New direct probabilistic approach for static responses of structures with uncertainties

Abstract

A new direct probabilistic approach (DPA) is presented for calculating the first- and second-order moments of the structural static response with random uncertainties. The approach treats both stiffness and load as uncertain factors. The proposed approach can reduce considerably the storage and computational complexities required to large structural systems. For practical engineering problems with random uncertainties, the prime problem is to avoid disadvantages of large calculation and much wall-clock time. In this study, the parallel arithmetic of the DPA will be presented, which can be used in large-scale computations in practical engineering to avoid much wall-clock time. It can also be seen that the parallel arithmetic is superior to traditional serial algorithm. The present approach is illustrated by two numerical examples that include the structure of 14-bar truss and three-beam structure and in comparison with the expanded first-order second moment method and Monte-Carlo method.

Keywords:

• random uncertainty
• structural static response
• moment equations
• direct probabilistic approach
• parallel arithmetic

2000 AMS Subject Classifications :

• 15A51
• 68Q10
• 68W10

Acknowledgements

The project is supported by the National Natural Science Foundation of China (Grant nos. 90816024, 10872017, and 10876100), the 111 Project (Grant No. B07009) and the Innovation Foundation of BUAA for PhD Graduates.