Research On Structural Reliability By Nonlinear Stochastic Finite Element Method

Some theoretical problems involved in nonlinear stochastic finiteelement reliability analysis processes are studied in this paper, and acorresponding analysis program is developed. Detailed works done in thispaper are summarized as follows:1. Uniformly distributed point is suggested as a tool to improve theefficiency of Monte Carlo simulation. Many kinds of new simulation methods,such as Importance Sampling Method, Directional Importance SamplingMethod, Adaptive Importance Sampling Method, Adaptive DirectionalImportance Sampling Method, are rearched in the thesis and correspondinganalysis program is developed.2. Many kinds of approximate methods calculating fail probability, suchas First Order Reliability Method, Second Order Reliability Method,Response Surface Method, Moment Method, are rearched in the thesis andcorresponding analysis program is developed.3. Many kinds of approximate and precise methods calculating systemfail probability, such as First Order Mutinormal Method, SequentialConditioned Importance Sampling Method, Narrow Bounds Method,Directional Importanc Sampling Method, β -Sphere Importance SamplingMethod, are rearched in the thesis and corresponding analysis program isdeveloped.4. Sensitivity coefficiences of single limit condition fail probability ormuti-limit condition system fail probability are defined, their calculatingformula are also deduce and corresponding analysis program is developed.BySensitivity coefficiences of single limit condition fail probability, major andminor random factor can be distinguished. By muti-limit condition system failprobability, important and unimportant failure mode can be judged.5. Elast-plastic and geometric nonlinear stochastic finite element method,which random field beams may be in structure, are studied deeply. The mehodhow to get stochastic finite element response gradients are demonstrated indetail and corresponding analysis program is developed..6. A bi-modal distribution, with two peaks, consisting of a weighted sumof two normal distributions to describe such vehicle load is developed. Afiltered composite renewal process are developed to describe the dense andnormal traffic states of the vehicle load stochastic processes consisting ofboth overloaded trucks and normal vehicles, respectively. Finally, the 0.95fractiles of the maximum distributions of both overloaded trucks and normalvehicles in the 20-year residual life of the national highway bridges areproposed to be the evaluation load.Based on the theoretical studies done in this thesis, an analysis programSYSREL is developed.