For the development of a new family of higher-order time integration algorithms for structural dynamics problems, the displacement vector is approximated over a typical time interval using the pth-degree Hermite interpolation functions in time. The residual vector is defined by substituting the approximated displacement vector into the equation of structural dynamics. The modified weighted-residual method is applied to the residual vector. The weight parameters are used to restate the integral forms of the weighted-residual statements in algebraic forms, and then, these parameters are optimized by using the single-degree-of-freedom problem and its exact solution to achieve improved accuracy and unconditional stability. As a result of the pth-degree Hermite approximation of the displacement vector, pth-order (for dissipative cases) and (p + 1)st-order (for the nondissipative case) accurate algorithms with dissipation control capabilities are obtained. Numerical examples are used to illustrate performances of the newly developed algorithms.
Effective Higher-Order Time Integration Algorithms for the Analysis of Linear Structural Dynamics
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 17, 2017; final manuscript received May 21, 2017; published online June 7, 2017. Editor: Yonggang Huang.
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Kim, W., and Reddy, J. N. (June 7, 2017). "Effective Higher-Order Time Integration Algorithms for the Analysis of Linear Structural Dynamics." ASME. J. Appl. Mech. July 2017; 84(7): 071009. https://doi.org/10.1115/1.4036822
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