Mixed level set method for topological optimization of functional gradient porous structure

Abstract

The invention discloses a mixed level set method for topological optimization of a functional gradient porous structure, and the method comprises the steps: constructing a mixed level set function through linear weighting of two porous unit cells, and carrying out the space-time decoupling of a Hamilton-Jacobian partial differential equation for controlling the evolution of the level set function; defining a global weight coefficient as a design variable, taking structural rigidity performance as a target function and taking the volume fraction of the porous structure as a constraint condition, and establishing a functional gradient porous structure topological optimization mathematical model based on the mixed level set method. By deducing a sensitivity column formula of a target function and a constraint condition about a design variable, iterative solution of a gradient-based optimization algorithm is carried out, and when an iterative process meets a convergence condition, a porous structure with geometry and functions in gradient distribution in space is obtained. The method provided by the invention can be combined with a mature gradient optimization algorithm, has rigorous mathematical theoretical derivation, can avoid the scale separation problem of the functional gradient porous structure, 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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