1. Stochastic perturbation finite elements
- Author
-
Zhang Yimin, Suhuan Chen, Tieqiang Liu, and Qiaoling Liu
- Subjects
Mechanical Engineering ,Numerical analysis ,MathematicsofComputing_NUMERICALANALYSIS ,Perturbation (astronomy) ,Finite element method ,Poincaré–Lindstedt method ,Computer Science Applications ,symbols.namesake ,Modeling and Simulation ,Kronecker delta ,Calculus ,symbols ,Applied mathematics ,General Materials Science ,Random variable ,Perturbation method ,Matrix calculus ,Civil and Structural Engineering ,Mathematics - Abstract
This paper extends the stochastic perturbation method to vector-valued and matrix-valued functions. The numerical method for the response and reliability of uncertain structures is formulated using matrix calculus, Kronecker algebra and perturbation theory. Random variables and system derivatives are conveniently arranged into two-dimensional matrices and generalized mathematical formulae are obtained. The results derived are easily amenable to computational procedures.
- Published
- 1996