While the theory of peridynamics(PD)holds significant potential in engineering,its application is often limited by the significant computational costs by the nonlocality of PD.This research is based on a three-dimensi...While the theory of peridynamics(PD)holds significant potential in engineering,its application is often limited by the significant computational costs by the nonlocality of PD.This research is based on a three-dimensional(3D)complex Timoshenko beam structure with six degrees of freedom.We propose a fast meshfree method based on the linear bond-based PD model of the stiffness matrix structure by ingeniously using the matrix decomposition strategy to maintain the Teoplitz structure of the stiffness matrix.This method significantly reduces the amount of calculation and storage without losing accuracy,reduces the amount of calculation from O(N^(2))to O(NlogN),and decreases the storage capacity from O(N^(2))to O(N).We validate the effectiveness of our approach through numerical examples,particularly in multibeam structures.We demonstrate that our method realizes algorithm acceleration in numerical simulations of multi-beam structures subjected to static concentrated loads.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(Nos.202042008 and 202264006)the National Natural Science Foundation of China(No.52071306).
文摘While the theory of peridynamics(PD)holds significant potential in engineering,its application is often limited by the significant computational costs by the nonlocality of PD.This research is based on a three-dimensional(3D)complex Timoshenko beam structure with six degrees of freedom.We propose a fast meshfree method based on the linear bond-based PD model of the stiffness matrix structure by ingeniously using the matrix decomposition strategy to maintain the Teoplitz structure of the stiffness matrix.This method significantly reduces the amount of calculation and storage without losing accuracy,reduces the amount of calculation from O(N^(2))to O(NlogN),and decreases the storage capacity from O(N^(2))to O(N).We validate the effectiveness of our approach through numerical examples,particularly in multibeam structures.We demonstrate that our method realizes algorithm acceleration in numerical simulations of multi-beam structures subjected to static concentrated loads.
