Numerični postopki za nelinearne statične in dinamične analize lupinskih sistemov različnih velikosti : doktorska disertacija

Lavrenčič, Marko (author), Brank, Boštjan (mentor)

Tema disertacije so mešani(-hibridni) končni elementi za lupine in integracijske sheme za dinamiko, ki ohranjajo osnovne konstante gibanja. Obravnavani končni elementi temeljijo na dveh geometrijsko točnih teorijah lupin: na modelu z velikimi rotacijami in neraztegljivim smernikom ter modelu brez rotacij z raztegljivim smernikom. Učinkovitost najsodobnejših mešanih(-hibridnih) končnih elementov za lupine je ocenjena na podlagi velikega števila numeričnih primerov. Predlagamo tudi nove, »skoraj optimalne« hibridne-mešane formulacije, ki omogočajo račun dolgih obtežnih korakov, izkazujejo skoraj optimalno konvergenco in so neobčutljive na popačenje mreže. Narejen je pregled implicitnih dinamičnih shem za nelinearno elastodinamiko, ki spadajo med posplošene ? metode in metode, ki ohranjajo (oziroma kontrolirano zmanjšujejo) energijo in ohranjajo gibalno in vrtilno količino. Primerjamo njihove spektralne lastnosti, nagnjenost k močni prekoračitvi analitične rešitve in njihovo natančnost. Z računom niza primerov, kjer rešujemo numerično toge nelinearne enačbe za lupine, ocenimo, kako se te lastnosti prenesejo v nelinearno elastodinamiko. Prikažemo sposobnost obravnavanih shem za kontrolirano disipacijo energije in zmožnost ohranjanja vrtilne količine, s kazalniki napake pa ocenimo njihovo natančnost za nelinearne primere. Izpeljemo sheme, ki ohranjajo/disipirajo energijo ter ohranjajo gibalno in vrtilno količino za hibridno-mešane formulacije lupin. Numerični primeri kažejo, da se robustnost in učinkovitost novih statičnih formulacij prenese tudi v dinamiko. Zaključni del disertacije je povezan z aplikacijo izpeljanih formulacij. Z numerično disipativnimi implicitnimi shemami proučujemo proces uklona lupin. Ocenimo sposobnost teh shem za opis zapletenih procesov uklona, tudi v postkritičnem območju, in pokažemo, da je numerična disipacija višjih frekvenc nujno potrebna za učinkovito dinamično simulacijo teh procesov. Na koncu izpeljane postopke uporabimo še za proučevanje površinskega gubanja ukrivljenih in tankih lupin na mehkih jedrih, vključno s preskoki uklonskih oblik.

• Language: Slovenian
• Keywords: lupine, mešani končni elementi, integracijske sheme v dinamiki, sheme ki ohranjajo/zmanjšujejo energijo in ohranjajo vrtilno količino, uklon, površinsko gubanje
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: [M. Lavrenčič]
• Year: 2020
• PID: 20.500.12556/RUL-121997
• UDC: 624.074.43:519.61/64(043)
• COBISS.SI-ID: 42990851
• Publication date in RUL: 14.11.2020

LAVRENČIČ, Marko, 2020, Numerični postopki za nelinearne statične in dinamične analize lupinskih sistemov različnih velikosti : doktorska disertacija [online]. Doctoral dissertation. M. Lavrenčič. [Accessed 14 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=121997

Secondary language

• Language: English
• Title: Numerical Procedures for Nonlinear Static and Dynamic Analyses of Shell Systems of Various Sizes : doctoral dissertation

Abstract

The topics of the thesis are mixed(-hybrid) finite element formulations for shell-like structures, and implicit time-stepping schemes that preserve basic constants of the motion. The considered finite elements are based on two geometrically exact shell models, in particular, large rotation inextensible-director model and rotation-less extensible-director model. The performance of the current state-of-the-art mixed(-hybrid) shell finite element formulations is assessed by studying a large number of numerical examples. Some novel “near optimal” mixed-hybrid shell finite element formulations are proposed that allow for large solution steps, show near optimal convergence characteristics and display little sensitivity to mesh distortion. As for the non-linear shell elasto-dynamics, we revisit implicit dynamic schemes that belong to the groups of generalized-α methods and energy-conserving/decaying and momentum-conserving methods. We compare their spectral characteristics, the tendency to overshoot and their accuracy. By performing a set of numerical tests for numerically stiff nonlinear shell-like examples, we assess how these features extend to nonlinear elasto-dynamics. We illustrate the ability of the considered schemes to dissipate the energy, to fully or approximately conserve the angular momentum, and we estimate the order of accuracy for nonlinear problems by error indicators. Novel energy-conserving/decaying and momentum-conserving schemes are derived for the previously introduced novel mixed-hybrid shell formulations. The numerical examples demonstrate that the robustness and efficiency of the novel static formulations can be prolonged to dynamics. The final part of the thesis is related to the application of the derived formulations. In particular, the shell buckling process is studied by applying numerically dissipative schemes. The ability of these schemes to handle complex buckling and post-buckling processes is assessed. It is demonstrated that controlled numerical dissipation of higher structural frequencies is absolutely necessary for an efficient simulation of a post-buckling response. Finally, we apply the derived procedures to study the problem of surface wrinkling on curved stiff-shell/soft-core substrates, including the transition between the wrinkling modes.

• Keywords: shells, mixed finite elements, dissipative integration schemes in dynamics, energy-conserving/decaying and momentum-conserving schemes, buckling, surface wrinkling