After successful completion of the course, students are able to ...

• apply the relations of the differential geometry of a curved surface to describe undeformed and deformed configurations of plates and shells in both the invariant (tensorial) and coordinate forms.
• assess the applicability of structural mechanics theories to academic and engineering problems for thin flat and curved structures.
• explain the basic principles of the theories of plates and shells, both for small deformation analysis as well as for geometrically nonlinear cases, including stability and vibration problems.
• formulate and solve the equations and the boundary conditions for certain simple examples.
• use energy-based principles such as the method of Ritz to solve boundary value problems.
• apply the solutions of the structural mechanics theory to engineering problems, evaluating the stress state in the three-dimensional body of the structural member.

Basics of the vector/tensor calculus in oblique basis.
Differential geometry of a surface. Asymptotic derivation of the equations of the theory of bending of plates using the equations of the theory of elasticity.
Methods for exact and approximate solving of simple static and dynamic (oscillations) problems of deformation of plates with various geometries and boundary conditions; example problems.
Small deformation theory of curved shells; investigation of simple cases.
Properties of solutions: membrane state and boundary layers with bending moments.
Derivation of the theory of thin-walled rods of open profile using shell equations.
Large deformation and stability analysis of curved shells. Example analytical and approximate solutions.

Classroom lectures featuring theoretical basics and solution of example problems.
Independent study of literature sources. Presentation and discussion of numerical simulations in the classroom.
Autonomous investigation of a suggested example problem under the supervision of the teacher.

Active contributions to lecture and exercises (20%), final assignment and accompanying discussion (80%)

It is recommended to complete the preceding courses beforehand (in particular Structural mechanics of rods), as they provide the preliminary knowledge regarding: tensor algebra, Lagrangian mechanics, classical structural theories and methods of approximate solution of engineering problems.