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

Miranda, Stefano de; Mancuso, Massimo; Ubertini, Francesco

doi:10.1002/nme.2826

Cited by 18 publications

(7 citation statements)

References 27 publications

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“…In the present authors' opinion, some of them are given in [57][58][59]. Wriggers's book [42] is updated up to the first years of 2000 and provides a very good introduction to stepwise integration schemes.…”

Section: Solution Of the Nonlinear Equations Of Motion By A Stepwise Strategymentioning

confidence: 99%

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

Turco

Barchiesi

Dell’Isola

2021

Mathematics and Mechanics of Solids

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This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.

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Section: Solution Of the Nonlinear Equations Of Motion By A Stepwise Strategymentioning

confidence: 99%

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

Turco

Barchiesi

Dell’Isola

2021

Mathematics and Mechanics of Solids

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“…As briefly discussed in the introduction, the technical literature is quite packed with contributions aiming to solve this kind of problem, see, e.g., [33–35] and references therein for some recent contributions and Wriggers’ book [36] for a systematic discussion of stepwise integration schemes, as updated up to the first years of this century. Starting from a time discretization, this approach tries to reconstruct the equilibrium path, that is, the pair time t and Lagrangian variables collected in the vectors u and u · , by solving a series of initial value problems.…”

Section: Casciaro’s Stepwise Integration Schemementioning

confidence: 99%

Stepwise analysis of pantographic beams subjected to impulsive loads

Turco

2020

Mathematics and Mechanics of Solids

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Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from a theoretical, experimental, and numerical point of view. Numerical simulations furnish an important contribution for the the design and optimization of such materials and, more generally, for metamaterials. Here, we consider the influence of inertial forces, removing the hypothesis of quasistatic loading. By using an intrinsically discrete model, inspired by Hencky’s ideas, already tested in a series of published works, here we add the contribution of inertial forces and, in the framework of stepwise schemes, we re-experience an adaptive integration scheme capable of reconstructing the best structural response corresponding to a prefixed time step. Several numerical simulations, although preparatory, inspire some remarks on materials based on pantographic cells and outline the way for future challenges.

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“…When moving structures are considered, the non-linear structure dynamics is computed by adopting the Time Discontinuous Galerkin (TDG) scheme. This choice over standard Newmark algorithms is motivated by its superior properties in terms of stability, accuracy and convergence [11][12][13]. In this paper, the LB, VOF, IB and TDG methods are combined within a staggered explicit coupling algorithm called FELBA (Finite Element Lattice Boltzmann Analysis), which has been validated by the authors for different applications, including mechanics [14,15], industry [16], flapping flight [17,18], and even shallow waters [19], among the others.…”

Section: Introductionmentioning

confidence: 99%

A numerical framework for simulating fluid-structure interaction phenomena

Rosis¹,

Miranda²,

Burrafato³

et al. 2014

Frattura Ed Integrità Strutturale

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In this paper, a numerical tool able to solve fluid-structure interaction problems is proposed. The lattice Boltzmann method is used to compute fluid dynamics, while the corotational finite element formulation together with the Time Discontinuous Galerkin method are adopted to predict structure dynamics. The Immersed Boundary method is used to account for the presence of an immersed solid in the lattice fluid background and to handle fluid-structure interface conditions, while a Volume-of-Fluid-based method is adopted to take trace of the evolution of the free surface. These ingredients are combined through a partitioned staggered explicit strategy, according to an efficient and accurate algorithm recently developed by the authors. The effectiveness of the proposed methodology is tested against two different cases. The former investigates the dam break phenomenon, involving the modeling of the free surface. The latter involves the vibration regime experienced by two highly deformable flapping flags obstructing a flow. A wide numerical campaign is carried out by computing the error in terms of interface energy artificially introduced at the fluid-solid interface. Moreover, the structure behavior is dissected by simulating scenarios characterized by different values of the Reynolds number. Present findings are compared to literature results, showing a very close agreement.

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

Cited by 18 publications

References 27 publications

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

Stepwise analysis of pantographic beams subjected to impulsive loads

A numerical framework for simulating fluid-structure interaction phenomena

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