A response surface approach for the static analysis of stochastic structures with geometrical nonlinearities

A response surface approach for the finite element analysis of uncertain structures undergoing large displacements is
presented. This method is based on the use of ad hoc response surface functions built up by ratios of polynomials. As
opposite to commonly used linear or quadratic polynomials, such functions are insensitive to the sampling point positions.
Once the response surface form is defined, response statistics can be approximated by analytical relationships or
statistical simulation taking full advantage of sensitivity analysis. Numerical investigations demonstrated that a remarkable
accuracy is achieved in the evaluation of both statistical moments and probability density functions of the response.