The present study deals with a combinatorial searching problem, that is closely correlated to the fundamental concept of AI technology, stemmed from the failure load analysis of rigid frames by the kinematically admissible approach. Hence, the essence of AI technology is in general to establish efficient techniques of search for the prescribed goal among enormous data-base or knowledge-base frequently generated from combination of elements as encountered in a travelling-salesman problem. Because of non-differentiability or discreteness the search of such combinations for the goal requires a large number of generate-and-test procedures which wastes indispensably enormous computer time. Of failure modes kinematically admissible to collapsed frames there are two types of mode: elementary failure modes and their linearly combined modes. By and large for even medium rigid frames the number of combined modes becomes explosively large. Thus, the problem is to establish an effective search technique without exploitation of any kind of continuity condition such as differentiation for the minimum load factor by virtual work equations for elementary modes and enormous combined modes. Some heuristics of AI technology to prune futile alternatives is applied to this problem, which shows excellent efficiency to searching.

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