2 semester


Name of the discipline

Nonclassical thin shell theory


Grade level, specialty

1, specialty “mechanics and mathematical modeling”


Semester of studying



Amount of credits



Full name of the lecturer

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


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.



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


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.


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.


Teaching methods

Lectures, laboratory exercises


Language of studying



Conditions (requirements)

Evaluation in the exam is set taking into account:

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


Form of current certification