A new computational scheme for structural static stochastic analysis based on Karhunen–Loève expansion and modified perturbation stochastic finite element method.

Shao, Zhanjun; Li, Xiumei; Xiang, Ping

Due to uncertainties, deterministic analysis cannot sufficiently reflect the performance of structures. Stochastic analysis can consider the influence of multiple uncertainties factors and improve the confidence of the analysis results. A new stochastic computational scheme, which has the features of Karhunen–Loève (K–L) expansion and modified perturbation stochastic finite element method (MPSFEM), is proposed for the structures with low-level uncertainties, called KL-MPSM for short. The material parameters are regarded as random fields and discretized by K–L expansion. The random variables obtained are substituted into MPSFEM to get the estimates of the first two order moments (mean and variance) of the structural responses. JC method is introduced to compute the reliability indexes and structures failure probability by utilizing the second-order estimates. A deep beam and a plane frame structure are presented as numerical examples to demonstrate the feasibility of KL-MPSM, and some random filed properties are studied. The results show that KL-MPSM has good accuracy, efficiency, and advantages in programming. Therefore, KL-MPSM is well suited for static stochastic analysis of structures with low-level uncertainties.

STOCHASTIC analysis; FINITE element method; POLYNOMIAL chaos; RANDOM fields; RANDOM variables; STRUCTURAL frames

Computational Mechanics, 2023, Vol 71, Issue 5, p917

0178-7675

Academic Journal

10.1007/s00466-022-02259-7