Department of Computational Methods

Research profile

The Department of Computational Methods develops and applies numerical approaches to problems in the mechanics of deformable solids, in particular to problems of statics, dynamics, stability and vibrations of shell systems of complex shape.

Main research areas

• Theory of thin layered shells assembled from anisotropic layers of variable thickness.
• Methods for solving stress-state problems for systems of shells of revolution of arbitrary shape under distributed and local loads, based on reduction to one-dimensional problems and their numerical solution by the stable method of discrete orthogonalization.
• Methods for boundary-value problems of statics of layered non-circular cylindrical shells, shells with curvilinear axes, and shallow shells.
• Non-classical models and methods for static problems of layered anisotropic shells.
• Contact problems in the theory of thin anisotropic shells.
• Static problems for anisotropic heterogeneous shells in a spatial formulation.
• Theory and methods for solving geometrically nonlinear deformation problems of shells in precritical and postcritical states.
• Methods for stress-state analysis of complex-shaped shells in non-orthogonal non-conjugate coordinate systems.
• Methods for free and forced vibration problems of shells based on different models.
• Analysis of shell structural elements.
• Application of solid mechanics methods to problems of dentistry.