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.

中文翻译：

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基于虚拟功率的梁模型的原理揭示了作为有轨电车轨道应力峰值的潜在来源的弹性支撑的不连续性

本文解决了弹性基础的刚度，特别是基础中发生的不连续性，在多大程度上影响搁置在这种基础上的梁所承受的应力的问题。这对于电车轨道尤其重要，因为在维护工作过程中可能会产生基础不连续性。在所呈现的工作中，基于虚拟功率原理，使用合适的虚拟速度场和与基础相关的牵引力矢量作为输入量，推导出基本数学框架。由内力和外力执行的虚拟功率的所得数学表达式基于有限元离散化进行近似，并最终相应地求解，以连续有限元分析的形式。在有轨电车轨道形梁上进行的数值研究证实，当从高刚度地基区域移动到低刚度地基区域时，地基不连续性确实会导致应力张量分量显着增加。因为如果有轨电车网络的特定部分得到更新，可能会发生这种情况。