Manufacturing tolerances of truss members' lengths in minimum weight design

Abstract

In most cases a safety of optimal construction may be limited by the violation of stress, buckling or displacement constraints. An unexpected exceed of these constraints may be caused by manufacturing tolerances of structural elements (differences between assumed and obtained dimensions). This requires an incorporation of tolerance problem in optimum design. One may deal with two different tolerances – the first case is when it's related to the members' cross-section variations, whereas the second notion represents the variation of elements' lengths. Considering operation conditions and manufacturing techniques the second case of tolerance seems to be more important. This approach states the problem of minimum weight design of a structure with initial distortions. A standard solution algorithm with the Kuhn-Tucker theorem was used with the adjoint variable method. Necessary optimality conditions have the form of equations and inequalities. The equality constraints were put forward for the average values of design variables l, while tolerances tj were introduced into inequality equations i.e. the limit values of stresses and displacements were diminished by the positive products of appropriate sensitivities and tolerances. The method was next illustrated by an example of a ten bar bench-mark problem - a typical one for testing algorithms in structural optimization. The idea presented in this paper may be used not only for truss structures but it can be easily extended to other kinds of structures like frames, composites etc.