A constraint-based approach for qualitative matrix structural analysis

Qualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.