On the calculation of rigidity characteristics of the stressed constructions

It has been shown by Kolpakov (1989) that the homogenization method must be applied directly to the initial body in order to incorporate correctly the preliminary (initial) stresses if the body is non-homogeneous. In the pape r mentioned above, this fact is noted and illustrated on examples. In the p resent paper, a complete analysis of the problem is given. In particular, t he case of small initial stresses (as compared with elastic constants) is c onsidered. This is the case realized in most natural and artificial stresse d structures. It was noted by Kolpakov (1992) that the realizing of the theoretical resul ts represent an independent problem for every type of definite structure. I n the present paper, the method of incorporating the initial stresses in ap plication to finite-dimensional constructions (framework and semimonocoque constructions) is given. (C) 2001 Elsevier Science Ltd. All rights reserved .