GEOMETRIC AND MATHEMATICAL ANALYSIS OF THE ASSUMPTION OF SMALL DEFORMATION1)

Small deformation, one of the basic assumptions in mechanics, plays a critical role in the derivations and the applications of many theories in mechanic, for example, the beam and plate theories, and the mechanics of materials. The interpretation and the use of the small deformation assumption are important since wrong results may come from the misunderstanding of the concept of "small deformation". This paper studies a simple example of statically indeterminate problems. In the statically indeterminate truss, the equilibrium equations derived from the free-body diagram of the member must be complemented by relations involving deformations and obtained from the geometry of the problem. The importance of the concept of small deformation in geometric relationships is shown. It is indicated that the same definition of small deformation but different geometric relationships can result in different complementary equations in which, of course, only one of them is correct. The wrong use of small deformation assumption in the geometric relationships is pointed out to further highlight the correct concept of the small deformation.