Stochastic spline Ritz method based on stochastic variational principle

In the previous versions of stochastic variational principles, the virtual displacements are often assumed to vary arbitrarily and independent of any uncertainties. This paper investigates the stochasticity of the virtual displacements via the relationship among virtual displacements, admissible displacements and real displacements. A stochastic variational principle is proposed so that the stochastic properties of the random parameters involved can be incorporated into the functional of the total potential energy. Cubic B-spline functions are employed as the trial functions to reduce the number of degrees of freedom. Then, the stochastic spline Ritz method is developed based on the stochastic variational principle via the second-order perturbation techniques. The spline Ritz method is applied to the structures consisting of elastic beams and plates by a local average of the homogeneous random field. Numerical examples are given to illustrate the efficiency and accuracy of the presented method.