Quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operator

Abstract

The invention discloses a quasi-periodic hierarchical structure topological optimization method based on a corrosion-diffusion operator. The method comprises the following steps: establishing a structure model; performing corrosion-diffusion operation on the microstructure to obtain a quasi-periodic microstructure library; predicting the equivalent elastic tensor of the microstructure in the alignment period microstructure library by using an asymptotic homogenization method; based on the obtained elasticity modulus of the microstructure database, establishing an explicit function relationshipbetween the microstructure elasticity modulus and the volume fraction ratio by adopting B spline function fitting, and establishing an optimization model; according to the optimization model, calculating the sensitivity of a flexibility function of the structure relative to two design variables, namely a macroscopic topology variable and a microcosmic topology variable; according to the obtainedsensitivity information, iteratively updating a design variable to finish collaborative optimization design of the microcosmic unit density and the macrocosmic unit density; and reconstructing macroscopic and microscopic optimization results obtained by the optimization model to obtain a geometric model of the whole heterogeneous structure.

Description

technical field [0001] The invention belongs to the technical field of structural topology optimization, in particular to a quasi-periodic hierarchical structure topology optimization method based on corrosion-diffusion operators. Background technique [0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art. [0003] Biological structures in nature, such as animal bones and plant stems, are mostly hierarchical. Its geometric characteristics are characterized by multiple scale configurations such as macroscopic, subscopic and microscopic, showing high specific stiffness, defect resistance and multi-functionality. Inspired by this, many artificial hierarchical structures, such as sandwich panels and lattice materials, are widely used in aerospace, biomedical and other fields. In recent years, the rapid development of advanced manufacturing technology, especially additive manufa...

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Problems solved by technology

However, this method does not optimize the microstructural topology

[0007] Document 4 (“Wang, Y.; Chen, F.; Wang, M.Y. (2017) Concurrent design with connectable graded microstructures. Computer Methods in Applied Mechanics and Engineering, 317, 84-101.”) discloses a method based on the level set framework The quasi-periodic hierarchical topology optimization method, but it cannot be directly applied to the most widely used topology optimization framework of variable density method

[0008] In summary, the hierarchical structure topology optimization method disclosed in the above prior art has irreconcilable contradictions in calculation efficiency, application range and structural performance.

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