Introduction to the Variational Formulation in Mechanics最新文献

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Vector and Tensor Algebra 向量和张量代数
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch1
R. Sulanke
{"title":"Vector and Tensor Algebra","authors":"R. Sulanke","doi":"10.1002/9781119600923.ch1","DOIUrl":"https://doi.org/10.1002/9781119600923.ch1","url":null,"abstract":"This notebook and the package tensalgv2.m contain besides of elementary vector algebra a complete tensor algebra as a part of affine geometry. In Mathematica there doesn’t exist a built-in Tensor definition, but some tensor operations, like e.g. TensorProduct are built-in. In the notebook I define a symbolic tensor object which admits to introduce covariant, contravariant and mixed type tensors. The concept can be used for symbolic calculations as well as for calculations with tensors whose coordinates are numerically or functionally specified. Tensor products, the wedge product as the base of exterior algebra, and contraction of tensors are introduced. Their properties are deduced and compared with the corresponding Mathematica built-in tensor functions. Since also in the commercial packages of Harald H. Soleng, Tensors in Physics, and Steven M. Christensen, MathTensor, an abstract tensor concept, as far as I know, is missing I hope that the notebook and the package presented here deliver useful tools for applications of Mathematica to problems in algebra, geometry and physics needing tensor calculus. The analytic part of tensor calculus is treated in connection with pseudo-Riemannian Geometry in the notebook RG.nb.","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132283889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bending of Beams 梁的弯曲
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch7
T. Nguyen
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引用次数: 0
Variational Formulations in Mechanics 力学中的变分公式
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.part2
{"title":"Variational Formulations in Mechanics","authors":"","doi":"10.1002/9781119600923.part2","DOIUrl":"https://doi.org/10.1002/9781119600923.part2","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131125229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Torsion of Bars 杆的扭转
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch8
{"title":"Torsion of Bars","authors":"","doi":"10.1002/9781119600923.ch8","DOIUrl":"https://doi.org/10.1002/9781119600923.ch8","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124713354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Materials Exhibiting Creep 表现蠕变的材料
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch5
{"title":"Materials Exhibiting Creep","authors":"","doi":"10.1002/9781119600923.ch5","DOIUrl":"https://doi.org/10.1002/9781119600923.ch5","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130718650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Materials Exhibiting Plasticity 具有可塑性的材料
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch6
{"title":"Materials Exhibiting Plasticity","authors":"","doi":"10.1002/9781119600923.ch6","DOIUrl":"https://doi.org/10.1002/9781119600923.ch6","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126780964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
B: Elements of Real and Functional Analysis B:实分析和功能分析的要素
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.app2
{"title":"B: Elements of Real and Functional Analysis","authors":"","doi":"10.1002/9781119600923.app2","DOIUrl":"https://doi.org/10.1002/9781119600923.app2","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121900942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Plates and Shells 板壳
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1007/978-3-030-20381-8_5
K. Naumenko, H. Altenbach
{"title":"Plates and Shells","authors":"K. Naumenko, H. Altenbach","doi":"10.1007/978-3-030-20381-8_5","DOIUrl":"https://doi.org/10.1007/978-3-030-20381-8_5","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133180902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
C: Functionals and the Gâteaux Derivative C:泛函和<s:1>特导数
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.app3
{"title":"C: Functionals and the Gâteaux Derivative","authors":"","doi":"10.1002/9781119600923.app3","DOIUrl":"https://doi.org/10.1002/9781119600923.app3","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123648125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Heat Transfer 传热
Introduction to the Variational Formulation in Mechanics Pub Date : 2019-12-13 DOI: 10.1002/9781119600923.ch10
日本機械学会
{"title":"Heat Transfer","authors":"日本機械学会","doi":"10.1002/9781119600923.ch10","DOIUrl":"https://doi.org/10.1002/9781119600923.ch10","url":null,"abstract":"","PeriodicalId":179652,"journal":{"name":"Introduction to the Variational Formulation in Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123456121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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