On continuity of the design-to-state mappings for trusses with variable topology

In this paper, we investigate the continuity of the mappings which, for a g iven set of cross-sectional areas of a truss, gives the bar forces and noda l displacements present in equilibrium. We allow the areas to approach and attain zero values, and hence analyse continuity of the state mappings even as the topology is altered. The main results are then applied to optimal d esign, primarily the stress-constrained minimum weight problem, to illustra te how they can be used to establish existence of solutions and validity of "epsilon -perturbations" that are common in computational topology optimiz ation. (C) 2001 Elsevier Science Ltd. All rights reserved.