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Optimization method of two-dimensional triangular mesh finite element model

A triangular grid and optimization method technology, applied in the field of finite element model, can solve the problems of complex optimization method algorithm, poor local minimum points, and low mesh quality

Pending Publication Date: 2020-12-18
CHONGQING UNIV
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Problems solved by technology

[0002] At present, the optimization method for the 2D triangular mesh finite element model is mainly to change the node position. Due to the change of the node position, the connection mode of the triangular elements and the shape of the triangular element are changed. Therefore, the optimization method for changing the node position is often complicated. ; Some optimization methods start with local optimization, but for a given initial model, it is easy to fall into a poor local minimum point, resulting in the quality of the generated mesh is not high

Method used

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  • Optimization method of two-dimensional triangular mesh finite element model
  • Optimization method of two-dimensional triangular mesh finite element model
  • Optimization method of two-dimensional triangular mesh finite element model

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Embodiment 1

[0067] see figure 1 To Fig. 6, a method for optimizing a two-dimensional triangular mesh finite element model, comprising the following steps:

[0068] 1) Obtain the initial triangular mesh finite element model of the workpiece.

[0069] 2) Establish node optimization model.

[0070] The objective function Δφ of the node optimization model is as follows:

[0071]

[0072] where f i for node v i degrees. The node degree indicates the number of adjacent triangular elements with the node as one of the vertices. For example, f i represents the node v i by f i shared by adjacent triangular units. f i for node v i normal degree of . Δφ is the degree of irregularity of the current triangular mesh finite element model.

[0073] 3) Determine the normal degree of each node, and write the normal degree set F={F 1 , F 2 ,...,F n}middle.

[0074] The steps to determine the normal degree of each node are as follows:

[0075] 3.1) Judgment node v i type.

[0076] when ...

Embodiment 2

[0117] A method for optimizing a two-dimensional triangular mesh finite element model, comprising the following steps:

[0118] 1) Obtain the initial triangular mesh finite element model.

[0119] 2) Establish node optimization objective function:

[0120] set node v i degree f i , the regular degree is F i , then when v i When it is an internal node, F i = 6; when node v i When it is a boundary node, according to v i Angle between two adjacent boundary lines to calculate f i , so that v i The interior angles of each adjacent triangular unit should be as close to π / 3 as possible. When F changes, the critical angle Should meet:

[0121]

[0122] When F i =2,3,…,7, respectively obtain:

[0123]

[0124] when In different intervals, the corresponding F i Values ​​such as figure 2 shown.

[0125] The irregularity of boundary nodes needs to be measured by introducing appropriate evaluation indicators. Define Degree Deviation:

[0126]

[0127] The ...

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Abstract

The invention discloses an optimization method of a two-dimensional triangular mesh finite element model. The optimization method comprises the following steps: 1) obtaining an initial triangular meshfinite element model; 2) establishing a node optimization model; 3) determining the normal degree of each node; 4) calculating degrees of all nodes; 5) if the objective function of the node optimization model is not reduced any more, turning to the step 8), otherwise, turning to the step 6); 6) optimizing a current triangular mesh finite element model node vi; 7) judging whether i is greater thanor equal to n; if yes, updating the triangular mesh finite element model, returning to the step 5), otherwise, enabling i to be equal to i+1, and returning to the step 6); 8) judging whether a non-acute triangle exists or not, if so, turning to the step 9), otherwise, outputting the current triangular mesh finite element model; and 9) optimizing the angle of the triangular mesh unit, and returning to the step 8). The overall coordination of the model is improved, the distortion degree of the model is reduced, and the actual industrial requirements can be met.

Description

technical field [0001] The invention relates to the field of finite element models, in particular to an optimization method for a two-dimensional triangular grid finite element model. Background technique [0002] At present, the optimization method for the 2D triangular mesh finite element model is mainly to change the node position. Due to the change of the node position, the connection mode of the triangular elements and the shape of the triangular element are changed. Therefore, the optimization method for changing the node position is often complicated. ; Some optimization methods start with local optimization, but for a given initial model, it is easy to fall into a poor local minimum point, resulting in the quality of the generated mesh is not high. [0003] Therefore, there is a need for an optimization method that is easy to implement and generates high-quality meshes. Contents of the invention [0004] The object of the present invention is to provide a kind of ...

Claims

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Application Information

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IPC IPC(8): G06F30/23
CPCG06F30/23
Inventor 段黎明盛晋银罗雪清方诚谭川东
Owner CHONGQING UNIV
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