Novel explicit time integration schemes for efficient transient analyses of structural problems

Kim, Wooram; Reddy, J. N.

doi:10.1016/j.ijmecsci.2020.105429

Cited by 35 publications

(8 citation statements)

References 37 publications

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“…There are many suitable explicit-integration algorithms used in structural wave propagation problems. [24][25][26][27][28][29] In this work we only apply the commonly used centered difference method. There are several possible re-formulations, cited for instance in Reference 26, and Algorithm 1 describes a variant particularly efficient with a diagonal damping matrix, which is what we assume in the examples below.…”

Section: Explicit Dynamics Of Linear Wave Propagation In Shell Struct...mentioning

confidence: 99%

Explicit dynamics of shells with a flat‐facet triangular finite element

Krysl

2022

Numerical Meth Engineering

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The use of a flat‐facet finite element with three nodes and six degrees of freedom per node for modeling of linear wave‐propagation events is discussed. The triangular shell finite element was presented in a preceding publication. The main novelty of the current approach is the treatment of the drilling rotations that decouples the drilling degree of freedoms on the global level, and hence makes it possible to eliminate negative effects of these degrees of freedom on the explicit time‐stepping algorithms employed to compute the dynamic response, such as deterioration in accuracy or artificially reduced time step. The element is shown to be robust for wave propagation simulations, and its performance is illustrated with examples including guided‐wave scenarios.

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Section: Explicit Dynamics Of Linear Wave Propagation In Shell Struct...mentioning

confidence: 99%

Explicit dynamics of shells with a flat‐facet triangular finite element

Krysl

2022

Numerical Meth Engineering

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“…28, the NB method exhibits very good performance in the analysis of wave propagation problems. Besides, worth of mention are some efforts devoted to developing higher-order explicit methods [19,33,35] using two and more sub-steps. The improvement of the accuracy order, however, often leads to a reduction of the stability region.…”

Section: Introductionmentioning

confidence: 99%

A novel explicit three-sub-step time integration method for wave propagation problems

Zhang

Zanoni

et al. 2022

Arch Appl Mech

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A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

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“…More details of advantages and disadvantages of explicit and implicit methods can be found in In recent years, a large number of researches were conducted to propose new explicit time integration methods where desirable algorithmic properties such as high calculation efficiency, small numerical dispersion, or dissipation errors are harvested. [15][16][17][18] For instance, to introduce controllable numerical dispersion, an explicit method evolved from the central difference (CD) method was presented by Tchamwa and Wielgosz (TW). 19,20 This method is proved to be very effective for wave propagation problems, but only first-order accurate.…”

Section: Introductionmentioning

confidence: 99%

“…21 After that, Kim and Reddy presented four novel sub-step explicit methods to achieve improved accuracy, and the new methods exhibit better numerical performances when compared with the recently developed improved sub-step methods without any additional procedures. 15 Recently, some novel explicit time integration methods based on high-order b-spline interpolation were presented to obtain high-order numerical solutions for linear dynamics. 22,23 Due to the specific approximation of physical variables, the precise theoretical prediction of accuracy order of these b-spline-based methods has not been obtained until now.…”

Section: Introductionmentioning

confidence: 99%

“…Then to obtain better solution of wave propagation problems, Noh and Bathe adopted a sub‐step technique to design a new second‐order accurate explicit method which illustrates good performance in reducing the dispersion errors 21 . After that, Kim and Reddy presented four novel sub‐step explicit methods to achieve improved accuracy, and the new methods exhibit better numerical performances when compared with the recently developed improved sub‐step methods without any additional procedures 15 …”

Section: Introductionmentioning

confidence: 99%

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A high‐order accurate explicit time integration method based on cubic b‐spline interpolation and weighted residual technique for structural dynamics

Wang

Deng

Duan

et al. 2020

Numerical Meth Engineering

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A novel explicit time integration method is proposed on the basis of cubic b-spline interpolation and weighted residual method. Its calculation formulation and procedure are presented. Accuracy, algorithmic damping, and period elongation are theoretically and numerically solved. The influence of two algorithmic parameters on basic properties of the proposed method is studied to obtain optimal parameters values for dynamic problems. Various linear and nonlinear dynamic problems are tested to demonstrate high efficiency of the proposed method.

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Novel explicit time integration schemes for efficient transient analyses of structural problems

Cited by 35 publications

References 37 publications

Explicit dynamics of shells with a flat‐facet triangular finite element

Explicit dynamics of shells with a flat‐facet triangular finite element

A novel explicit three-sub-step time integration method for wave propagation problems

A high‐order accurate explicit time integration method based on cubic b‐spline interpolation and weighted residual technique for structural dynamics

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