Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

Bursi, Oreste S.; Mancuso, Massimo

doi:10.1002/eqe.188

Cited by 11 publications

(13 citation statements)

References 26 publications

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“…Hence, displacement and velocity are approximated as in the classical formulation, see Equations (24) and (25), while the approximations used for the test functions are formally analogous to those given in Equations (26) and (27), with the exception that now W is a matrix of ( p −1)-order polynomial functions. Based on these assumptions, the energy corrected TDG formulation in the typical time step can be rewritten in the same form of Equations (28) and (29) of the classical 331 formulation, by simply replacing R, W, e, P and F with, respectively,R,Ŵ,ê,P andF defined as follows:…”

Section: Methodsmentioning

confidence: 99%

Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

Miranda

Mancuso

Ubertini

2010

Numerical Meth Engineering

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SUMMARYIn this paper a new time discontinuous Galerkin (TDG) formulation for non-linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher-order accuracy and high-frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation.

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Section: Methodsmentioning

confidence: 99%

Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

Miranda

Mancuso

Ubertini

2010

Numerical Meth Engineering

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“…Both pendula and spring-pendula were studied theoretically, numerically and experimentally in the context of time integration and dynamic substructuring [32,33]. The emulated or uncoupled case is considered in this section.…”

Section: The Spring-pendulum Oscillator: the Uncoupled Casementioning

confidence: 99%

“…It is well known that systems including pendula may exhibit large amplitude subharmonic and chaotic motions as well as simple periodic behaviour [22,31]. Both pendula and spring-pendula were studied theoretically, numerically and experimentally in the context of time integration and dynamic substructuring [32,33]. The emulated or uncoupled case is considered in this section.…”

Section: The Spring-pendulum Oscillator: the Uncoupled Casementioning

confidence: 99%

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

Bursi

Cui

Vulcan

et al. 2010

Earthq Engng Struct Dyn

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SUMMARYIn this paper, Rosenbrock-based algorithms originally developed for real-time testing of linear systems with dynamic substructuring are extended for use on nonlinear systems. With this objective in mind and for minimal overhead, both two-and three-stages linearly implicit real-time compatible algorithms were endowed with the Jacobian matrices requiring only one evaluation at the beginning of each time step. Moreover, these algorithms were improved with subcycling strategies. In detail, the paper briefly introduces Rosenbrock-based L-Stable Real-Time (LSRT) algorithms together with linearly implicit and explicit structural integrators, which are now commonly used to perform real-time tests. Then, the LSRT algorithms are analysed in terms of linearized stability with reference to an emulated spring pendulum, which was chosen as a nonlinear test problem, because it is able to exhibit a large and relatively slow nonlinear circular motion coupled to an axial motion that can be set to be stiff. The accuracy analysis on this system was performed for all the algorithms described. Following this, a coupled spring-pendulum example typical of real-time testing is analysed with respect to both stability and accuracy issues. Finally, the results of representative numerical simulations and real-time substructure tests, considering nonlinearities both in the numerical and the physical substructure, are explored. These tests were used to demonstrate how the LSRT algorithms can be used for substructuring tests with strongly nonlinear components.

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“…While predictor-corrector Time Discontinuous Galerkin algorithms are not appealing in a PDT context owing to the evaluation of unknown extra displacement and velocity fields (Bursi and Mancuso, 2002;Bonelli et al, 2001Bonelli et al, , 2002b, the implementation of a predictor-multicorrector technique into the implicit CH-a method is feasible and is the main issue that the paper explores further. Therefore, the CH-a algorithm has been implemented in a predictor-corrector form, the IPC-r 1 method in short, without resorting to iterative schemes; and in view of advanced real-time applications also the explicit ECH-a method has been implemented in the PDT method: the EPC-r b scheme.…”

Section: Introductionmentioning

confidence: 99%

Predictor‐corrector procedures for pseudo‐dynamic tests

Bonelli

Bursi

2005

Engineering Computations

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -To propose novel predictor-corrector time-integration algorithms for pseudo-dynamic testing. Design/methodology/approach -The novel predictor-corrector time-integration algorithms are based on both the implicit and the explicit version of the generalized-a method. In the non-linear unforced case second-order accuracy, stability in energy, energy decay in the high-frequency range as well as asymptotic annihilation are distinctive properties of the generalized-a scheme; while in the non-linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized-a algorithm has been implemented in a predictor-one corrector form giving rise to the implicit IPC-r 1 method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC-r b method, endowed with user-controlled dissipation properties. The resulting schemes have been tested experimentally both on a two-and on a six-degrees-of-freedom system, exploiting substructuring techniques. Findings -The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo-dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non-linear multiple-degrees-of-freedom systems reproduced with the Bouc-Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized-a methods. Research limitations/implications -Further developments envisaged for this study are the application of the IPC-r 1 method and of EPC-r b scheme to partitioned procedures for high-speed pseudo-dynamic testing with substructuring. Practical implications -The implicit IPC-r 1 and the explicit EPC-r b methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterati...

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Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

Cited by 11 publications

References 26 publications

Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

Predictor‐corrector procedures for pseudo‐dynamic tests

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