Determination of influence lines for structural responses with uncertainties in properties of the structure

Classical ways of determination of influence lines for structural responses are often inefficient due to high computational cost, especially if properties of the structure are uncertain. The combination of Muller-Breslau principle and the finite element analysis can resolve this problem. In this study, formulations for new finite elements tailored for use in determination of influence lines for structural responses are proposed. They are then used in the problem of uncertainty propagation to obtain uncertain ordinates of the influence lines. The expressions for the element stiffness matrix and equivalent nodal load vector are derived consistently from the proposed displacement field of the element. The proposed finite elements can be adapted directly in existing finite element packages since they do not need remeshing. Studied examples show the correctness and the efficiency of the proposed method. From the results of uncertainty propagation problem, large uncertainties in the ordinates of influence lines for structural responses due to small uncertainties in structural properties should be aware of.