A new family of two-stage explicit time integration methods with dissipation control capability for structural dynamics

Kim, Wooram

doi:10.1016/j.engstruct.2019.05.095

Cited by 33 publications

(20 citation statements)

References 36 publications

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“…[13]. The case 3-3 is spectrally identical to the scheme developed by the author [18]. The explicit scheme proposed by Soares [40] also uses two stages like the explicit composite schemes, and its spectral properties are almost identical to the case 3-2 for the undamped case (i.e., = 0 ).…”

Section: Explicit Schemesmentioning

confidence: 90%

“…In this study, important numerical characteristics, such as the accuracy, the stability, and the algorithmic dissipation, are also investigated by using the single-degree-of-freedom problem given in Eqs. ( 17)- (18) and the amplification matrix given in Eq. (19).…”

Section: Implicit Schemesmentioning

confidence: 99%

“…To demonstrate general advantages of using the composite schemes, 0 =̇0 = 0.0, = 0.05, = 2 , ( ) = 10.0 sin( ) + 5.0 cos � 3 � are used for the single-degree-of-freedom problem given in Eqs. ( 17)- (18), and the problem is numerically solved by using the composite schemes and the implicit and explicit generalized-methods [5,26]. Then, numerical results are compared with each other.…”

Section: General Advantages Of Composite Schemesmentioning

confidence: 99%

“…Occasionally, they are also called the two-stage time integration scheme. Implicit and explicit schemes of this type are known to possess improved numerical performances when compared with the conventional single-stage time integration schemes [8,12,13,14,15,16,17,18,19]. In composite schemes, two different kinds of schemes are employed in the first and second sub-steps, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A critical assessment of two-stage composite time integration schemes with a unified set of time approximations

Kim

Reddy

2021

Lat. Am. j. solids struct.

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A simple unified set of displacement and velocity approximations is presented to express various two-stage composite time integration schemes. Based on the unified approximations, two novel sets of optimized parameters are newly proposed for the implicit composite schemes to enhance the capability of conserving total energy. Two special cases of the unified approximations are also considered to overcome some shortcomings of the existing schemes. Besides, the newly proposed unified set of approximations can include many of the existing composite time integration schemes. To be specific, both implicit and explicit composite schemes can be expressed by using the unified set of approximations. Thus, both implicit and explicit types of composite schemes can be selected from the unified set by simply changing algorithmic parameters. To demonstrate advantageous features of the proposed unified set of approximations, various numerical examples are solved, and results are analyzed.

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Section: Explicit Schemesmentioning

confidence: 90%

Section: Implicit Schemesmentioning

confidence: 99%

Section: General Advantages Of Composite Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A critical assessment of two-stage composite time integration schemes with a unified set of time approximations

Kim

Reddy

2021

Lat. Am. j. solids struct.

Self Cite

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“…To achieve higher accuracy, the three-and four-sub-step implicit composite methods [8,18,29,30,42] were also developed, adopting similar ideas. In addition, many efforts have been devoted to the development of explicit composite methods, producing several good candidates, such as the Noh and Bathe [34], the Soares [37], and many other methods [21,24,43].…”

Section: Introductionmentioning

confidence: 99%

Improved second-order unconditionally stable schemes of linear multi-step and equivalent single-step integration methods

Zhang

Masarati

2020

Comput Mech

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Second-order unconditionally stable schemes of linear multi-step methods, and their equivalent single-step methods, are developed in this paper. The parameters of the linear two-, three-, and four-step methods are determined for optimal accuracy, unconditional stability and tunable algorithmic dissipation. The linear three- and four-step schemes are presented for the first time. As an alternative, corresponding single-step methods, spectrally equivalent to the multi-step ones, are developed by introducing the required intermediate variables. Their formulations are equivalent to that of the corresponding multi-step methods; their use is more convenient, owing to being self-starting. Compared with existing second-order methods, the proposed ones, especially the linear four-step method and its alternative single-step one, show higher accuracy for a given degree of algorithmic dissipation. The accuracy advantage and other properties of the newly developed schemes are demonstrated by several illustrative examples.

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Development of an explicit time integration algorithm based on optimal integration parameter updating

Fu,

Li,

2023

Earthq Engng Struct Dyn

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Integration algorithm is an important mean to solve the discrete time equations of structural dynamics in earthquake engineering. In this paper, a new model‐based explicit integration algorithm, featured by optimization‐based integration parameter updating, is developed for a more accurate and efficient solution of structural dynamic problems. The new integration algorithm is designed to yield minimum error and controllable numerical dispersion under the premise of stability by defining objective functions and constraints. Numerical properties of the new integration algorithm are investigated in details using the amplification matrix method for a linear elastic single degree‐of‐freedom system. Meanwhile, representative numerical examples and complex structure examples are analyzed and compared with other representative algorithms. As a result, the proposed algorithm yields comparable numerical characteristics with other methods, but exhibits pronounced superiority in controllable algorithmic dissipation, higher precision, and better efficiency. Therefore, the new integration algorithm possesses extensive application prospect in solving complicated linear and nonlinear structural dynamic problems.

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A new family of two-stage explicit time integration methods with dissipation control capability for structural dynamics

Cited by 33 publications

References 36 publications

A critical assessment of two-stage composite time integration schemes with a unified set of time approximations

A critical assessment of two-stage composite time integration schemes with a unified set of time approximations

Improved second-order unconditionally stable schemes of linear multi-step and equivalent single-step integration methods

Development of an explicit time integration algorithm based on optimal integration parameter updating

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