Interval elastoplastic analysis of structures

Abstract

This thesis proposes an extended elastoplastic analysis of nonlinear structures that consider the influences of uncertain data (i.e. material properties and forces). The uncertainties are modeled as intervals (or convex models), which are deterministic but lie within known upper and lower bound ranges. The analysis determines the most maximum and the most minimum values of some specified (e.g. displacement at some location) variable.

The proposed scheme uses a step-by-step interval holonomic analysis of structures under load control. Each incremental step involves formulation and solution of a pair of nonstandard optimization problems (with one problem capturing the most maximum response and the other the most minimum). These problems are called interval mathematical programs with equilibrium constraints (or interval MPECs). In addition to the difficulties underlying standard MPECs, the presence of interval data makes the problems very challenging to solve. Common searching techniques (such as Monte Carlo simulations) by simply predefining the intervals as some feasible deterministic parameters and exhaustively processing the associated (noninterval) mixed complementarity problem (MCP) do not guarantee accurate interval response bound solutions.

A novel and simple technique is proposed to determine in a single step the most maximum response in one case and the most minimum in the other case for a given load step. The algorithm first transforms the governing interval MPECs into noninterval MPECs simply by replacing the intervals with unknown variables and additional constraints describing the bounds of these variables. Such unknown variables describe the critical interval parameters associated with each of the maximum and minimum response limits, and can be obtained directly from the optimization process. The reformulated (noninterval) MPECs are processed using some regularized nonlinear programming (NLP) approaches. The efficiency and robustness of the proposed scheme are illustrated through various engineering applications. The main ones are the analysis of interval structures considering elastoplastic materials, semi-rigid beam-to-column steel connections and/or geometric nonlinearity. This direct numerical tool fruitfully assists engineers to assess the effects of interval parameters and hence the safety of various realistic structures with uncertainties.