claims 1 to 7 when the computer program is executed by the processor.
  10. 10. A computer-readable storage medium having stored thereon a computer program, wherein the computer program causes a computer to perform a multi-stage self-supporting constrained topology optimization method that combines projection and virtual pyramids as recited in any one of claims 1-7.

Description

Multistage self-supporting constraint topology optimization method and system combining projection and virtual pyramid Technical Field The invention relates to the technical field of additive manufacturing structural design and topology optimization, in particular to a multistage self-supporting constraint topology optimization method and system combining projection and virtual pyramid. Background The topology optimization technology can find the optimal distribution of materials in a given design domain, so that a lightweight structure with excellent mechanical properties is obtained, and the topology optimization technology is widely applied to various fields such as aerospace, automobile manufacturing, precision machinery, biomedical treatment and the like. The development of additive manufacturing (3D printing) technology makes it possible to manufacture structures with complex topological configurations, greatly releasing the design potential of topological optimization and realizing the design, i.e. manufacturing, landscape. However, the topology optimization design for additive manufacturing at the present stage has the following difficulties that firstly, the structure generated by the traditional topology optimization method often contains overhang features (such as large-angle overhangs or horizontal beams) which do not meet the requirements of the additive manufacturing process, so that collapse or deformation occurs in the printing process due to lack of support, and secondly, a large number of external support structures are usually required to be added for solving the overhang problem, so that the material consumption and the printing time are obviously increased, and the difficulty and cost of post-treatment (such as support removal and surface polishing) are greatly increased, so that the manufacturability and the economical efficiency of the structure are difficult to realize while the superior mechanical property is ensured. Disclosure of Invention The invention aims to provide a multistage self-supporting constraint topology optimization method and system combining projection and virtual pyramid, which are used for solving the problems of large material consumption, high post-processing difficulty, increased manufacturing cost and the like caused by adding a large amount of external supports in the additive manufacturing process due to overhang features in a traditional topology optimization structure. In order to achieve the purpose, the technical scheme provided by the invention is that the multistage self-supporting constraint topology optimization method combining projection and virtual pyramid comprises the following steps: S1, initializing a design domain of a beam structure, dispersing the design domain into grid cells, giving different initial density values to each grid cell according to position coordinates of each grid cell, and introducing a boundary effect function to locally correct the initial density values of each grid cell to generate a non-uniform gradient initial density field comprising a uniform distribution region and a gradient region; S2, applying a total load vector generated by superposition of a bearing working condition and a guide load with a preset amplitude on an initial density field, and defining a key area for keeping the density of a material at a preset position of a design domain; S3, calculating the projection supporting quantity of each grid cell according to the density value of other grid cells in the projection coverage area of the grid cell, and when the projection supporting quantity is lower than a preset projection supporting quantity threshold value, applying punishment to the grid cell and recording the punishment as a projection supporting punishment item; S4, after projection support penalty items are applied, constructing a multi-layer pyramid support domain which is downwards conical and expanded for each grid unit, calculating virtual pyramid support quantity, and when the virtual pyramid support quantity does not meet a preset support layer number mode and a support density threshold value, applying cross-layer penalty to the grid unit, and recording as a virtual pyramid penalty item; S5, overlapping the projection support penalty term and the virtual pyramid penalty term to the original sensitivity according to a preset sequence to obtain corrected sensitivity, wherein the sensitivity is the partial derivative of the cantilever structure flexibility on the grid cell density value; and S6, updating the density value of each grid cell by using the corrected sensitivity, performing protective correction on the density value of the grid cells in the key area, and repeating the steps S3 to S5 until the optimization converges and outputting the optimized structure of the beam structure. In order to optimize the technical scheme, the specific measures adopted further comprise: further, in step S1, the specific process of generating the non-