Analysis of moving loads using force-based finite elements

An analysis method for moving loads computes the internal force history in a structural member at the integration points of force-based finite elements as opposed to the end forces of a refined displacement-based finite element mesh. The force-based formulation satisfies strong equilibrium of internal section forces with the element end forces and the moving load. This is in contrast with displacement-based finite element formulations that violate equilibrium between the section forces and the equivalent end forces computed for the moving load. A new approach to numerical quadrature in force-based elements allows the specification of integration point locations where the section demand is critical while ensuring a sufficient level of integration accuracy over the element domain. Influence lines computed by numerical integration in force-based elements converge to the exact solution and accurate results are obtained for practical applications in structural engineering through the new low-order integration approach. The proposed methodology for moving load analysis has been incorporated in automated software to load rate a large number of bridges efficiently.