Optimal stresses and load capacity for structures

For a statically indeterminate structure we examine the class of internal forces that are in equilibrium with a given external loading f. We define the optimal stress φ^opt as the smallest possible magnitude of any equilibrating internal force distribution. The stress sensitivity k = max _f{φ^opt_f/||f||}, a purely geometric property of structure, is a measure of the sensitivity of the structure to variable external loading. Using the result for optimal stresses, an expression for the stress sensitivity factor is obtained in terms of the structure 's kinematic interpolation mapping. These notions, the corresponding theoretical results, and a simple implementation to finite element models are presented using linear and conic programming.