NWU 2013 : Advances in Computational Mechanics with Emphasis on Fracture and

The reciprocity theorem is a fundamental theorem of the Theory of Elasticity (Betti 1872, Rayleigh 1873). The theorem connects the body forces, the surface tractions and the displacements of two elastodynamic states in a domain of an elastic body, by a volume integral and a surface integral. In this talk it is shown that the reciprocity theorem of elastodynamics can be used to solve actual problems. We consider the example of wave motion generated in a half-space by a time-harmonic force. This fundamental problem is known as Lamb’s problem (1904). It is shown that the radiated surface waves, which Lamb obtained by a complicated Fourier transform method, can be obtained from a “back of an envelope” calculation using the elastodynamic reciprocity theorem [1].