2011
DOI: 10.1007/s11831-011-9060-y
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An Overview and Recent Advances in Vector and Scalar Formalisms: Space/Time Discretizations in Computational Dynamics—A Unified Approach

Abstract: An overview of recent advances in computational dynamics for modeling and simulation is described. The targeted objectives are towards a wide variety of science and engineering applications in particle and continuum dynamics of structures and materials which fall in this class. Starting with the supposition that in the beginning, the well known Newton's law of motion for N-body systems is given, and is a statement of the principle of balance of linear momentum, subsequently, using this as a landmark, firstly, … Show more

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Cited by 44 publications
(24 citation statements)
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References 83 publications
(253 reference statements)
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“…Based on the above summary here and more developments described elsewhere [26,27], we can see that a time integration algorithm suitable for various complex nonlinear dynamic structural systems is lacking, which should inherit the desirable properties including unconditional stability, at least second-order accuracy, ease of use (no additional parameter), ease of implementation, and high computational efficiency. Some delightful latest achievements are indicating that the conception of composition can be the outlet [28][29][30].…”
Section: Introductionmentioning
confidence: 92%
“…Based on the above summary here and more developments described elsewhere [26,27], we can see that a time integration algorithm suitable for various complex nonlinear dynamic structural systems is lacking, which should inherit the desirable properties including unconditional stability, at least second-order accuracy, ease of use (no additional parameter), ease of implementation, and high computational efficiency. Some delightful latest achievements are indicating that the conception of composition can be the outlet [28][29][30].…”
Section: Introductionmentioning
confidence: 92%
“…There are many widely used TIMs, such as the Houbolt method, 1 the Newmark method, 2 the Wilson-method, 3 the HHT-method, 4 the WBZ-method, 5 the generalized-method, 6 and other methods mentioned in the overview paper. 7 As the pursuit of advanced methods is endless, many novel TIMs emerged for different purposes after 2000. For example, composite methods [8][9][10] and BDF (Backward Differentiation Formula)-like methods 11 were shown to be stable and effective for general nonlinear systems.…”
Section: Introductionmentioning
confidence: 99%
“…Hence, more advanced numerical methods have been developed to efficiently and accurately predict the dynamic response of the structure. In the past, multiple implicit [1][2][3][4][5][6][7] and explicit [8][9][10][11][12] integration algorithms have been developed, whose relationship [13] and design methods are comprehensively analyzed [14][15][16]. The explicit method has high computational efficiency, while the implicit method has higher stable.…”
Section: Introductionmentioning
confidence: 99%