Advanced numerical methods for modelling of elastic wave propagation in solids and contact-impact problems
Typ dokumentu
habilitační prácehabilitation thesis
Autor
Kolman, Radek
Instituce přidělující hodnost
České vysoké učení technické v Praze. Fakulta dopravní.Metadata
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This habilitation thesis summarizes relevant advancements in numerical modelling of elastic wave
propagation in solids and contact-impact problems. The advanced numerical methods for accurate
numerical wave modelling in solids and contact-impact modelling are presented to improve cardinal
phenomena which pollute the numerical results as spurious oscillations of the stress eld in the wave
propagation, improve convergence rate for free vibration tasks, analysis of dispersion errors in the
nite element modelling in explicit time schemes and avoid the stability trouble in the penalty-based
dynamic contact-impact modelling with stabilization of contact force oscillations. On that topics, the
author of the thesis worked for twelve years to improving standard numerical technologies in FEM
which can be implemented into commercial software for dynamics, wave propagation and contactimpact
problems.
The rst Section presents the analysis of the dispersive properties of the nite element method
in elastic wave propagation. The dispersive properties of plane square bilinear and biquadratic
FEs are analyzed for the full spatial/grid disctretization and also for the temporal-spatial semidiscretization
with the explicit and implicit time integration. The higher-order FEM discretization via
the spline-based shape functions is studied with intention to describe dispersion and e ects of order
and smoothness of the spline shape function are discussed with respect to the the dispersion behaviour.
The second Section summaries the activities in the area of the advanced time stepping for the
nite element discretized equations of motions, the analysis of its accuracy and stability. The main
attention is paid to diminishing the dispersion errors and spurious stress oscillations of the numerical
results. The partitioned longitudinal and shear wave algorithm was found, implemented and
tested. The spline based FEM together with several time explicit and implicit schemes are studied
with respect to the spurious oscillations. Finally, the heterogenous time stepping algorithm for
elastic wave propagation is presented. It is based on the localized Lagrange multilpliers and solving
of the interface problems without dissipation of the energy on the interfaces.
The third Section focuses on applications of the nite element method in elastic wave propagation
in layered and heterogeneous media. The veri cation of the numerical results by the
experimental and analytical approaches are presented. The applications of the FEM for time reversal
tasks and in nondestructive testing of materials and structures are mentioned. The review of elastic
wave propagation in 3D printed structures and identi cation of the residual stresses in bodies is
introduced.
In the fourth Section, the advanced numerical methods based on higher-order FEM are presented.
Mainly, the isogeometric analysis applied into the free vibration problems is shown with the
discussion on convergence rate in eigen-value computations. The direct inversion mass matrix -
called reciprocal mass matrix - in free vibration problems is mentioned and discussed.
The fth Section focuses on the advanced numerical methods for modelling of the contact-impact
problems based on the bipenalty method as an extension of the classical penalty method. On
the numerical tests, the accuracy and stability of the nominated methods for contact-impact are
summarized and commented for one-dimensional and two-dimensional problems.
The thesis nishes with the summary and comments of possible future works and today challenging
directions for the studies in the areas of the thesis.
Kolekce
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