A principle of virtual power-based beam model reveals discontinuities in elastic support as potential sources of stress peaks in tramway rails

Abstract

This paper addresses the question to which extent the stiffness of an elastic foundation in general, and of a discontinuity occurring in the foundation in particular, affects the stresses to which a beam resting on such a foundation is exposed to. This is particularly relevant for tramway rails, where foundation discontinuities may be generated in the course of maintenance works. In the presented work, the underlying mathematical framework was derived based on the principle of virtual power, using a suitable virtual velocity field and a foundation-related traction force vector as input quantities. The resulting mathematical expressions for the virtual powers performed by the internal and external forces were approximated based on Finite Element discretizations, and eventually solved correspondingly, in the format of sequential Finite Element analyses. Numerical studies, performed on a tramway rail-shaped beam, have confirmed that foundation discontinuities indeed induce substantial increases in the stress tensor components, when moving from regions of a high-stiffness foundation to regions of a low-stiffness foundation; as it may occur if specific sections of the tramway network get renewed.

Data-driven analytical mechanics of aging viscoelastic shotcrete tunnel shells

“…The principle of virtual power is particularly suitable tool for deriving theories for structural components, such as beams, arches, or plates [13,16,34,40]. In this context, the virtual velocity field governing the equilibrium conditions is further restricted; and this yields differential equations of lower dimensions than those of ( 5) and (6).…”