CN112329228B - Assembly-oriented structural topology optimization method - Google Patents
Assembly-oriented structural topology optimization method Download PDFInfo
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- CN112329228B CN112329228B CN202011209162.8A CN202011209162A CN112329228B CN 112329228 B CN112329228 B CN 112329228B CN 202011209162 A CN202011209162 A CN 202011209162A CN 112329228 B CN112329228 B CN 112329228B
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Abstract
The invention discloses an assembly-oriented structural topology optimization method, which comprises the following steps: performing edge detection on the design model to obtain the sidelines of the design model, assembling and determining the assembly sidelines according to the determined design model, forming a new optimization area by biasing the assembly sidelines to the center of the design model to perform topological optimization on the optimization area. According to the invention, before the topology is optimized, the Canny operator is adopted to carry out sideline detection on the design model, and the boundary with a certain size of the design model is reserved through equidistant bias, so that the effective assembly with other models is ensured, and the overall performance after the assembly is ensured to be in a use range.
Description
Technical Field
The invention belongs to the field of topology optimization, and particularly relates to an assembly-oriented structural topology optimization method.
Background
The topological optimization is an optimization method for determining the connectivity of the shape and the cavity position through material distribution in a fixed design area under the condition of meeting design constraint conditions, and realizing the optimized layout and light weight structure of materials so as to achieve the optimization process. Compared with size optimization and shape optimization methods, topology optimization is one of the most promising structure optimization methods, and flexibility of generating and eliminating small cavities is realized in the optimization process, so that topology optimization is researched in a large amount in the academic field and developed into a plurality of branches, and various methods such as a density-based method, an Evolutionary Structure Optimization (ESO) method, a level set method and the like are provided.
At present, most of design models are directly optimized when the topology optimization is carried out on the design models, model assembly characteristics are not considered, so that the contact edges are lost or the sizes are too small, the technical indexes after assembly are difficult to meet the requirements, and meanwhile, the greater difficulty is added to the post-processing stage of the topology optimization models.
Disclosure of Invention
The invention aims to provide an assembly-oriented structural topology optimization method, which can effectively ensure effective assembly with other models by reserving edges of a design model before topology optimization is carried out on the design model.
In order to achieve the purpose, the invention adopts the following technical scheme:
an assembly-oriented structure topology optimization method comprises the following steps: performing edge detection on the design model to obtain the sidelines of the design model, assembling and determining the assembly sidelines according to the determined design model, forming a new optimization area by biasing the assembly sidelines to the center of the design model to perform topological optimization on the optimization area.
Further, the edge detection adopts a Canny operator to carry out edge detection.
Further, forming a new optimization region according to the bias curve of the edge line to the center of the design model specifically includes: and forming a new optimization area by offsetting delta t from the edge line to the center of the design model, judging the optimization area, performing topology optimization if the optimization area meets the design requirement, and re-offsetting and modifying the offset value delta t if the optimization area does not meet the design requirement.
Further, the initial bias Δ t is 1/10 of the longest edge of the design model.
Further, the composite design requirement of the optimized region refers to: the optimized region is greater than 90% of the region enclosed by the first identified edge.
Further, the topological optimization adopts a partition density correction sensitivity filtering method based on a variable density method.
Furthermore, the partition density correction sensitivity filtering method has the basic idea that an original sensitivity filtering area is divided into different sub-areas, different sensitivity filtering factors are adopted for the different areas, and the influence of a central position short-distance unit on the sensitivity of a central unit is reduced while the influence of the central position short-distance unit on the sensitivity of the central unit is improved.
Further, the different sub-regions are the original filtering radius rminThe area of (a) is divided into concentric circles with different radiuses.
Furthermore, the concentric circles comprise inner circles and outer circles, the area of the inner circles is divided into a subregion I, the area between the inner circles and the outer circles is divided into a subregion II, and sensitivity filter factors of the subregion I and the subregion II are different.
