Precise integration method without inverse matrix calculation
for structural dynamic equations
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Wang Mengfu (ÍôÃθ¦)1
and F. T. K. Au2
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1. Department of Civil Engineering, Hunan University, China
2. Department of Civil Engineering, The University of Hong Kong, China
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Abstract: The precise
integration method proposed for linear time-invariant homogeneous dynamic
systems can provide accurate numerical results that approach an exact solution
at integration points. However, difficulties arise when the algorithm is used
for non-homogeneous dynamic systems due to the inverse matrix calculation
required. In this paper, the structural dynamic equalibrium equations are
converted into a special form, the inverse matrix calculation is replaced by the
Crout decomposition method to solve the dynamic equilibrium equations, and the
precise integration method without the inverse matrix calculation is obtained.
The new algorithm enhances the present precise integration method by improving
both the computational accuracy and efficiency. Two numerical examples are given
to demonstrate the validity and efficiency of the proposed algorithm.
Keywords:structural
dynamics; numerical integration; inverse matrix calculation; matrix exponential
function; Crout decomposed method
