A Hybrid Level Set Method for Topology Optimization of Functionally Gradient Porous Structures

Abstract

The invention discloses a mixed level set method for topology optimization of functionally gradient porous structures. The mixed level set function is constructed by linear weighting of two kinds of porous unit cells, and the Hamilton-Jacobi partial differential equation controlling the evolution of the level set function is carried out in time and space. Decoupling. The global weight coefficient is defined as the design variable, the structural stiffness performance is used as the objective function, and the volume fraction of the porous structure is used as the constraint condition. A functionally gradient porous structure topology optimization mathematical model based on the mixed level set method is established. By deriving the sensitivity of the objective function and constraint conditions with respect to the design variables, the iterative solution of the gradient-based optimization algorithm is carried out. When the iterative process meets the convergence conditions, a porous structure with a gradient distribution of geometry and function in space is obtained. The method proposed by the invention can be combined with a mature gradient optimization algorithm, has rigorous mathematical theory derivation, can avoid the problem of scale separation of functionally gradient porous structures, and improves the continuity between unit cells.

Description

technical field [0001] The invention belongs to the technical field related to digital design, and more specifically relates to a mixed level set method for topology optimization of functionally gradient porous structures. Background technique [0002] Functionally graded porous structure is a porous structure with spatially varying properties. Its mechanical properties show a gradient change along a certain direction, which can meet the mechanical properties that conventional uniform structure materials do not have, such as high mechanical strength and bending resistance. , load-carrying and energy-absorbing characteristics, etc., so it has been widely used in aerospace, bionic design and many other aspects. Traditional functionally graded porous structure materials have a single distribution form, which cannot meet the needs of complex engineering environments. Among the optimization design methods for functionally graded porous structures, some optimization methods contr...

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Problems solved by technology

Traditional functionally graded porous structure materials have a single distribution form, which cannot meet the needs of complex engineering environments

Among the optimization design methods for functionally graded porous structures, some optimization methods control the volume fraction of porous structures based on the stress distribution of finite element analysis, which improves the performance of functionally graded porous structures, but cannot achieve the optimal design

[0003] In recent years, it has become a trend to use topology optimization methods to optimize the design of functionally graded porous structures. The macroscopic configuration design of the method is separated from the unit cell configuration design, which cannot give full play to the performance of the porous structure

In addition, the topology optimization method based on the numerical homogenization method is also widely used in the optimization design of functionally gradient porous structures because of its rigorous theoretical derivation and mathematical formulas. In practical applications, the homogenization method is more suitable for small-scale, large-scale, The topology optimization of a single type of periodic porous structure is difficult to ensure the connectivity between the porous structures due to its scale-separated characteristics

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