For the development of a new family of implicit higher-order time integration algorithms, mixed formulations that include three time-dependent variables (i.e., the displacement, velocity, and acceleration vectors) are developed. Equal degree Lagrange type interpolation functions in time are used to approximate the dependent variables in the mixed formulations, and the time finite element method and the modified weighted-residual method are applied to the velocity–displacement and velocity–acceleration relations of the mixed formulations. Weight parameters are introduced and optimized to achieve preferable attributes of the time integration algorithms. Specific problems of structural dynamics are used in the numerical examples to discuss some fundamental limitations of the well-known second-order accurate algorithms as well as to demonstrate advantages of using the developed higher-order algorithms.
A New Family of Higher-Order Time Integration Algorithms for the Analysis of 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). "A New Family of Higher-Order Time Integration Algorithms for the Analysis of Structural Dynamics." ASME. J. Appl. Mech. July 2017; 84(7): 071008. https://doi.org/10.1115/1.4036821
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