Solving dynamical systems involving piecewise restoring force using state event location / Joseph P. Wright in Journal of engineering mechanics, Vol. 138 N° 8 (Août 2012)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 138 N° 8 (Août 2012) . - pp.997–1020. Titre : Solving dynamical systems involving piecewise restoring force using state event location Type de document : texte imprimé Auteurs : Joseph P. Wright, Auteur ; Jin-Song Pei, Auteur Année de publication : 2012 Article en page(s) : pp.997–1020. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Nonlinear hysteretic restoring force Differential-algebraic equations Piecewise solutions Discontinuities Explicit methods Adaptive Runge-Kutta State event location Résumé : Many theoretical and experimental studies of complex path-dependent dynamic systems lead to restoring forces expressed as piecewise nonlinear algebraic equations. Examples include, but are not limited to, bilinear hysteretic, Ramberg-Osgood, Masing, generalized Masing, Clough, and Takeda models, which are popular in engineering mechanics applications. These models relate restoring force to displacement and velocity by means of piecewise relations having only continuity, which leads to two sorts of challenges in numerical simulation. First, the equations of motion may not simply be a set of ordinary differential equations, rather they may fall within the framework of differential-algebraic equations (DAEs). Second, there are unknown locations of discontinuities of low-order derivatives of the solution. This study seeks accurate and efficient numerical solutions of the DAEs with continuity, enabling robust simulation of these complex nonlinear dynamic systems. This study focuses on explicit time integration for single degree-of-freedom problems, while presenting a suitable problem formulation, detailed guidelines, case studies, and convincing insights, while exploiting two built-in MATLAB functions (ode45.m and the Events option). User-defined options are carefully examined, and recommendations are made based on a systematic study of approximation accuracy and computational efficiency, particularly as they relate to global error and tolerance proportionality when using an explicit, adaptive Runge-Kutta (RK) solver. Obtaining accurate values of state event locations results in a robust approach to solving the identified class of problems. This work initiates the possibility of treating many similar models by using the proposed programming module and, more importantly, by applying and further advancing the underlying theoretical concepts. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000404 [article] Solving dynamical systems involving piecewise restoring force using state event location [texte imprimé] / Joseph P. Wright, Auteur ; Jin-Song Pei, Auteur . - 2012 . - pp.997–1020. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 8 (Août 2012) . - pp.997–1020. Mots-clés : Nonlinear hysteretic restoring force Differential-algebraic equations Piecewise solutions Discontinuities Explicit methods Adaptive Runge-Kutta State event location Résumé : Many theoretical and experimental studies of complex path-dependent dynamic systems lead to restoring forces expressed as piecewise nonlinear algebraic equations. Examples include, but are not limited to, bilinear hysteretic, Ramberg-Osgood, Masing, generalized Masing, Clough, and Takeda models, which are popular in engineering mechanics applications. These models relate restoring force to displacement and velocity by means of piecewise relations having only continuity, which leads to two sorts of challenges in numerical simulation. First, the equations of motion may not simply be a set of ordinary differential equations, rather they may fall within the framework of differential-algebraic equations (DAEs). Second, there are unknown locations of discontinuities of low-order derivatives of the solution. This study seeks accurate and efficient numerical solutions of the DAEs with continuity, enabling robust simulation of these complex nonlinear dynamic systems. This study focuses on explicit time integration for single degree-of-freedom problems, while presenting a suitable problem formulation, detailed guidelines, case studies, and convincing insights, while exploiting two built-in MATLAB functions (ode45.m and the Events option). User-defined options are carefully examined, and recommendations are made based on a systematic study of approximation accuracy and computational efficiency, particularly as they relate to global error and tolerance proportionality when using an explicit, adaptive Runge-Kutta (RK) solver. Obtaining accurate values of state event locations results in a robust approach to solving the identified class of problems. This work initiates the possibility of treating many similar models by using the proposed programming module and, more importantly, by applying and further advancing the underlying theoretical concepts. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000404

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