Applied Mathematics and Mechanics >
A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints
Received date: 2023-09-14
Online published: 2024-01-27
Supported by
the National Natural Science Foundation of China(12072007);the National Natural Science Foundation of China(12072006);the National Natural Science Foundation of China(12132001);the National Natural Science Foundation of China(52192632);the Ningbo Natural Science Foundation of Zhejiang Province of China(202003N4018);the Defense Industrial Technology Development Program of China(JCKY2019205A006);the Defense Industrial Technology Development Program of China(JCKY2019203A003);the Defense Industrial Technology Development Program of China(JCKY2021204A002);Project supported by the National Natural Science Foundation of China (Nos. 12072007, 12072006, 12132001, and 52192632), the Ningbo Natural Science Foundation of Zhejiang Province of China (No. 202003N4018), and the Defense Industrial Technology Development Program of China (Nos. JCKY2019205A006, JCKY2019203A003, and JCKY2021204A002)
Copyright
A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication. The expression of the geometric stiffness matrix is derived, the finite element linear buckling analysis is conducted, and the sensitivity solution of the linear buckling factor is achieved. For a specific problem in linear buckling topology optimization, a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells. The aggregation function method is used to consider the high-order eigenvalues, so as to obtain continuous sensitivity information and refined structural design. With cyclic matrix programming, a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted. To maximize the buckling load, under the constraint of the given buckling load, two types of topological optimization columns are constructed. The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm. The vertex method and the matching point method are used to carry out an uncertainty propagation analysis, and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance. Finally, the differences in the structural topology optimization under different reliability degrees are illustrated by examples.
Lei WANG, Yingge LIU, Juxi HU, Weimin CHEN, Bing HAN . A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints[J]. Applied Mathematics and Mechanics, 2024 , 45(2) : 321 -336 . DOI: 10.1007/s10483-024-3078-6
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