The stochastic finite element method was developed based on second moment method for the probabilistic analysis of laminated composite structures in which physical properties have uncertainties and variability. The material properties, fiber angles, laminate thickness, and curvatures were modeled as random parameters. The random thickness and fiber angles affect the strain-displacement relations and principal material directions. This randomness was considered in the formulation to obtain accurate statistical responses.
A procedure of system reliability analysis using the stochastic finite element method was also presented. Composite structure was considered as a random structure to involve the effect of uncertainties of structure itself on reliability. Composite laminates were assumed to be multicomponent series system, and the correlations between possible failure modes of different components were considered to obtain consistent probability of system failure. The system reliability is obtained by bi-modal bounds of probability of system failure.
The methods were verified through comparison of the results with those obtained by the Monte Carlo simulations for two example problems. Statistics of structural responses were derived very accurately. Narrow bounds of failure probability were obtained with acceptable accuracy. The developed methods can be applied to practical design and analysis of composite structures. A design procedure of bolted joint in composite structures under the requirement of reliability was exemplified. The developed methods are very efficient and accurate enough to be applied to engineering problems, and can assess the risk of structures quantitatively and logically.
