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Implicit and Explicit Method in nonlinear Dynamics
Vaněčková, Adéla ; Hradil, Petr (referee) ; Němec, Ivan (advisor)
The final thesis „Explicit and Implicit methods in nonlinear dynamics“ deals with the issue of geometrical and physical nonlinear analysis of structures exposed to seismic loading by the methods of direct integration of equations of motion. Solution by the explicit and the implicit method is compared for three material models. While the differences between the results of the explicit method and the implicit Newmark method are small as expected, the differences are substantial between the results of different material models. However, these differences are explained and they are in full concordance with the theoretical assumptions for the pertinent material models. The conclusion of the final thesis is check of correctness of the results of the new module of the program system RFEM for both tested numerical methods and all three analyzed material models. (linear elastic, plastic Drucker-Prager and the Mazars damage model). With sufficient precision of results, both explicit and implicit numerical methods showed to be suitable for seismic analysis. The implicit method can provide several times faster calculation than the explicit one, but the determination of the optimal time step is problematic and time consuming, so the suitability of use of both methods for seismic analysis is comparable.
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Implicit and Explicit Method in nonlinear Dynamics
Vaněčková, Adéla ; Hradil, Petr (referee) ; Němec, Ivan (advisor)
The final thesis „Explicit and Implicit methods in nonlinear dynamics“ deals with the issue of geometrical and physical nonlinear analysis of structures exposed to seismic loading by the methods of direct integration of equations of motion. Solution by the explicit and the implicit method is compared for three material models. While the differences between the results of the explicit method and the implicit Newmark method are small as expected, the differences are substantial between the results of different material models. However, these differences are explained and they are in full concordance with the theoretical assumptions for the pertinent material models. The conclusion of the final thesis is check of correctness of the results of the new module of the program system RFEM for both tested numerical methods and all three analyzed material models. (linear elastic, plastic Drucker-Prager and the Mazars damage model). With sufficient precision of results, both explicit and implicit numerical methods showed to be suitable for seismic analysis. The implicit method can provide several times faster calculation than the explicit one, but the determination of the optimal time step is problematic and time consuming, so the suitability of use of both methods for seismic analysis is comparable.
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