A complete set of corollaries of the reciprocal theorems in elasticit

This work presents a complete set of corollaries derived from the classical reciprocal theorems in the linear theory of elasticity. It is shown that the strain energy required to produce a given effect (reactive generalised force or displacement) at a certain position A of a linearly elastic body or structure by means of the application of the corresponding dual action (imposed generalised displacement or force, respectively) at another position B, attains its minimum when A coincides with B. This fact turns out to be a simple and general property of any linearly elastic model and from a qualitative point of view it can be related to the well-known local perturbation principle of Boussinesq. The assertions made can prove themselves useful in the interpretation of terms arising in several engineering problems, like boundary elements analyses or structural monitoring procedures. Copyright 0 1996 Elsevier Science Ltd