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

• apply the relations of the differential geometry to describe undeformed and deformed configurations of strings and rods in both the invariant (tensorial) and coordinate forms.
• assess the applicability of structural mechanics theories to academic and engineering problems for thin elongated structures.
• explain the basic principles of the theories of strings and thin rods for in-plane and three-dimensional problems, 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 Castigliano theorem and 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 thin rod.

Recapitulation of the basics of differential geometry of a curved material line, direct vector/tensor calculus, variational principles and analytical mechanics, as well as the theory of elasticity.
Theory of extensible and inextensible strings with simple examples. Asymptotic derivation of the equations of beam theory using the equations of the theory of elasticity.
Direct approach to geometrically linear theory of thin elastic rods in three dimensions with bending and torsion; example problems.
Oscillations of spatial rod structures with multiple segments and curvature.
Large deformation theory of thin elastic rods with demonstrations of solutions of boundary value problems using Wolfram Mathematica. Stability analysis.

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 Mechanics 3), as they provide the preliminary knowledge regarding: tensor algebra, Lagrangian mechanics, classical structural theories and methods of approximate solution of engineering problems.