On bending and stability of beams and plates laying on a continuous nonlocally elastic foundation

Abstract

When designing beams and plates laying on a continuous elastic foundation, the simplest foundation model proposed by Winkler is normally used. This hypothesis was frequently criticized with good reason, for it does not consider involvement in the work of those areas of the foundation in the vicinity of the concentrated reaction point. In order to refine Winkler’s hypothesis, numerous authors have proposed other models that enable the drawbacks of Winkler’s model to be smoothed out to different degrees. In recent years, a different approach to solving the same problems is considered when the foundation is regarded as nonlocally elastic. Here, the effect of nonlocality of the foundation on the deformed state and the stability of beams and plates laying on a continuous elastic foundation is analyzed.