참고문헌
- Alamatian, J. (2013), "New implicit higher order time integration for dynamic analysis", Struct. Eng. Mech., 48(5), 711-736. https://doi.org/10.12989/sem.2013.48.5.711.
- Bathe, K.J. (2007), "Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme", Comput. Struct., 85(7-8), 437-445. https://doi.org/10.1016/j.compstruc.2006.09.004.
- Bathe, K. (1996), Finite Element Procedures, Prentice-Hall Englewood Cliffs, NJ.
- Carrer, J.A.M. and Mansur, W.J. (2006), "Solution of the two-dimensional scalar wave equation by the time-domain boundary element method: lagrange truncation strategy in time integration", Struct. Eng. Mech., 23(3), 263-278. https://doi.org/10.12989/sem.2006.23.3.263.
- Chang, S.Y. (2010), "A new family of explicit methods for linear structural dynamics", Comput. Struct., 88(11-12), 755-772. https://doi.org/10.1016/j.compstruc.2010.03.002.
- Chang, S.Y. (2014), "Family of structure-dependent explicit methods for structural dynamics", J. Eng. Mech., 140(6), 06014005. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000748.
- Chang, S.Y. (2014), "Numerical dissipation for explicit, unconditionally stable time integration methods", Earthq. Struct., 7(2), 159-178. https://doi.org/10.12989/eas.2014.7.2.159.
- Fung, T. (2003), "Numerical dissipation in time-step integration algorithms for structural dynamic analysis", Prog. Struct. Eng. Mater., 5(3), 167-180. https://doi.org/10.1002/pse.149.
- Gopalakrishnan, S., Ruzzene, M. and Hanagud, S. (2011), Spectral Finite Element Method, Springer
- Guddati, M.N. and Yue, B. (2004), "Modified integration rules for reducing dispersion error in finite element methods", Comput. Meth. Appl. Mech. Eng., 193(3-5), 275-287. https://doi.org/10.1016/j.cma.2003.09.010.
- Hilber, H.M. and Hughes, T.J. (1978), "Collocation, dissipation and [overshoot] for time integration schemes in structural dynamics", Earthq. Eng. Struct. Dyn., 6(1), 99-117. https://doi.org/10.1002/eqe.4290060111.
- Kuhl, D. and Crisfield, M. (1999), "Energy-conserving and decaying algorithms in non-linear structural dynamics", Int. J. Numer. Meth. Eng., 45(5), 569-599. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C569::AID-NME595%3E3.0.CO;2-A.
- Malakiyeh, M.M., Shojaee, S. and Bathe, K.J. (2019), "The Bathe time integration method revisited for prescribing desired numerical dissipation", Comput. Struct., 212, 289-298. https://doi.org/10.1016/j.compstruc.2018.10.008.
- Mullen, R. and Belytschko, T. (1982), "Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation", Int. J. Numer. Meth. Eng., 18(1), 11-29. https://doi.org/10.1002/nme.1620180103.
- Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., 85(3), 67-94. https://doi.org/10.1061/JMCEA3.0000098
- Noh, G. and Bathe, K.J. (2019), "The Bathe time integration method with controllable spectral radius: The ρ∞-Bathe method", Comput. Struct., 212, 299-310. https://doi.org/10.1016/j.compstruc.2018.11.001.
- Noh, G., Ham, S. and Bathe, K.J. (2013), "Performance of an implicit time integration scheme in the analysis of wave propagations", Comput. Struct., 123, 93-105. https://doi.org/10.1016/j.compstruc.2013.02.006.
- Pezeshk, S. and Camp, C. (1995), "An explicit time-integration method for damped structural systems", Struct. Eng. Mech., 3(2), 145-162. https://doi.org/10.12989/sem.1995.3.2.145.
- Rezaiee-Pajand, M., Esfehani, S. and Karimi-Rad, M. (2018), "Highly accurate family of time integration method", Struct. Eng. Mech., 67(6), 603-616. https://doi.org/10.12989/sem.2018.67.6.603.
- Rogers, D. (2001), An Introduction to NURBS: With Historical Perspective. Morgan Kaufmann, San Francisco, CA.
- Rostami, S. and Shojaee, S. (2017), "Alpha-modification of cubic B-spline direct time integration method", Int. J. Struct. Stab. Dyn., 17(10), 1750118. https://doi.org/10.1142/S0219455417501188.
- Rostami, S. and Shojaee, S. (2018), "A family of cubic B-spline direct integration algorithms with controllable numerical dissipation and dispersion for structural dynamics", Iran. J. Sci. Technol. Tran. Civil Eng., 42(1), 17-32. https://doi.org/10.1007/s40996-017-0083-y.
- Rostami, S., Shojaee, S. and Moeinadini, A. (2012), "A parabolic acceleration time integration method for structural dynamics using quartic B-spline functions", Appl. Math. Model., 36(11), 5162-5182. https://doi.org/10.1016/j.apm.2011.11.047.
- Rostami, S., Shojaee, S. and Saffari, H. (2013), "An explicit time integration method for structural dynamics using cubic B-spline polynomial functions", Scientia Iranica, 20(1), 23-33. https://doi.org/10.1016/j.scient.2012.12.003.
- Shojaee, S., Rostami, S. and Abbasi, A. (2015), "An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method", Comput. Struct., 153, 98-111. https://doi.org/10.1016/j.compstruc.2015.02.030.
- Shojaee, S., Rostami, S. and Moeinadini, A. (2011), "The numerical solution of dynamic response of SDOF systems using cubic B-spline polynomial functions", Struct. Eng. Mech., 38(2), 211-229. https://doi.org/10.12989/sem.2011.38.2.211.
- Wang, Y.C., Murti, V. and Valliappan, S. (1992), "Assessment of the accuracy of the Newmark method in transient analysis of wave propagation problems", Earthq. Eng. Struct. Dyn., 21(11), 987-1004. https://doi.org/10.1002/eqe.4290211104.
- Yasamani, K. and Mohammadzadeh, S. (2017), "A novel two sub-stepping implicit time integration algorithm for structural dynamics", Earthq. Struct., 13(3), 279-288. https://doi.org/10.12989/eas.2017.13.3.279.