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Comparisons of structure-dependent explicit methods for time integration. (English) Zbl 1359.74469

Summary: The Chang explicit method (CEM) [the author, “Explicit pseudodynamic algorithm with unconditional stability”, J. Eng. Mech. 128, No. 9, 935–947 (2002; doi:10.1061/(asce)0733-9399(2002)128:9(935)); “Improved explicit method for structural dynamics”, ibid. 133, No. 7, 748–760 (2007; doi:10.1061/(asce)0733-9399(2007)133:7(748))] and the CR explicit method (CRM) [C. Chen and J. M. Ricles, “Development of direct integration algorithms for structural dynamics using discrete control theory”, ibid. 134, No. 8, 676–683 (2008; doi:10.1061/(asce)0733-9399(2008)134:8(676))] are two structure-dependent explicit methods that have been successfully developed for structural dynamics. The most important property of both integration method.s is that they involve no nonlinear iterations in addition to unconditional stability and second-order accuracy. Thus, they are very computationally efficient for solving inertial problems, where the total response is dominated by low frequency modes. However, an unusual overshooting behavior for CR explicit method is identified herein and thus its practical applications might be largely limited although its velocity computing for each time step is much easier than for the CEM.

MSC:

74S20 Finite difference methods applied to problems in solid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
74H55 Stability of dynamical problems in solid mechanics
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[1] DOI: 10.1061/(ASCE)0733-9399(2002)128:9(935) · doi:10.1061/(ASCE)0733-9399(2002)128:9(935)
[2] DOI: 10.1061/(ASCE)0733-9399(2007)133:7(748) · doi:10.1061/(ASCE)0733-9399(2007)133:7(748)
[3] DOI: 10.1061/(ASCE)0733-9399(2008)134:8(676) · doi:10.1061/(ASCE)0733-9399(2008)134:8(676)
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