Finite element interval analysis of external loads identified by displacement input with uncertainty Original Research Article

A finite element formulation is proposed for the interval estimation of the nodal forces identified by displacement input with uncertainty. The stiffness matrix of the structural system in problem of linear, elastic body under static loading is assumed to be known and determinate. This assumption enables us to derive the governing equation of the nodal forces to be identified with respect to the nominal displacement input from the stiffness equation based on the Moore-Penrose generalized inverse solution of the unknown remnant displacements. We assume that the uncertain errors involved in the nodal displacements obtained somehow by measurement and used as input are confined in a convex hull. The effect of the uncertainty on the identified nodal forces is evaluated by the sensitivity analysis of the forces with respect to the uncertain displacements. How to estimate the scatter of the identified nodal forces corresponding to the uncertain displacements confined in the convex hull is devised by means of the Lagrange multiplier method. The validity of the proposed method for identification and interval estimation of the nodal forces is shown by the numerical example of an elastic square plate in the plane stress state and subject to in-plane loading.