A monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics

Mahjoubi, Najib; Gravouil, Anthony; Combescure, Alain; Greffet, Nicolas

doi:10.1016/j.cma.2010.12.004

Cited by 37 publications

(40 citation statements)

References 34 publications

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“…Comparing with (6), we observe that (24) is very similar to (6), except that there is more degrees of freedom in (24). Hence, in Section 4, we will use (6) to simplify the presentation of the coupling strategy.…”

Section: -D Beammentioning

confidence: 86%

“…We shall now make the hypothesis that

{\overset{λ}{falsemml-overline}}_{s MathClass-punc, i} MathClass-rel= {\overset{λ}{falsemml-overline}}_{f} MathClass-rel\forall i MathClass-rel\in 1 MathClass-punc, m

, the resulting interface energy over the large time step

([], t_{f}^{n} MathClass-punc, t_{f}^{n MathClass-bin+ 1})

Δ {scriptW}_{I}^{d} MathClass-rel= {\overset{λ}{falsemml-overline}}_{f} {MathClass-op\int}_{t_{f}^{n}}^{t_{f}^{n MathClass-bin+ 1}} (v_{s} MathClass-bin- v_{f}) normald t MathClass-punc.

…”

Section: Coupling Strategymentioning

confidence: 99%

See 1 more Smart Citation

Coupling of finite volume and finite element subdomains using different time integrators

Combescure

Leboeuf

2013

Numerical Methods in Fluids

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Section: -D Beammentioning

confidence: 86%

“…We shall now make the hypothesis that

{\overset{λ}{falsemml-overline}}_{s MathClass-punc, i} MathClass-rel= {\overset{λ}{falsemml-overline}}_{f} MathClass-rel\forall i MathClass-rel\in 1 MathClass-punc, m

, the resulting interface energy over the large time step

([], t_{f}^{n} MathClass-punc, t_{f}^{n MathClass-bin+ 1})

Δ {scriptW}_{I}^{d} MathClass-rel= {\overset{λ}{falsemml-overline}}_{f} {MathClass-op\int}_{t_{f}^{n}}^{t_{f}^{n MathClass-bin+ 1}} (v_{s} MathClass-bin- v_{f}) normald t MathClass-punc.

…”

Section: Coupling Strategymentioning

confidence: 99%

Coupling of finite volume and finite element subdomains using different time integrators

Combescure

Leboeuf

2013

Numerical Methods in Fluids

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“…Here, we summarize methods of direct time integration suitable for usage in dynamic FE computations [13]: explicit methods [2,3,5,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], implicit methods [32][33][34][35][36][37][38], implicit-explicit methods [39][40][41], multi-time step and time sub-cycling methods [31,42,43], heterogeneous and asynchronous time integrators [44][45][46], variational time integrators [47,48], various local stepping approaches in time [49][50][51][52][53], time schemes for higher-order FEM and isogeometric analysis [2,54], and methods based on binary partitioning using a variable time step size…”

Section: Introductionmentioning

confidence: 99%

Efficient implementation of an explicit partitioned shear and longitudinal wave propagation algorithm

Kolman

Cho

Park

2015

Int. J. Numer. Meth. Engng

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SUMMARYThe paper complements and extends the previous works on partitioned explicit wave propagation analysis methods, which were presented for discontinuous wave propagation problems in solids. An efficient implementation of the partitioned explicit wave propagation analysis methods is introduced. The present implementation achieves about 25% overall computational effort compared with the previous implementation with the same accuracy. The present algorithm tracks, with different integration time step sizes in accordance with their different wave speeds, the propagation fronts of longitudinal and shear waves. This is accomplished by integrating separately the element-by-element partitioned longitud inal and shear equations of motion. The state vectors (displacements, velocity and accelerations) of the longitudinal and shear components are reconciled at the end of each time step. The reconciliation procedure does not require any system parameters such as material properties, density, unlike conventional artificial viscosity methods. Numerical examples are presented as applied to linear and non-linear wave propagation problems, which demonstrate high-fidelity wavefront tracking ability of the present method, and compared with existing conventional wave propagation analysis methods.

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“…These constituents interact to form a collective system, herein referred to as coupled model . Such focus is relevant as many numerical models in civil and infrastructure engineering are indeed coupled models that are an amalgam of multiple constituents or systems of constituents; see, for instance, the published literature on soil–structure interaction (Provenzano, 2003; Qian and Zhang, 1993), fluid–structure interaction (Kutay and Aydilek, 2009; Caracoglia et al, 2009), human–structure interaction (Macdonald, 2009; Wang et al, 2011), and the broad field of substructuring (or subdomains), which essentially focuses on structure–structure interaction (Mahjoubi et al, 2009; Mahjoubi et al, 2011). While aiming to improve the predictive accuracy of such coupled simulation models, one obvious question arises: to achieve the greatest reduction in model uncertainty and bias, which constituent must be given the highest priority for further code development?…”

Section: Introductionmentioning

confidence: 99%

Prioritization of Code Development Efforts in Partitioned Analysis

Hegenderfer

Atamturktur

2012

Computer aided Civil Eng

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In partitioned analysis of systems that are driven by the interaction of functionally distinct but strongly coupled constituents, the predictive accuracy of the simulation hinges on the accuracy of individual constituent models. Potential improvement in the predictive accuracy of the simulation that can be gained through improving a constituent model depends not only on the relative importance, but also on the inherent uncertainty and inaccuracy of that particular constituent. A need exists for prioritization of code development efforts to cost‐effectively allocate available resources to the constituents that require improvement the most. This article proposes a novel and quantitative code prioritization index to accomplish such a task and demonstrates its application on a case study of a steel frame with semirigid connections. Findings show that as high‐fidelity constituent models are integrated, the predictive ability of model‐based simulation is improved; however, the rate of improvement is dependent upon the sequence in which the constituents are improved.

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A monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics

Cited by 37 publications

References 34 publications

Coupling of finite volume and finite element subdomains using different time integrators

Coupling of finite volume and finite element subdomains using different time integrators

Efficient implementation of an explicit partitioned shear and longitudinal wave propagation algorithm

Prioritization of Code Development Efforts in Partitioned Analysis

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