First solve the problem and then write a code

Session 286

February 19, 2024

A.V. Lukin (SPbPU)
Synthesis of geometrically nonlinear reduced-order models for distributed elastic systems based on the finite element method.
The report is devoted to the problems of development and verification of computational algorithms for the synthesis of compact models of the dynamics of continual elastic systems in a geometrically nonlinear formulation (primarily thin-walled structures: strings, membranes, beams, plates, shells) based on the finite element method. The approaches under consideration are based on the idea of​​identifying a nonlinear (quadratic-cubic) stiffness characteristic of an elastic system in its modal coordinates with the subsequent application of the apparatus of the theory of nonlinear normal modes and Poincaré normal forms to construct an invariant manifold tangent to the modal subspace of interest. The resulting dynamic reduced-order model takes into account the nonlinear elastic coupling of the working vibration modes with high-frequency longitudinal and volume modes of the structure, which ensures the correctness of the calculated nonlinear stiffness characteristic of the system for the selected principal coordinates. The developed algorithm is applied to a number of problems of nonlinear dynamics of strings and beams that admit an approximate analytical solution using asymptotic methods of nonlinear mechanics. The features of the software implementation of the presented method based on the ABAQUS finite element analysis software system are discussed.
Lukin Alexey V. – PhD, Associate Professor of the Higher School of Mechanics and Control Processes of the Physics and Mechanical Institute of Peter the Great St. Petersburg Polytechnic University. Research interests: nonlinear dynamics; strength, stability and vibrations in engineering; computational mechanics; nano- and microelectromechanical systems.