A new explicit variable time‐integration self‐starting methodology for computational structural dynamics

Tamma, Kumar K.; D’Costa, Joseph F.

doi:10.1002/nme.1620330605

Cited by 11 publications

(8 citation statements)

References 14 publications

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“…Thus, the first positive feature of the method is that it is truly self‐starting, eliminating any kind of cumbersome initial procedure, such as the computation of initial accelerations (which usually requires an extra system of equations to be dealt with) and/or the computation of multistep initial values. Of course, there are several other techniques that are also self‐starting (this is a standard feature of all momentum based methods, for instance), and it is interesting to observe that the explicit self‐starting methodology proposed by Tamma and D'Costa can be reproduced by the present technique by always considering α = 1 and γ = 0.…”

Section: Governing Equations and Time Integration Strategymentioning

confidence: 82%

A model/solution‐adaptive explicit‐implicit time‐marching technique for wave propagation analysis

Soares

2019

Numerical Meth Engineering

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Summary In this work, an explicit‐implicit time‐marching procedure with model/ solution‐adaptive time integration parameters is proposed for the analysis of hyperbolic models. The two time integrators of the methodology are locally evaluated, enabling their different spatial and temporal distributions. The first parameter defines the explicit/implicit subdomains of the model, and it is defined in a way that stability is always ensured, as well as period elongation errors are reduced; the second parameter controls the dissipative properties of the methodology, allowing spurious high‐frequency modes to be properly eliminated, rendering reduced amplitude decay errors. In addition, the proposed explicit‐implicit approach allows contracted systems of equations to be obtained, reducing the computational effort of the analysis. The main features of the novel methodology can be summarized as follows: (i) it is simple; (ii) it is locally defined; (iii) it has guaranteed stability; (iv) it is an efficient noniterative single‐step procedure; (v) it provides enhanced accuracy; (vi) it enables advanced controllable algorithmic dissipation in the higher modes; (vii) it considers a link between the temporal and the spatial discretization; (viii) it stands as a single‐solve framework based on reduced systems of equations; (ix) it is truly self‐starting; and (x) it is entirely automatic.

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Section: Governing Equations and Time Integration Strategymentioning

confidence: 82%

A model/solution‐adaptive explicit‐implicit time‐marching technique for wave propagation analysis

Soares

2019

Numerical Meth Engineering

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“…with so called local subcycling. Proposed methods that use different time steps at different nodes are for example reported in Belytschko et al [50], Neal and Belytschko [292] or Tamma and D'Costa [384]. Some of them still struggle with problems of momentum conservation at time step interfaces.…”

Section: Explicit or Implicit Time Integration Schemes?mentioning

confidence: 99%

Structures Under Crash and Impact

Hiermaier¹

2008

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“…1 (continued) allocation of timesteps, and by having some dissipation of high frequencies present, to prevent these instabilities. This could be done by applying partial velocity subcycling to the ''self-starting'' algorithm of Tamma and DÕCosta [4]. In this algorithm, new velocities are first found and then dissipation is introduced when displacements are updated, by making the update using a weighting v c of velocities at the start and end of the current timestep i…”

Section: Stability Analysismentioning

confidence: 99%

“…This problem will be discussed further later. These problems are shared by related algorithms which use a nodal interface and update the large timestep side first, such as that due to Tamma and DÕCosta [4].…”

Section: Introductionmentioning

confidence: 99%

A partial velocity approach to subcycling structural dynamics

Daniel

2003

Computer Methods in Applied Mechanics and Engineering

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Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition, extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or ''statistical stability''. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method, this approach is simple, and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method, it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However, coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface.

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A new explicit variable time‐integration self‐starting methodology for computational structural dynamics

Cited by 11 publications

References 14 publications

A model/solution‐adaptive explicit‐implicit time‐marching technique for wave propagation analysis

A model/solution‐adaptive explicit‐implicit time‐marching technique for wave propagation analysis

Structures Under Crash and Impact

A partial velocity approach to subcycling structural dynamics

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