Compared with the prior art, the invention has the following beneficial effects:
(1) before topology optimization, a Canny operator is adopted to carry out sideline detection on a design model, and a boundary with a certain size of the design model is reserved through equidistant bias, so that effective assembly with other models is guaranteed, and further, the overall performance after assembly is guaranteed to be in a use range.
(2) The design model is optimized by adopting a partition density method, a topological structure with clear boundaries can be obtained, the iteration speed is stable, the dispersion rate and gray scale rate indexes are low, meanwhile, the flexibility convergence value can be reduced, the structural rigidity of the design model is improved, and the structural integrity of the design model is ensured.
Drawings
FIG. 1 is a schematic view of the flow structure of the present invention.
Fig. 2 is a schematic diagram of an example of the present embodiment of the invention.
FIG. 3 is a schematic diagram of the edge detection according to the present invention.
FIG. 4 is a schematic diagram of the present invention after curve offset.
FIG. 5 is a schematic diagram of the division of the sensitivity filtering region for topology optimization according to the present invention.
Fig. 6 shows the results output by the method of the present invention.
Fig. 7 is the result of an output optimized using a prior art topology.
Detailed Description
In this embodiment, a two-dimensional planar stress structure shown in fig. 2 is used to explain an assembly-oriented structural topology optimization method provided in this embodiment, where a design area of the structure in the drawing is 150 × 40mm, a grid computation density is 150 × 40, full-plane fixation constraints are applied to left and right ends of the design area, and a vertical downward load action of a load F ═ 1 is applied to a middle node on the top of the illustrated structure. As shown in fig. 1, the assembly-oriented structure topology optimization method provided in this embodiment includes the following steps:
(1) the method comprises the steps of adopting a Canny operator to carry out edge detection on a design model, extracting effective boundary lines of the design model, and as shown in figure 3, carrying out noise reduction on an image through Gaussian smooth denoising, then calculating image gradient to obtain possible edges, then inhibiting and filtering non-edge pixels through a non-maximum value, finally carrying out double-threshold screening to determine potential boundaries, and finishing contour line connection to form side lines.
(2) Determining a boundary line connected with the assembly body, forming a new design area by equidistantly biasing the boundary extracted in the step (1) to the center of the design model by adopting a curve equidistant biasing method, wherein the bias value delta t is set according to the size of the specific model, the bias delta t is 1/10 of the longest boundary line of the design model for the first time, the specific bias value is set according to the specific design model, the boundary line is the boundary line on two sides of the assembly body, the bias delta t is set to be 3, updating the optimization area, judging the updated optimization area as shown in fig. 4, performing topology optimization if the result meets the design requirement, and re-biasing the re-bias value delta t to form the new optimization area if the result does not meet the design requirement.
The step of determining the updated optimization area means that the optimization area is greater than 90% of the initially identified edge bounding area C, the biased optimization area in this embodiment is 144 × 40mm, and is 96% of the initially identified edge bounding area C, and the current area is determined to be the optimization area C' according to the design requirement.
(3) And (3) carrying out topology optimization on the optimized region C' meeting the requirements in the step (2) by adopting a partition density correction sensitivity filtering method based on a variable density method, wherein the optimization steps are as follows:
selecting isotropic materials, and establishing an expression definition of a variable density interpolation model as follows:
wherein E isminIs the elastic modulus, rho, of the blank materialeFor design variables being piecewise constant cell density, E0Selecting E as the Young modulus of the solid material and p as a penalty factorminIs 10-9MPa，E01MPa, Poisson's ratio of 0.3, penalty factor of 3, volume fraction of 0.5.
Under the given volume constraint condition, the optimization problem of the topology optimization can be expressed as:
min：
subject to：
where C (ρ) is the compliance of the given topology, U is the global displacement vector, F is the global load vector, K is the global stiffness matrix,
is the matrix of elemental stiffness in units of Young's modulus, V (ρ) is the volume of the material, V0Is the volume of the design domain, f is the predetermined volume fraction, ρminIs a vector containing the lowest allowable relative density.
