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

Abstract

In this paper, we investigate the continuity of the mappings which, for a given set of cross-sectional areas of a truss, gives the bar forces and nodal 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 design, primarily the stress-constrained minimum weight problem, to illustrate how they can be used to establish existence of solutions and validity of “ ε-perturbations” that are common in computational topology optimization.