Efficient upper-bound limit analysis (Q1111063)

This paper develops an efficient and general, yet physically understandable, new scheme to obtain the collapse load factor of an arbitrary framed structure using an upper-bound approach. Loading conditions examined include concentrated forces and couples. Main features are: (i) the preliminary computation of all basic collapse mechanisms by means of an automatic matrix method, after which a general mechanism of collapse is expressed by a linear combination of these mechanisms and the corresponding load multiplier \(\chi\) is obtained from an energy equation; the minimum of \(\chi\) is the required collapse load; and (ii) a new matrix method to find the minimum of \(\chi\), having examined its properties. A simple example illustrates the calculations. The new method of minimization does not require non-negative variables in previous schemes based on Linear Programming, and thus results in an algorithm which reduces computer storage and time requirements.