Improved level set topology optimization method for stable hole formation

Abstract

The invention belongs to the technical field of structural topology optimization, and discloses an improved level set topology optimization method for stable hole formation. The method includes: (a) dividing the finite element mesh into design domains, initially dividing the mesh into solid and cavity domains, and initially assigning values to the level set functions; (b) calculating a displacement vector in the design domain; (c) calculating the sensitivity of each grid cell in the velocity field and the physical region; (d) optimizing the initialized solid region, the cavity region and the level set function for the first time by using the sensitivity number; (e) using the velocity field to update the level set function of each grid cell in the entity and the cavity region respectively so as to redivide the entity region and the cavity region, thereby realizing the second optimization; (f) judging whether the result of the second optimization converges or not according to the flexibility and volume error. The invention overcomes the defect that the traditional level set topology optimization method cannot form holes in the structure, and solves the dependence of the optimizationproblem on the initial design, which is stable and effective.

Description

technical field [0001] The invention belongs to the technical field of structural topology optimization, and more specifically relates to an improved level set topology optimization method for stably forming holes. Background technique [0002] Structural topology optimization is a new digital structure design method. By establishing a mathematical model including design variables, objective functions and constraints, finite element analysis is performed on the structure, and in the design domain, iteratively obtains the results that satisfy the constraints according to optimization criteria or mathematical programming methods. Conditions and achieve the material layout of the design goals. Structural topology optimization has great application value in industries such as automobiles, aerospace, and high-end equipment. [0003] Level set topology optimization method and BESO (Bidirectional Progressive Structural Optimization) method are two commonly used methods in structur...

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Problems solved by technology

[0004] In the traditional level set topology optimization method, due to the nature of the Hamilton-Jacobi equation, holes cannot be generated inside the structure

Therefore, the initial design of the structure in level set topology optimization needs to have many holes, which causes the method to depend on the initial design, especially for two-dimensional problems. In order to overcome the dependence on the initial design, the level set method has been improved a lot, such as Combining topological derivatives or using radial basis functions, but these improvements need to define many holes in the design domain in the initial design, and the position, number and size of the holes will have a great impact on the final optimization results; in addition, these The concept of improvement measures is complex, it is difficult to carry out numerical analysis, and it is difficult to apply in actual engineering. At present, there is no effective method for level set topology optimization to stably form holes and be feasible in engineering applications

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