M.Sc Thesis
M.Sc Student Saffury Johny Limit Loads of Stochastically Heterogeneous Structures Department of Mechanical Engineering Professor Emeritus Eli Altus

Abstract

The collapse load (or limit load) of a structure can be obtained, under certain assumptions, by means of Plastic Limit Analysis (PLA) whose bases were set up 50-60 years ago. The PLA provides lower and upper bounds to the collapse load by the static and kinematic theorems, respectively.

For structures with stochastic strength, it is essential to evaluate the reliability against collapse. Extension of the PLA to structures with stochastic strengths (SLA) was first introduced by Augusti and Baratta in 1972.

The SLA static approach yields upper (safe) bound to the probability of collapse (Pc), but the bound is not tight, especially at small failure probabilities which are those of major concern in practice. The SLA kinematic approach is easier to use and yields a close lower (unsafe) bound to the Pc by considering finite set of collapse mechanisms. Theoretically, considering the whole infinite class of possible failure modes yields the exact Pc.

In this research, a new method is proposed for evaluating the collapse load and its statistical characteristics analytically for beam structures with elastic perfectly plastic material and stochastic continuous strength field. The method depends on the kinematic approach of PLA and it allows considering infinite subclass of mechanisms.

Suitable Monte Carlo Simulations, reveals that the method is good for a specific range of strength correlation length and that the proposed method yields better upper bound to the collapse load average than other two SLA-based methods. The proposed method is analytical and presents explicitly the relation between the strength statistical properties and the collapse load average and variance. Through the method a strength related correlation term, which is not familiar in the present SLA, is needed.

Finally, in order to include the whole infinite class of failure modes, a new approach for obtaining the collapse load for beams as a functional of the strength field is proposed.

The functional formulation is an irregular one since it involves integrals on Dirac related operators. For simplifying the functional and for extending to the stochastic case, the Functional Perturbation Method (FPM) is adopted. However, the results are still not satisfying and therefore improved FPM tools should be developed.