A review of automatic time-stepping strategies on numerical time integration for structural dynamics analysis

Rossi, D. F.; Ferreira, Walnório Graça; Mansur, Webe João; Calenzani, Adenilcia Fernanda Grobério

doi:10.1016/j.engstruct.2014.08.016

Cited by 40 publications

(11 citation statements)

References 17 publications

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“…which can be derived from (41) in the absence of damping (C = 0) as, e.g., in [54]. If the spatial discretization is performed with finite differences [71,77], then M = I and there is no need of transformations from (41) to (48). Most authors have considered the acoustic wave equation [54,71,77,78], but the Lax-Wendroff approximation has also been applied to the elastic wave equation [79,80].…”

Section: Lax-wendroff Methodsmentioning

confidence: 99%

“…Most authors have considered the acoustic wave equation [54,71,77,78], but the Lax-Wendroff approximation has also been applied to the elastic wave equation [79,80]. Following [77], let us derive the fourth-order Lax-Wendroff method for (48). We refer to [78] for higher-order approximations.…”

Section: Lax-wendroff Methodsmentioning

confidence: 99%

“…where T is the final time of the simulation. The time step will depend on the smallest grid length in space and the chosen approximation method for the time derivatives, and in general it can be dynamically selected by means of error estimators [46][47][48]. One of the greatest difficulties with temporal discretization is the situation where some elements in the spatial grid are extremely small (such as slivers generated from 3D unstructured mesh-generation codes [49]), forcing an equally small time step and undermining the efficiency of the wave-propagation simulation.…”

Section: Temporal Discretizationmentioning

confidence: 99%

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Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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The numerical modeling of mechanical waves is currently a fundamental tool for the study and investigation of their propagation in media with heterogeneous physical properties and/or complex geometry, as, in these cases, analytical methods are usually not applicable. These techniques are used in geophysics (geophysical interpretation, subsoil imaging, development of new methods of exploration), seismology (study of earthquakes, regional and global seismology, accurate calculation of synthetic seismograms), in the development of new methods for ultrasonic diagnostics in materials science (non-destructive methods) and medicine (acoustic tomography). In this paper we present a review of numerical methods that have been developed and are currently used. In particular we review the key concepts and pioneering ideas behind finite-difference methods, pseudospectral methods, finite-volume methods, Galerkin continuous and discontinuous finite-element methods (classical or based on spectral interpolation), and still others such as physics-compatible, and multiscale methods. We focus on their formulations in time domain along with the main temporal discretization schemes. We present the theory and implementation for some of these methods. Moreover, their computational characteristics are evaluated in order to aid the choice of the method for each practical situation.

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Section: Lax-wendroff Methodsmentioning

confidence: 99%

Section: Lax-wendroff Methodsmentioning

confidence: 99%

Section: Temporal Discretizationmentioning

confidence: 99%

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Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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“…Taking into account approximations (4) and (5), Equation (3) may be rewritten as the following recursive relation:…”

Section: Introductionmentioning

confidence: 99%

A simple and effective single‐step time marching technique based on adaptive time integrators

Soares

2016

Numerical Meth Engineering

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Summary In this work, a novel time marching procedure is presented in which adaptive time integration parameters are locally computed, allowing different spatial and temporal distributions. As a consequence, a more versatile technique arises, enabling an enhanced performance. The main features of the proposed technique are: (1) it is simple; (2) it has guaranteed stability; (3) it is an efficient non‐iterative adaptive single‐step procedure; (4) it provides enhanced accuracy; (5) it enables advanced controllable algorithmic dissipation in the higher modes; (6) it is truly self‐starting; and (7) it is entirely automatic, requiring no input parameter from the user. The proposed technique is very complete, providing the main positive attributes that are requested from an effective time marching procedure. Numerical results are presented along the paper, illustrating the excellent performance of the method. Copyright © 2016 John Wiley & Sons, Ltd.

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“…A good example of such investigation is time integration that is used for dynamic analysis. Algorithms of time integration 3) are well established in solid continuum and structural mechanics, but are considered old-fashioned. There is plenty of room for improving their efficiency and accuracy by employing new algorithms that are developed in computational science and making necessary modification; see, for instance, symplectic time integration 4),5), 6) .…”

Section: Introductionmentioning

confidence: 99%

Rigorous Derivation of Hamiltonian From Lagrangian for Solid Continuum

et al. 2018

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This paper provides rigorous derivation of a Hamiltonian from a given Lagrangian of solid continuum, for a possible improvement of dynamic analysis. The derived Hamiltonian, unlike an ordinary one, has momentum and strain as argument, and the associated canonical equation includes spatial derivative in it. Characteristics of the Hamiltonian of this form are studied. The appearance of strain rate in the canonical equation, which has been overlooked in the past researches, is pointed out. For numerical computation, a Hamiltonian for discretized functions is derived. It is shown that discretized strain rate appears in the canonical equation when suitable discretization scheme is applied.

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A review of automatic time-stepping strategies on numerical time integration for structural dynamics analysis

Cited by 40 publications

References 17 publications

Numerical modeling of mechanical wave propagation

Numerical modeling of mechanical wave propagation

A simple and effective single‐step time marching technique based on adaptive time integrators

Rigorous Derivation of Hamiltonian From Lagrangian for Solid Continuum

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