{"title":"局部线弹性杆的大位移和大旋转","authors":"S. du Toit, M. Labuschagne, Alna van der Merwe","doi":"10.1002/zamm.202200586","DOIUrl":null,"url":null,"abstract":"The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Large displacements and rotations of a local linear elastic rod\",\"authors\":\"S. du Toit, M. Labuschagne, Alna van der Merwe\",\"doi\":\"10.1002/zamm.202200586\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.\",\"PeriodicalId\":23924,\"journal\":{\"name\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/zamm.202200586\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202200586","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Large displacements and rotations of a local linear elastic rod
The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.