Beam-like and frame structures with singularities: review and new advances

The causes of discontinuities and singularities occurring along structural elements are very frequent in a number of engineering problems. Dedicated approaches alternative to classical numerical procedures are of great importance particularly when leading to exact explicit closed-form solutions. In this paper a review of a recent distributional approach of beam-like and frame structures undergoing different types of singularities is presented. The basic idea, combined with suitable integration procedures, is modelling the singularities as concentrated stiffness reductions by means of generalised functions such as Dirac’s deltas and Heaviside distributions. Besides, recent new advances towards explicit solutions regarding, among others, tensile buckling of damaged beams, formulation of dynamic and stability matrices of damaged frames are presented and discussed.