{"title":"张量符号中的纯扭转问题","authors":"S. Karaś","doi":"10.24358/bud-arch_19_181_06","DOIUrl":null,"url":null,"abstract":"The paper examines the application of the tensor calculus to the classic problem of the pure torsion of prismatic rods. The introduction contains a short description of the reference frames, base vectors, contravariant and covariant vector coordinates when applying the Einstein summation convention. Torsion formulas were derived according to Coulomb’s and Saint-Venant’s theories, while, as a link between the theories, so-called Navier’s error was discussed. Groups of the elasticity theory equations were used.","PeriodicalId":55831,"journal":{"name":"Budownictwo i Architektura","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pure torsion problem in tensor notation\",\"authors\":\"S. Karaś\",\"doi\":\"10.24358/bud-arch_19_181_06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper examines the application of the tensor calculus to the classic problem of the pure torsion of prismatic rods. The introduction contains a short description of the reference frames, base vectors, contravariant and covariant vector coordinates when applying the Einstein summation convention. Torsion formulas were derived according to Coulomb’s and Saint-Venant’s theories, while, as a link between the theories, so-called Navier’s error was discussed. Groups of the elasticity theory equations were used.\",\"PeriodicalId\":55831,\"journal\":{\"name\":\"Budownictwo i Architektura\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Budownictwo i Architektura\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24358/bud-arch_19_181_06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Budownictwo i Architektura","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24358/bud-arch_19_181_06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The paper examines the application of the tensor calculus to the classic problem of the pure torsion of prismatic rods. The introduction contains a short description of the reference frames, base vectors, contravariant and covariant vector coordinates when applying the Einstein summation convention. Torsion formulas were derived according to Coulomb’s and Saint-Venant’s theories, while, as a link between the theories, so-called Navier’s error was discussed. Groups of the elasticity theory equations were used.