Analysis for Elastic Strips Under Concentrated Loads

Abstract

The problem of a general anisotropic elastic strip under concentrated loads is analyzed. By using the Stroh formalism for anisotropic elasticity in conjunction with the Fourier transform, the elastic fields for a concentrated load are expressed as integrals which can be evaluated by residue theory to give eigenfunction expansions. The eigenfunction expansions can be divided into two parts. The first part arises from the singularities at the origin of the integrands of the Fourier integrals and corresponds to classical beam bending and stretching solutions. The second part consists of the other terms in the eigenfunction expansions and corresponds to exponentially decaying self-equilibrium solutions. The solution for a concentrated load is used to investigate the problems of a pair of collinear compressive loads and three-point bending.