Stability of heterogeneous beams with three supports through Green functions

Abstract

The present paper is devoted to the issue how the critical load of some heterogeneous beams with three supports can be determined by using Green functions. The stability problems of these beams are equivalent to three-point boundary value problems, paired with homogeneous boundary conditions. If the Green functions of these boundary value problems are known, the eigenvalue problems that provide the critical load can be transformed into eigenvalue problems governed by homogeneous Fredholm integral equations. The later eigenvalue problems can be reduced to algebraic eigenvalue problems which then can be solved numerically with effective algorithms.