{"id":1984,"date":"2021-06-28T12:06:13","date_gmt":"2021-06-28T10:06:13","guid":{"rendered":"https:\/\/dottorati.unica.it\/dotticar\/?p=1984"},"modified":"2021-06-28T12:26:59","modified_gmt":"2021-06-28T10:26:59","slug":"summer-school-tensor-analysis-with-applications-in-continuum-mechanics","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/dotticar\/summer-school-tensor-analysis-with-applications-in-continuum-mechanics\/","title":{"rendered":"Summer School “Tensor Analysis with Applications in Continuum Mechanics”"},"content":{"rendered":"

Summer School<\/em>
\n12 – 16 July 2021
\nTeacher Victor Eremeyev<\/p>\n

 <\/p>\n

Summer School<\/em><\/strong>
\n12 – 16 July 2021<\/strong>
\nTeacher Victor Eremeyev<\/strong><\/p>\n

The Summer School will be held both in presence and online.<\/p>\n

Enter the online classroom<\/a><\/span><\/h3>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

The course, of about 28 hours, aims to provide a short but comprehensive introduction into direct (index-free) tensor calculus together with a few applications in Continuum Mechanics.<\/p>\n

Timetable<\/strong><\/h3>\n

Monday 12 July – Thursday 15 July<\/strong> session 9:00-13:00, session 15:00-17:00<\/p>\n

Friday 16 July<\/strong> session 9:00-13:00<\/p>\n

 <\/p>\n

Tentative program<\/strong><\/h3>\n

 <\/p>\n

1. Vectors and Transformations <\/strong><\/p>\n

1.1 Change of basis and the reciprocal basis<\/p>\n

1.2 The cross product and other operation<\/p>\n

2. Tensors and Tensor Fields<\/strong><\/p>\n

2.1 Dyadic quantities<\/p>\n

2.2 Second-order tensors<\/p>\n

2.3 Third- and higher-order tensors<\/p>\n

2.4 Isotropic tensors<\/p>\n

2.5 Tensor-valued functions of tensor arguments<\/p>\n

2.6 Differentiation of tensorial functions<\/p>\n

2.7 Tensor fields, differential operations.<\/p>\n

2.8 Pseudovectors, pseudoscalars, and pseudotensors<\/p>\n

2.9 Invariants of tensors and vectors<\/p>\n

3. Elements of Differential Geometry \u2013 Curves, Surfaces, etc.<\/strong><\/p>\n

4. Continuum Mechanics<\/strong><\/p>\n

4.1 Kinematics: motion, gradient of deformations, strains.<\/p>\n

4.2. Stress tensors<\/p>\n

4.3. Notion of constitutive relations: some basic principles (objectivity, locality,<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 equipresence, etc.)<\/p>\n

4.4. Linear elasticity. Hooke\u2019s law. Stiffness tensor and its symmetries.<\/p>\n

4.5. Elements of nonlinear elasticity.<\/p>\n

4.6. Fluids.<\/p>\n

4.7. \u201cA few words\u201d on generalized models.<\/p>\n

4.8. Elements of shells theory.<\/p>\n

\u00a0<\/strong><\/p>\n

Contact and registration<\/h3>\n

For information and registration contact:<\/p>\n

Victor A. Eremeyev victor.eremeev@unica.it<\/a><\/p>\n

Maria Cristina Porcu mcporcu@unica.it<\/a><\/p>\n

Emanuele Reccia emanuele.reccia@unica.it<\/a><\/p>\n

 <\/p>\n

Recommended literature<\/strong><\/h3>\n
    \n
  • B. Wilson, Vector Analysis, Founded upon the Lectures of G. W. Gibbs. Yale University Press, New Haven, 1901.<\/li>\n
  • G. Simmonds, A Brief on Tensor Analysis<\/em>, 2nd Edition, Springer, New York, 1994.<\/li>\n
  • P. Lebedev, M.J. Cloud, V.A. Eremeyev, Tensor Analysis with Applications in Mechanics, World Scientific, New Jersey, 2010.<\/li>\n
  • A. Eremeyev, M.J. Cloud, L.P. Lebedev, Applications of Tensor Analysis in Continuum Mechanics. World Scientific, New Jersey, 2018.<\/li>\n<\/ul>\n

     <\/p>\n

     <\/p>","protected":false},"excerpt":{"rendered":"

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