TABLE OF CONTENTS Comparisons are odorous W. Shakespeare.
The same mathematical problem can be solved by different means R. Courant.
The test of a first-rate intelligence is the ability to hold two oposite ideas in the mind at the same time, and still retain the ability to function F. S. Fitzgerald.
Intellect is an ability to find a difference in similar, and similarity in the different Ch. Montesquie.
In this chapter, structural uncertainties are modeled by using both the stochastic and interval methods to quantify the uncertainties in the response quantities. Through a suitable discretization, stochastic and interval FEMs are constructed. A comparison of these methods is illustrated using a shear frame with uncertain stiffness properties.
Response quantities, in the form of internal forces, stresses, displacements, and strains, are needed to evaluate the safety and serviceability of structures. In many real-life structural engineering problems neither the initial conditions, nor external forces, nor the parameters of the constitutive relations used in the procedures to calculate response quantities can be perfectly described because of the lack of detailed knowledge and also due to the inherent uncertainties.
Presently, there are three paradigms to describe uncertainty: (i) the theory of probability and random processes; (ii) fuzzy sets; and (iii) convex set-theoretical analysis. These three corners of the uncertainty triangle (1990) can be combined in various ways. The hybrid stochastic fuzzy approach was developed by Hoh and Hagaki (1989). Convex modeling of uncertainty was studied in the monograph by Ben Haim and Elishakoff (1990). A complete literature survey of continuous systems...