The design variable iteration formula can be expressed as:
where η is used to control the range of intermediate densities. Introducing a parameter β to the above formula smoothing process can be written as:
and (3) applying load and constraint conditions to the model to be optimized according to the actual working condition, and optimizing by adopting a partition density correction sensitivity filtering method to perform finite element analysis. The zonal density correction sensitivity filtering method described in this embodiment uses concentric circles with unequal radii for analysis and calculation, which includes radius rminHas an outer circle and a radius rmAs shown in fig. 5, the area of the inner circle is divided into sub-regions i, and a constant 1 is used as a sensitivity filtering factor to improve the influence degree of sub-region units on the central unit. The area between the inner circle and the outer circle is divided into subareas II, so that the weight values of subarea units can be reduced, and the sensitivity of the central unit can be ensured to be iteratedThe process is not excessively averaged.
The zoning factor may be expressed as:
in the formula (I), the compound is shown in the specification,
k and lambda are correction parameters for adjusting HzSize of (a), rminAnd Δ (e, i) is consistent with the convolution factor definition in the Sigmund sensitivity filtering method;
beta is used to adjust the size of zone i and thereby control the number of units in zone i.
And when the difference value is larger than a preset threshold value, the density correction weight value is adopted to further weaken the problem of boundary diffusion. Can be expressed as:
wherein the preset density correction weight q is 10-3，|ρi-ρeAnd | is the density difference of the two discrete units, eta is a preset threshold, the iteration speed is too slow when the eta is too large, and a fine structure is easy to appear when the eta is too small through numerical calculation and verification, and the eta is preferably 0.8.
In summary, the sensitivity filtering method for partition density correction can be expressed as:
(4) and (4) iterative convergence judgment, namely, when the optimization target reaches the convergence standard, iteratively ending to output the optimization result, otherwise, resetting the parameters to perform topology optimization again until the optimization result is output, and finally, the result of the embodiment is shown in fig. 6.
As shown in fig. 7, the result of directly outputting topology optimization without using the prior art is obtained, the method adopted by the present invention ensures that the optimized components and other components are effectively assembled, selects a smaller volume fraction when setting the optimization parameters, and reduces the difficulty of the reconstruction stage of the topology optimization model to a certain extent.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any modification and replacement based on the technical solution and inventive concept provided by the present invention should be covered within the scope of the present invention.
Claims (2)
1. An assembly-oriented structure topology optimization method is characterized by comprising the following steps: performing edge detection on the design model to obtain a sideline of the design model, determining an assembly sideline according to the design model, biasing a curve from the assembly sideline to the center of the design model to form a new optimization area, and performing topological optimization on the optimization area;
specifically, forming a new optimization region according to the bias curve of the edge line to the center of the design model is as follows: forming a new optimization area by offsetting delta t from the edge line to the center of the design model, wherein the delta t is an offset value, judging the optimization area, performing topology optimization if the optimization area meets the design requirement, and performing offset again if the optimization area does not meet the design requirement to modify the offset value delta t; the composite design requirement of the optimized area is as follows: the optimized area is larger than 90% of the area enclosed by the first identified edge line;
the topology optimization adopts a partition density correction sensitivity filtering method based on a variable density method, and the partition density correction sensitivity filtering method comprises the following steps: dividing the original sensitivity filtering area into different subregions, and adopting different sensitivity filtering factors for the different subregions; the different sub-areas are the original filtering radius rminThe area of the device is divided into concentric circles with different radiuses; the concentric circles comprise inner circles and outer circles, the area of each inner circle is a divided subregion I, the area between each inner circle and each outer circle is a divided subregion II, and the subregions I and the subregions IIAre different in sensitivity filter factor.
2. The assembly-oriented architecture topology optimization method of claim 1, wherein: and performing edge detection by adopting a Canny operator.
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