Chaos–Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos–Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos–Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos–Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering.