2 semester

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Name of the discipline

Nonclassical thin shell theory

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Grade level, specialty

1, specialty “mechanics and mathematical modeling”

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Semester of studying

2

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Amount of credits

4

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Full name of the lecturer

Doctor of Phys.-Math. Sciences, Professor Mihasev GI

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Objectives of studying the discipline

The aim of the course is to get acquainted with nonclassical thin shell theory, including high-order theories taking into account transverse shifts, the theory of thin layered shells, and shell theories based on the gradient distribution of material properties.

As a result of the study, the master student should be able to: formulate the main hypotheses underlying the various theories, write out the equations of the physical state, put the marginal and initial-boundary problems within the framework of a particular theory.

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Prerequisites

Mechanics of continuous media (elasticity theory). Strength of materials. Equations of mathematical physics. The theory of oscillations and stability of thin-walled shells.

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Contents of the discipline

The shell theory, based on the hypotheses of Kirchhoff-Love. The shell theory, based on the hypotheses of Tymoshenko. Generalized kinematic hypotheses of Tymoshenko for multilayer shells. Hypotheses of a broken curve, kinematic hypotheses of higher order. Equations of motion of multilayer shells, based on the equivalent theory of single-layer isotropic shells with allowance for transverse shifts. Equations of motion of thin layered shells containing layers made of composite “intelligent” materials (electro-, magneto-rheological elastomers and liquids). The shell theory with a gradient in thickness distribution of material properties. Solution of problems on oscillations and waves in thin shells within the framework of nonclassical theories.

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Recommended literature

  1. Mikhasev GI, Tovstik PE Localized oscillations and waves in thin shells: Asymptotic methods. – M: Fizmatlit. – 2009. 292p.
  2. Mikhasev G., Botogova M., Korobko E.  Theory of Thin Adaptive Laminated Shells Based on Magnetorheological Materials and its Application in Problems on Vibration Suppression. In book  “Shell-like Structures”, Ser. “Advanced Structured Materials”(Eds. H. Altenbachand V. Eremeyev), Vol. 15. Chapter 48. – Springer.‑2011, – P. 727-750.
  3. Shell-Like Structures: Advanced Theories and Applications (H. Altenbach, V. Eremeeveds.). CISM International Center for Mechanical Sci. Courses and Lectures, V. 572- Springer. – 2017.-288pp.
  4. Reddy J. N. Mechanics of Laminated Composite Plates: Theory and Analysis (2nd ed.).Boca Raton: CRC Press. -2004.
  5. Timoshenko, S. P.Woinowsky-Krieger, S. Theory of Plates and Shells. NewYork: McGrawHill.-1985.

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Teaching methods

Lectures, laboratory exercises

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Language of studying

Russian

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Conditions (requirements)

Evaluation in the exam is set taking into account:

60% – laboratory work, seminars, individual work 40% – oral answer in the exam

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Form of current certification

Exam