TY - JOUR
T1 - Effective Higher-Order Time Integration Algorithms for the Analysis of Linear Structural Dynamics
PB - ASME
AU - Kim, Wooram
AU - Reddy, J. N.
Y1 - 2017/06/07
N1 - 10.1115/1.4036822
JO - Journal of Applied Mechanics
SP - 071009
EP - 071009-13
VL - 84
IS - 7
N2 - 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 (pā+ā1)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.
SN - 0021-8936
M3 - doi: 10.1115/1.4036822
UR - http://dx.doi.org/10.1115/1.4036822
ER -