Nonlinear Stochastic Finite Elemet Method

There are a certain amount of uncertainties which affect structural behaviors in design and application of engineering structures. The research on the contribution of stochastic factors to structure behavior in structure analysis has become one of the hotspots in modern computational mechanics. The nonlinear stochastic finite element method (NSFEM) is the method to solve nonlinear problems, just as its name implies. Nowadays this method, because of its short development history, is only limited to simple trusses and can't be used in practices. The NSFEM's general method to deal with stochastic factors adopts perturbation technique, which, as it has been seen, becomes more difficult while taking the partial differential of stiffness matrix to stochastic factors and difficult to be implemented. An exploratory research aiming at this nodus will be presented in this thesis. Firstly, based on the perturbation technique of stochastic finite element method, the general recursion expression of nonlinear stochastic finite element analysis is derived in this thesis by using perturbation technique to deal with the stochastic factors of the nonlinear problem. An approximate method to deal with the random loads applied on structures is developed, in which the random loads are separated into two parts: one is determinate and another is perturbation, and to solve the material-nonlinear problems by use of the conventional nonlinear finite element method. Another method which adopts perturbation technique and Monte-Carlo method is introduced. Then a computer program for the approximate method is designed. Some numerical examples are presented by using the program to show the application of the procedure lastly.