A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

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.

Electric field and force characteristic of dust aerosol particles on the surface of high-voltage transmission line

High-voltage transmission lines play a crucial role in facilitating the utilization of renewable energy in regions prone to desertification. The accumulation of atmospheric particles on the surface of these lines can significantly impact corona discharge and wind-induced conductor displacement. Accurately quantifying the force exerted by particles adhering to conductor surfaces is essential for evaluating fouling conditions and making informed decisions. Therefore, this study investigates the changes in electric field intensity along branched conductors caused by various fouling layers and their resulting influence on the adhesion of dust particles. The findings indicate that as individual particle size increases, the field strength at the top of the particle gradually decreases and eventually stabilizes at approximately 49.22 k V/cm, which corresponds to a field strength approximately 1.96 times higher than that of an unpolluted transmission line. Furthermore,when particle spacing exceeds 15 times the particle size, the field strength around the transmission line gradually decreases and approaches the level observed on non-adhering surface. The electric field remains relatively stable. In a triangular arrangement of three particles, the maximum field strength at the tip of the fouling layer is approximately 1.44 times higher than that of double particles and 1.5 times higher compared to single particles. These results suggest that particles adhering to the transmission line have a greater affinity for adsorbing charged particles. Additionally, relevant numerical calculations demonstrate that in dry environments, the primary adhesion forces between particles and transmission lines follow an order of electrostatic force and van der Waals force. Specifically, at the minimum field strength, these forces are approximately74.73 times and 19.43 times stronger than the gravitational force acting on the particles.