The Spatial Theory of Linear Elastic Members by Direct Kinematic Method

Abstract

<p> In this work the direct, kinematic, small-displacement theory has been developed for the analysis of thin, elastic members which are curved and twisted in their natural configurations. Principles of continuum mechanics have been used to derive the equations of equilibrium. Throughout this investigation the three-dimensional aspect of the problem is preserved. Local kinematic compatibility of the displacement field has been investigated by the formal Saint-Venant's method. This development serves to substantiate the validity of the kinematic tridimensional approach. By the judicious neglection of small terms of higher order throughout this analysis, the basic system of equations arrived at by the author admit favourable comparison with the existing equations by other authors.</p>