Response Bounds of Elastic Structures in the Presence of Interval Uncertainties

Abstract

A mathematical-programming (MP)-based approach is proposed to directly determine the two extreme [(1) minimum, and (2) maximum] bounds of some static response quantity for elastic structures subject to the simultaneous application of interval applied forces and interval elastic material properties. Such a direct determination scheme reformulates the interval finite-element (FE) analysis into a pair of standard nonlinear programming (NLP) problems that can be solved by any available NLP code. Not only does the proposed method advantageously bypass any computationally expensive combinatorial searches to capture the response limits, but it can also directly accommodate any dependency in the interval data. Some examples are presented to illustrate the robustness and efficiency of the method.