ISSN:
0029-5981
Keywords:
structural dynamics
;
time finite elements
;
Hermitian shape functions
;
unconditionally stable algorithms
;
higher-order accurate algorithms
;
time-step integration
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
In this paper, single step time finite elements using the cubic Hermitian shape functions to interpolate the solution over a time interval are considered. The second-order differential equations are manipulated directly. Both the effects of modal damping and external excitation are considered. The accuracy of the solutions at the end of the time interval and the interpolated solutions within the time interval is investigated. The weighted residual approach is adopted to derive the time-integration algorithms. Instead of specifying the weighting functions, the weighting parameters are used to control the characteristics of the time finite elements. The weighting parameters are chosen to eliminate the higher-order truncation error terms or to enforce the asymptotic annihilation condition. A one-parameter family of third-order accurate asymptotically annihilating algorithms and another one-parameter family of fourth-order accurate non-dissipative algorithms are presented. The ranges of the weighting parameters for unconditionally stable algorithms are given. It is found that one of the members in each family corresponds to the Padé approximants of the exponential function in solving the first-order differential equations. Some of the existing unconditionally stable higher-order accurate algorithms are re-derived by the present unified approach.
Additional Material:
7 Ill.
Type of Medium:
Electronic Resource
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