Palmeri, A. and Cicirello, A. (2011) Physically-Based Dirac’s Delta Functions in the Static Analysis of Multi-Cracked Euler-Bernoulli and Timoshenko Beams. International Journal of Solids and Structures, 48, 2184-2195.
http://dx.doi.org/10.1016/j.ijsolstr.2011.03.024

has been cited by the following article:

• TITLE: On Applications of Generalized Functions in the Discontinuous Beam Bending Differential Equations

  AUTHORS: Dimplekumar Chalishajar, Austin States, Brad Lipscomb

  KEYWORDS: Mechanics of Solids, Discontinuities in a Beam Bending Differential Equations, Generalized Functions, Jump Discontinuities

  JOURNAL NAME: Applied Mathematics, Vol.7 No.16, October 25, 2016

  ABSTRACT: This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.