Insight into an implicit time integration scheme for structural dynamics

Bathe, Klaus‐Jürgen; Noh, Gunwoo

doi:10.1016/j.compstruc.2012.01.009

Cited by 230 publications

(153 citation statements)

References 9 publications

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“…The high-order nature of the DE 3 scheme is well established over the other considered methods. By order of increasing accuracy, we observe the following ranking: Newmark's scheme ((β, γ) = (1/4, 1/2)) is less accurate than Bathe's method [10]-both are second-order methods-than the DE 3 scheme that is third-order accurate in its dissipative setting (ρ ∞ = 0.5) and fourth-order accurate in its conservative setting (ρ ∞ = 1). It is observed that the requirement of twelve points per lowest period is not sufficient to ensure proper accuracy with the second-order methods whereas it does for the DE 3 scheme.…”

Section: Demonstrative Examplementioning

confidence: 98%

“…For this specific model, the Ω 1 case corresponds to imposing a rigid link between degree-of-freedom 1 and the boundary with imposed displacement. In the first part of this example, we compare the accuracy achieved by the DE 3 scheme to two other well-known integration schemes, namely the ones proposed by Newmark [1] and Bathe [10]. In the second part, we illustrate the utility of numerical damping in structural simulations and, in particular, the property of spectral annihilation that the DE 3 scheme enjoys when used in its most dissipative setting.…”

Section: Demonstrative Examplementioning

confidence: 99%

See 1 more Smart Citation

De3: Yet Another High-Order Integration Scheme for Linear Structural Dynamics

Depouhon¹,

Detournay²,

Denoël³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper, we present the DE 3 integration scheme. This unconditionally stable scheme is dedicated to the numerical integration of linear structural dynamics problems and offers a simple and easy to use high-order alternative to the second-order accurate ones that are usually employed. Its symmetric formulation makes it an interesting candidate to simulate large-scale problems. In addition, the scheme offers the possibility to control the introduced numerical damping via a single algorithmic parameter, which is very convenient for the filtering of the spurious oscillations that can arise from large stiffness contrasts in certain models. The properties of high-order accuracy and numerical damping are illustrated by way of a demonstrative example. 1216A. Depouhon, E. Detournay and V. Denoël

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Section: Demonstrative Examplementioning

confidence: 98%

Section: Demonstrative Examplementioning

confidence: 99%

De3: Yet Another High-Order Integration Scheme for Linear Structural Dynamics

Depouhon¹,

Detournay²,

Denoël³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…We consider the solution of the 3 degree-of-freedo m spring system [20]. For simp licity, all the three masses are assumed to be unity.…”

Section: Spring-mass Systemmentioning

confidence: 99%

A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

Zhu

Gang

Liu

et al. 2016

MATEC Web of Conferences

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Abstract. Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case wh ich the system is badly stiff. High Precision Direct integration based on variational principle is given (HP D-VP) for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is m uch precise an d is stiff A-stable, but also can avoid the truncation error of the computer. For the large systems, especially, the systems with different frequency or the stiff systems, our methods are stable, accurate and efficient. Numerical experiments show the convergence order of the scheme derived from the variational principle, and is much precise and is effective in engineering.

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“…An alternate method to construct time integration methods with reliable numerical dissipation for nonlinear problems is the use of a composite algorithm as presented by Bathe and coworkers [5,3,4,6]. The main idea of this approach is to combine a non-dissipative method and a dissipative method into a one-step but multistage composite scheme.…”

Section: Introductionmentioning

confidence: 99%

A robust composite time integration scheme for snap-through problems

et al. 2015

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A robust time integration scheme for snapthrough buckling of shallow arches is proposed. The algorithm is a composite method that consists of three sub-steps. Numerical damping is introduced to the system by employing an algorithm similar to the backward differentiation formulas (BDF) method in the last substep. Optimal algorithmic parameters are established based on stability criteria and minimization of numerical damping. The proposed method is accurate, numerically stable, and efficient as demonstrated through several examples involving loss of stability, large deformation, large displacements and large rotations.

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Insight into an implicit time integration scheme for structural dynamics

Cited by 230 publications

References 9 publications

De3: Yet Another High-Order Integration Scheme for Linear Structural Dynamics

De3: Yet Another High-Order Integration Scheme for Linear Structural Dynamics

A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

A robust composite time integration scheme for snap-through problems

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