Worst-Scenario of Deficiency of Structural Elements in Plastic Limit Analysis

Abstract eng:
The redundancy of a structure usually refers to the extent of degradation which the structure can suffer without losing some specified functionality. For example, Frangopol and Curley (1987) defined the strength redundant factor by l_i/(l_i ..l_d), where l_i is the ultimate strength of the intact (i.e., undamaged) structure, and ld is that of the damaged structure. In such a redundancy analysis, it is often that the plastic limit analysis is performed with the given set of deficient structural elements (Ohi et al., 2004). However, for a real-world structure, we cannot predict in advance which structural elements will be actually damaged. This contribution discusses the worst scenario of deficiency of structural elements. Specifically, we consider the deterioration of the plastic limit load factor of a finitedimensional structure. When the maximum number of damaged structural elements is specified, the worst scenario is defined as the set of damaged elements with which the limit load factor attains the minimum (i.e., worst) value. Thus redundancy is related to robustness against uncertainty in structural deficiency (Kanno and Ben- Haim, 2011). A major difficulty of this worst-scenario detection problem stems from the fact that the worst scenario corresponds to the global optimal solution of a nonconvex optimization problem. Therefore, conventional nonlinear programming approaches are not guaranteed to find the worst scenario. To overcome this difficulty, the present study proposes to reformulate the worst-scenario detection problem as a mixed integer linear programming (MILP) problem. An MILP problem is minimization (or maximization) of a linear function under linear inequality constraints, in which some of the unknown design variables are required to be integers. We can obtain the global optimal solution of an MILP problem with, e.g., a branch-and-cut method. This means that the reformulated worst-scenario detection problem can be solved globally. Numerical examples show that the worst scenario of the deficiency of structural elements depends on the number of damaged numbers.

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