Acceleration of uncertainty propagation through Lagrange multipliers in partitioned stochastic method

A partitioned stochastic method (PSM) is proposed for the solution of static structural mechanics problems with uncertainties, whose solution vectors are the displacements for each partition and Lagrange multipliers along with the partition interfaces. The proposed partitioned stochastic method employs three stochastic basis selection steps: an arbitrary initial choice of displacement random bases, a set of conjugate bases for the Lagrange multipliers, and finally modification of the displacement bases affected by those of the Lagrange multipliers. The present PSM thus propagates the uncertainties instantly across partitioned substructures, resulting in an improved rate of convergence. Numerical experiments illustrate the proposed PSM outperforms a conventional partitioned solution method for structural mechanics problems.