{"title":"Construction method for circular arc elements in rational absolute nodal coordinate formulation","authors":"","doi":"10.1016/j.mechmachtheory.2024.105811","DOIUrl":null,"url":null,"abstract":"<div><div>The Rational Absolute Nodal Coordinate Formulation (RANCF) element nodal coordinates and weights can be obtained through a rational Bézier description, which is relatively cumbersome for engineering applications. In this paper, a method for directly defining RANCF elements is proposed for circular arc geometric configurations. In this method the nodal coordinates and weights can be expressed directly by the position coordinates of geometric configurations. By utilizing position coordinates in defining RANCF elements for a geometric configuration, it becomes easier to adjust continuity conditions between elements and apply constraint equations during the preprocessing phase before simulation initiation. As a result, there is no longer a need to use knot multiplicity in NURBS representation to adjust continuity conditions. To address the arbitrary and diverse definitions of RANCF elements, a parameterization method for RANCF elements is proposed, along with an assessment criterion and an optimal parameterization method for RANCF circular arc elements. Numerical examples are presented to compare the performance of various parametric RANCF circular arc elements. The results demonstrate that convergence can be achieved by using fewer optimal parametric elements.</div></div>","PeriodicalId":49845,"journal":{"name":"Mechanism and Machine Theory","volume":null,"pages":null},"PeriodicalIF":4.5000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanism and Machine Theory","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0094114X24002386","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The Rational Absolute Nodal Coordinate Formulation (RANCF) element nodal coordinates and weights can be obtained through a rational Bézier description, which is relatively cumbersome for engineering applications. In this paper, a method for directly defining RANCF elements is proposed for circular arc geometric configurations. In this method the nodal coordinates and weights can be expressed directly by the position coordinates of geometric configurations. By utilizing position coordinates in defining RANCF elements for a geometric configuration, it becomes easier to adjust continuity conditions between elements and apply constraint equations during the preprocessing phase before simulation initiation. As a result, there is no longer a need to use knot multiplicity in NURBS representation to adjust continuity conditions. To address the arbitrary and diverse definitions of RANCF elements, a parameterization method for RANCF elements is proposed, along with an assessment criterion and an optimal parameterization method for RANCF circular arc elements. Numerical examples are presented to compare the performance of various parametric RANCF circular arc elements. The results demonstrate that convergence can be achieved by using fewer optimal parametric elements.
期刊介绍:
Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal.
The main topics are:
Design Theory and Methodology;
Haptics and Human-Machine-Interfaces;
Robotics, Mechatronics and Micro-Machines;
Mechanisms, Mechanical Transmissions and Machines;
Kinematics, Dynamics, and Control of Mechanical Systems;
Applications to Bioengineering and Molecular Chemistry