Error estimation and adaptivity in deformable solid dynamics

Lacoma Aller, Luis María (2006). Error estimation and adaptivity in deformable solid dynamics. Thesis (Doctoral), E.T.S.I. Caminos, Canales y Puertos (UPM).

Description

Title: Error estimation and adaptivity in deformable solid dynamics
Author/s:
  • Lacoma Aller, Luis María
Contributor/s:
  • Romero Olleros, Ignacio
Item Type: Thesis (Doctoral)
Date: May 2006
Subjects:
Freetext Keywords: time integration; error estimation; solid dynamics; adaptivity; control theory
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Mecánica de Medios Continuos y Teoría de Estructuras
Creative Commons Licenses: Recognition

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Abstract

In this dissertation we study the error due to the temporal discretization in numerical simulations of deformable solid dynamics . For that, we start from the semidiscrete equations of motion and analyze the conditions that an estimator must satisfy to compute accurate results. With them, two typical error estimators are analyzed. Later, we propose a novel methodology for the formulation of a posteriori error estimators for the most common time-stepping methods employed in solid and structural dynamics. The estimators obtained by means of this methodology are accurate even in non-smmoth problems, they can be applied both in linear and non-linear problems and can be easily implemented in _nite element codes. The proposed methodology is applied to construct error estimators for Newmark's method and for the HHT method. The good performance of these new estimators is investigated in several numerical simulations. The information given by these estimators is the starting point for developing adaptive algorithms. They change automatically the time step size to ensure that the error is smaller than a tolerance, but keeping the computational cost as low as possible. The algorithms presented are based on control theory, and di_erent techniques applied in this _eld are employed to optimize the adaptive strategies. The _nal adaptive schemes are very simple formulas which are easily implemented in existing codes. Three non-linear numerical examples are presented to validate the good behaviour of the adaptive algorithms described.

More information

Item ID: 678
DC Identifier: http://oa.upm.es/678/
OAI Identifier: oai:oa.upm.es:678
Deposited by: D. Luis Maria Lacoma Aller
Deposited on: 13 Nov 2007
Last Modified: 20 Apr 2016 06:26
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