Multi-scale topological optimization method based on isogeometric analysis

Abstract

The invention discloses a multi-scale topological optimization method based on isogeometric analysis, and belongs to the field of structure optimization. Comprising the steps that macro-scale geometric models, micro-scale geometric models and isogeometric grids are constructed based on an NURBS primary function, design variable fields are arranged in the macro-scale geometric models and the micro-scale geometric models respectively, the macro design variable field is used for describing distribution of microstructures, and the micro design variable field is used for describing configuration of the microstructures; an isogeometric analysis-based homogenization method is adopted to calculate the elastic tensor of the microstructure; endowing the microstructure elastic tensor to a macroscopic isogeometric grid unit, constructing a multi-scale isogeometric topological optimization model based on an NURBS primary function, and optimizing the distribution and configuration of the microstructure at the same time according to an optimization criterion method; and filling the microstructure configuration into the macroscopic geometric model according to an isogeometric mapping strategy to obtain a porous structure. Due to the fact that the regular design variable field can be mapped into the specified irregular geometric model through the isogeometric mapping strategy, multi-scale optimization can be carried out on the special-shaped structure.

Description

technical field [0001] The invention belongs to the field of structural optimization, and more specifically relates to a multi-scale topology optimization method based on isogeometric analysis. Background technique [0002] Porous structures are widely used in various fields due to their excellent mechanical properties beyond traditional structures, such as aerospace ultra-lightweight structures, energy-absorbing bumpers for vehicles, and thermal insulation materials in civil engineering. Multiscale topology optimization is an effective method for designing porous structures, which can simultaneously optimize the layout and topological configuration of microstructures in porous structures, making porous structures with lower mass and better mechanical properties. At the same time, as a substitute for the traditional finite element analysis method, isogeometric analysis can realize the unified expression of CAD model and CAE model and improve the calculation accuracy. Theref...

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Problems solved by technology

[0004] Although this method has a large design space and can optimize the porous structure more comprehensively, its computational efficiency is low, and the connectivity between various microstructures is difficult to be guaranteed, so it can only be applied to multi-scale topology optimization of regular boundary microstructures.

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