TY - JOUR
T1 - A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model
AU - Tian , Hao
AU - Yang , Xianchu
AU - Liu , Chenguang
AU - Liu , Guilin
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 305
EP - 330
PY - 2024
DA - 2024/01
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0059
UR - https://global-sci.org/intro/article_detail/aamm/22333.html
KW - Bond-based peridynamics, beam model, fast methods, Teoplitz matrix.
AB - <p style="text-align: justify;">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 $\mathcal{O}(N^2)$ to $\mathcal{O}(N{\rm log}N),$ and decreases the storage capacity from $\mathcal{O}(N^2)$ to $\mathcal{O}(N).$ We validate
the effectiveness of our approach through numerical examples, particularly in multi-beam structures. We demonstrate that our method realizes algorithm acceleration in
numerical simulations of multi-beam structures subjected to static concentrated loads.</p>