Efficiency of simulation-based SFE structural analysis: Modeling and solution issues

Many engineering systems have parameters that demonstrate significant random variation in space or in time. The stochastic finite element method. (SFEM), which incorporates the uncertainty of system parameters into the finite element formulation, has become a powerful tool in analyzing complex engineering problems. The commonly used lower-order perturbation-based SFE analysis is often limited to linear or mildly nonlinear problems with small variability. Simulation-based SFE analysis is more flexible, and is applicable to virtually all types of problems. However, the efficiency of simulation-based SFE analysis is a research issue due to the computational cost of the repetitive FE analyses involved in the simulation.; The need to properly model system uncertainties gives rise to many of the numerical difficulties in a simulation-based SFE analysis and such models must be developed to achieve computational efficiency. This study addresses the effect of uncertainties on the modeling and solution of stochastic problems from a different perspective by identifying characteristics introduced by the uncertainties that can be utilized to improve the efficiency of the SFE structural analysis. Stochastic ensemble averaging was found to have a positive impact on the efficiency of the calculation of lower-order response statistics by enabling the use of coarser mesh and/or larger time steps in SFE analyses. The process of selecting proper initializations for random eigenvalue analyses can be made more efficient by reordering random samples and using the solution of the closest neighboring sample as the initialization. A computationally efficient method based on a n a sample tree data structure was developed to implement this optimal initialization strategy. These methods were applied in stability and modal analyses of random beam and frame structures. While uncertainty often introduces numerical complexity, it also has features that, when considered appropriately, can alleviate the numerical difficulty and improve the overall efficiency of a stochastic analysis.