A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model (Advances in Applied Mathematics and Mechanics, 2024)
While the theory of peridynamics (PD) holds significant potential in engineering, its application is often limited by the significant computational costs by thenonlocality of PD. This research is based on a three-dimensional (3D) complex Timoshenko beam structure with six degrees of freedom. We propose a fast meshfreemethod based on the linear bond-based PD model of the stiffness matrix structure byingeniously using the matrix decomposition strategy to maintain the Teoplitz structureof the stiffness matrix. This method significantly reduces the amount of calculationand storage without losing accuracy, reduces the amount of calculation from $\mathcal{O}(N^2)$ to $\mathcal{O}(N{\rm log}N),$ and decreases the storage capacity from $\mathcal{O}(N^2)$ to $\mathcal{O}(N).$ We validatethe effectiveness of our approach through numerical examples, particularly in multi-beam structures. We demonstrate that our method realizes algorithm acceleration innumerical simulations of multi-beam structures subjected to static concentrated loads.