{"title":"A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model","authors":"H. Tian, Xianchu Yang, Chenguang Liu","doi":"10.4208/aamm.oa-2023-0059","DOIUrl":null,"url":null,"abstract":". 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 Tim-oshenko 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 ( N log N ) , and decreases the storage capacity from O ( N 2 ) to 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.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2023-0059","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. 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 Tim-oshenko 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 ( N log N ) , and decreases the storage capacity from O ( N 2 ) to 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.
期刊介绍:
Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.