New results in finite element method for stochastic structures

Abstract

New approaches in the finite element method for stochastic structures are proposed. The FEM based on exact inverse of stiffness matrix is first proposed for bar extension problems with stochastic stiffness. The method is exemplified by the direct exact inverse of stiffness matrix for the deformation of the bar under extension. The second new FEM is based on the diagonalization of the element stiffness matrix and the inverse of the global stiffness matrix. The method is proposed for beam bending problems with stochastic stiffness. The third new FEM is based on the element-level flexibility and its idea is general applicable. The new methods avoid the error due to truncating the expansion series of random stiffness matrix, which appears in conventional finite element methods for stochastic structures based on either series expansion or perturbation technique. Examples of a stochastic bar under tension and stochastic beams under uniform pressure are analyzed. Comparison of the new finite element solution by new approaches and conventional finite element solution by the first-order perturbation is performed. Numerical results illustrates the superiority of the new proposed methods over the conventional FEM for stochastic structures.