Fundamental boundary matrices for 36 elementary boundary value problems of finite beam deflection on elastic foundation

Abstract

<abstract><p>We consider the boundary value problem of finite beam deflection on elastic foundation with two point boundary conditions of the form $ u^{(p)}(-l) = u^{(q)}(-l) = u^{(r)}(l) = u^{(s)}(l) = 0 $, $ p < q $, $ r < s $, which we call elementary. We explicitly compute the fundamental boundary matrices corresponding to 7 special elementary boundary conditions called the dwarfs, and show that the fundamental boundary matrices for the whole 36 elementary boundary conditions can be derived from those for the seven dwarfs.</p></abstract>